Calling Next with 1 trump + off ace, an EV analysis

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Wes (aka the legend)
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Calling Next with 1 trump + off ace, an EV analysis

Post by Wes (aka the legend) » Thu May 02, 2019 4:33 pm

Ok so we're going to create an EV model here (EV = expected value). EV models are not mathematical proofs but rather mathematical arguments that can often help lead us to correct play. An EV model is only as good as the assumptions that underpin it, and those assumptions are often guesswork (hopefully born from expert intuition) but that's not necessarily a bad thing as far as leading us to the correct/incorrect play.

For example, if all our assumptions are conservative, I.E. they err on the side of caution, the side that actually goes against our argument, then we have a very strong, compelling EV argument. IOW, the most compelling EV model would be one that is based on unrealistic assumptions, as long as those assumptions are conservative, meaning unrealistic in the direction that actually goes against the claim an EV model is trying to establish.

In contrast, watch out for EV models purporting to establish a correct strategy in euchre, poker, or any card game when all their assumptions are highly favorable to their argument. Any EV model can spit out the answers you want if you tweak the assumptions enough. That's why EV models can't PROVE anything but they can be excellent teaching tools, and they can sometimes make very powerful arguments.

Ok so now I'm going to make a simple EV model that suggests that calling Next with 1 trump + an off ace is correct. Here we go, and remember the best way to attack my model is to attack its assumptions.

The score is 0-0, we're in seat 1 and the dealer just turned down the (Card_9-S)

We have (Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)

And we call next.

Assumptions: If we call next with this weak holding we will get euchred 65% of the time, we will make a point 30% of the time, and we will score 2 points 5% of the time.

The big key assumption of the model: If we pass seat 2 will always call something. This is the weakest part of the model. It is not a conservative assumption, but nevertheless a necessary one. The model simply gets too complex, overloaded with too many other permutations to account for if we allow Seat 2 to pass. The good news is the assumption is a decent approximation of reality vs many good opponents.

Given that you're passing a hand that blocks nothing, a hand with no bowers, and assuming that seat 2 is good enough to know how to call to hit his partner's range those times he's marginal which won't be that often given your holding (I.E. making good reverse next calls when the cards warrant it), Seat 2 will not be passing very often. Odds are Seat 2 has a hand to call with when you pass such a weak holding.

I would love to know my passing % after seat 1 passes with a hand that blocks nothing. I bet it approximates 0% when you factor out euchre hands I would pass and other hands I would pass when I have all suits blocked, and seat 2 passing those type of hands doesn't hurt the model becuz those are basically aggressive passes that have more in common with calling then a legit pass, in the mathematical sense.

Ok more assumptions: If we pass, Seat 2 will complete a loner sweep 5% of the time, get euchred 10% of the time, score 1 point 65% of the time, and score 2 points 20% of the time.

OK time to do the EV calcs!

First step, do the math on your next call: (.65 x -2) + (.30) + (.05 x 2) = -.9

I.E. every time you make this call you lose .9 points in a vacuum on average.

2nd step do the math on a 2 seat call should you pass instead:

(.05 x 4) + (.10 x -2) + (.65) + (2 x .20) = 1.05

I.E. every time you pass you your team losses 1.05 points on average.

Since 1.05 is greater than .9, we are better off calling Next with this holding than passing.

Ok, what I want from you guys:

Plug your own numbers into this model, your own best guesses, see what conclusion it churns out and post it in this thread. I don't care if it reaches a different conclusion than mine. There are no wrong answers here. Or I should say there are no provable wrong answers here. :)

Some follow up questions. Are there any assumptions in my model that you vehemently disagree with? Or are the numbers acceptable enough that you are now convinced that calling next with 1 trump and an off ace is the right move? Let me know what you guys think.



mekane
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Post by mekane » Thu May 02, 2019 5:29 pm

This seems way off.

Based on my games, I would think the chance of a pass from seat 2 would be about 50%, so that's a pretty big difference from 100%.

I think your mistake is saying that if you are seat #2, you would call 100% of the time and then saying that the odds of making it are still 90%. By your aggressive bidding methods, you wouldn't be making it anywhere near 90% of the time, so one of those 2 things has to give (either your calling it less often than 100% of the time or you are not making it 90% of the time)

RedDuke
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Post by RedDuke » Fri May 03, 2019 12:08 am

Based on my games, I would think the chance of a pass from seat 2 would be about 50%, so that's a pretty big difference from 100%.
That's the biggest assumption here and it very much depends on your opponents' tendencies. Very, very few players are truly good euchre players. A good player in second seat knows that if first seat passed in second round then he's got every single loner blocked (ie. has a guaranteed trick in his hand no matter what trump suit is). The guy in third seat knows this too. And he'll also know then where two of the jacks are (since first seat is holding one black and one red jack for certain). If he's holding the other jack and a somewhat strong hand in either next or reverse next, which is very likely if second seat doesn't have that, then he's calling a loner from third seat. Thus, by calling anything, the guy in second seat can stop that scenario. Thus, a good player in second seat is never going to pass unless he's sure that he can stop third seat from making a loner should he try.

Wes (aka the legend)
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Joined: Wed Jun 13, 2018 3:03 pm

Post by Wes (aka the legend) » Fri May 03, 2019 7:23 am

RedDuke wrote:
Fri May 03, 2019 12:08 am
Based on my games, I would think the chance of a pass from seat 2 would be about 50%, so that's a pretty big difference from 100%.
That's the biggest assumption here and it very much depends on your opponents' tendencies.


It sux that I have to have that assumption (that seat 2 never passes) but if we have seat 2 passing some percentage of time, then that opens up a bunch of probabilities we now have to assign to Seat 3 and Seat 4 (the dealer). It just get's too complicated. And I honestly didn't think this hangup was that big of a deal. In the home game I used to play in, we could play the whole night without the action ever getting to the 2 seat in the 2nd round let alone the 3 seat. Admittedly, everyone was aggressive. The same dynamic also happens when I play with some of the top players from my euchre tournament or when I'm playing with strong players on the app. It just so rarely gets to the 3rd seat, 2nd round. So yeah my experience is colored by that to a degree, but certainly I realize there are other game textures.
RedDuke wrote:
Fri May 03, 2019 12:08 am
very few players are truly good euchre players. A good player in second seat knows that if first seat passed in second round then he's got every single loner blocked (ie. has a guaranteed trick in his hand no matter what trump suit is).
I wouldn't go that far. I would say a really strong player is not gonna pass from Seat 1, 2nd rd at a neutral score if he doesn't block reverse next, but he doesn't necessarily have to have Next blocked. Theoretically, he's partner will have that suit covered pretty often. When I play euchre vs randoms or most people, I don't assume that they necessarily have ANYTHING blocked when they pass from Seat 1, 2nd rd. I just assume they don't like their hand, and that's it. Most people in euchre just play their cards, not the situation. I think a good player from the 2 seat should assume Seat 1 sux until proven otherwise. But if it is established that Seat 1 is a strong player, then Seat 2 would have to tighten up his reverse next calling range a tad, but this dynamic is so rarely in action.

Anyways, ignoring the 2 seat always calling contention, what do you think of my other assumptions? Do they seem ok? I mean they are just guesstimates. What would your guesses be for the euchre rate, 1 point rate, 2 point rate of a Next call with 1 trump and an ace? And what percentages would you assign for a 2 seat loner sweep, 1 pt, 2 pt, -2 pt, hand if 1 seat passed?
Last edited by Wes (aka the legend) on Fri May 03, 2019 7:41 am, edited 1 time in total.

Wes (aka the legend)
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Post by Wes (aka the legend) » Fri May 03, 2019 7:41 am

mekane wrote:
Thu May 02, 2019 5:29 pm
This seems way off.

Based on my games, I would think the chance of a pass from seat 2 would be about 50%, so that's a pretty big difference from 100%.
That is a problem with my assumption. It mimics more of a tough game than maybe your average game. There are many game textures I've played in where it so rarely even gets to 3rd Seat, 2nd round, and when it does it often means someone has everything blocked. And frankly I'm more interested in how this model would do in a tough game than your average euchre game where everybody is just trying not to get euchred.
mekane wrote:
Thu May 02, 2019 5:29 pm
I think your mistake is saying that if you are seat #2, you would call 100% of the time and then saying that the odds of making it are still 90%.


Yeah this could be a problem. My thinking was the average euchre rate for my app is around 14%, but I lowered the euchre rate for seat 2 to 10% in my model to account for the fact that this is not an average scenario since we already know that seat 1 is passing with a very weak hand, blocking nothing. This means that Seat 2's calls will get euchred significantly less than usual. However, the fact that seat 2 is always calling would suggest that his euchre rate would be higher than normal. So we have two countervailing aspects to this problem.

mekane wrote:
Thu May 02, 2019 5:29 pm
By your aggressive bidding methods, you wouldn't be making it anywhere near 90% of the time, so one of those 2 things has to give (either your calling it less often than 100% of the time or you are not making it 90% of the time)
Since the constraints of the model forces us to go with Seat 2 always calls, we can only go with the latter possibility that we "are not making it 90% of the time".

What I now want from you Mekane is to give me your percentages: I.E. how often is seat 1 getting euchred on this weak next call, getting 1 point, and 2 points. And how often is Seat 2 is getting euchred, 4 point loner, 1 pt, 2 pt. Remember there is no wrong answer. I'm not trying to WIN an argument here. Just curious what probabilities you guys would assign here.

mekane
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Joined: Mon Apr 29, 2019 3:58 pm

Post by mekane » Fri May 03, 2019 11:55 am

My guess is probably 90% of the games where they get that 14% rate is of players who pass a lot not like you guys, and you have to modify that number drastically. What is your personal rate of getting Euchred? I would use that as your base value then adjust for the weak hand from seat 1.

Also, consider not adjusting the percentage at all, since you're already assuming they are going to call in seat 2 because you have a weak hand?

RedDuke
Posts: 267
Joined: Sun Dec 02, 2018 2:22 am

Post by RedDuke » Fri May 03, 2019 8:03 pm

mekane wrote:
Fri May 03, 2019 11:55 am
My guess is probably 90% of the games where they get that 14% rate is of players who pass a lot not like you guys, and you have to modify that number drastically. What is your personal rate of getting Euchred? I would use that as your base value then adjust for the weak hand from seat 1.

Also, consider not adjusting the percentage at all, since you're already assuming they are going to call in seat 2 because you have a weak hand?
I know Wes is a lot higher than I am. I think he's in the 20s or 30s. I'm at 18 or 19% I think, would have to check.

The assumption that seat 2 has a strong hand if seat 1 has a weak one comes from the fact that 20 out of 24 cards in a euchre hand are in play. You know where one of them is (the rejected turn card). You know the good cards aren't in seat 1's hand so you can conclude that they're either in somebody's hand or in the kitty and since there's only 3 cards in the kitty that you don't know, it's very likely that somebody is holding a good hand. There are more cards in your opponents' hands than in your partner's so each seat 2 or the dealer is most likely.

Richardb02
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Joined: Mon Dec 10, 2018 8:57 pm

Post by Richardb02 » Sun May 05, 2019 4:44 pm

Wes (aka the legend) wrote:
Thu May 02, 2019 4:33 pm
Ok so we're going to create an EV model here (EV = expected value). EV models are not mathematical proofs but rather mathematical arguments that can often help lead us to correct play. An EV model is only as good as the assumptions that underpin it, and those assumptions are often guesswork (hopefully born from expert intuition) but that's not necessarily a bad thing as far as leading us to the correct/incorrect play.

Ok more assumptions: If we pass, Seat 2 will complete a loner sweep 5% of the time, get euchred 10% of the time, score 1 point 65% of the time, and score 2 points 20% of the time.

OK time to do the EV calcs!

First step, do the math on your next call: (.65 x -2) + (.30) + (.05 x 2) = -.9

I.E. every time you make this call you lose .9 points in a vacuum on average.

2nd step do the math on a 2 seat call should you pass instead:

(.05 x 4) + (.10 x -2) + (.65) + (2 x .20) = 1.05

I.E. every time you pass you your team losses 1.05 points on average.

Since 1.05 is greater than .9, we are better off calling Next with this holding than passing.

Ok, what I want from you guys:

Plug your own numbers into this model, your own best guesses, see what conclusion it churns out and post it in this thread. I don't care if it reaches a different conclusion than mine. There are no wrong answers here. Or I should say there are no provable wrong answers here. :)

Some follow up questions. Are there any assumptions in my model that you vehemently disagree with? Or are the numbers acceptable enough that you are now convinced that calling next with 1 trump and an off ace is the right move? Let me know what you guys think.
First, I will answer Wes with my percentages:
I complete a loner sweep 3% of the time, get euchred 15% of the time, score 1 point 67% of the time, and score 2 points 15% of the time.

The math:
(.03 x 4) + (.15 x -2) + (.67) + (2 x .15) = 0.79

So the model now says every time we pass our opponents average 0.79 points, whereas if we Donate we lose 1.05 points. (I created 2 more complex models, the least conservative projecting 0.36 points and the conservative model 0.70 points. I got a headache making these models. So I don't want to get a migraine explaining them)! Having said all of that I am happy with 0.79, even rounding to 0.80 for this post.

So let's simplify even more to discuss the strategy:
If you call you can expect to lose 1 point.
If you pass you can expect Opponents to gain 1 point.

Let's build a strategy based on this 1:1 simplification:
Calling locks in a 2 point loss vs passing a 1 point loss. Net -1
But passing carries a risk of losing 4 points to a successful Loner.
You pay a 1 point premium to eliminate a potential 4 point loss. Net -3

I am willing to pay the premium to eliminate the 4 point loss when:
Opponent will end up with 5 points or less.
So not only 0-0 but 0-1, ,0-2, 0-3, it makes sense to call.
I am siding with Wes, based on his Advanced Quiz answers and explanations.
I am also defining an edge point of Donating when working with a low Opponents' score.

If the score is in my favor by 2 points or more and Opponents have 5, 6 and even 7 points it makes sense to call. Making sense = I think my odds of winning the game has improved.
At 9-7 donating makes the score 9-9 and I have a 70% chance of winning as dealer on the next hand.
Why risk losing to a 4 point Loner when you have a 70% chance of winning the game?
At 8-6, and 7-5, the concept is the same

Everyone, what are your thoughts?

RedDuke
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Joined: Sun Dec 02, 2018 2:22 am

Post by RedDuke » Sun May 05, 2019 9:50 pm

So let's simplify even more to discuss the strategy:
If you call you can expect to lose 1 point.
If you pass you can expect Opponents to gain 1 point.
Those two net out even. If you call, you expect to have your opponents gain two points. If you pass, they will probably gain one or two. The two is more likely since they're more likely to have strong cards given your terrible holding and so will make the sweep more often than not. In the end then, you aren't giving up much of anything by calling. However, what you do is stop them from making the four point loner sweep.

Richardb02
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Joined: Mon Dec 10, 2018 8:57 pm

Post by Richardb02 » Wed May 08, 2019 6:17 am

The score is 0-0, we're in seat 1 and the dealer just turned down the (Card_9-S)

We have (Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)
Would you call next with this hand down 0-5 or up 9-7?

RedDuke
Posts: 267
Joined: Sun Dec 02, 2018 2:22 am

Post by RedDuke » Wed May 08, 2019 5:41 pm

Richardb02 wrote:
Wed May 08, 2019 6:17 am
The score is 0-0, we're in seat 1 and the dealer just turned down the (Card_9-S)

We have (Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)
Would you call next with this hand down 0-5 or up 9-7?
Up 9-7, you absolutely have to call something here. You have no way to stop a second seat reverse next loner and if the enemy makes a loner then its game over. The question is what to call. Your strongest suit is diamonds, but you're not strong enough to make it trump since Ace-King isn't a guaranteed trick from first seat. It might be as the dealer, but not from first. Actually, Ace-King is a much stronger holding as a green suit because then you have the two boss cards.

Statistically, next is more likely to hit your partner's hand than a diamond call. Conclusion: Call next, lead the ten of clubs, and hope your partner has a bower. Try to take a diamond trick at the first opportunity (maybe even throw off the Ace if your partner leads trump to give him a leadback).

At a score of 9-7, you can risk a euchre because it won't end the game and next deal is yours with a 70% chance to win the game. That's not the case with a 0-5 deficit. There, you don't really want to get euchred but you still don't really want the reverse next loner sweep. Either scenario will give you a very difficult time winning the game. Since you are going to be at a deficit either way, I might argue that the loner isn't really worth worrying about since it's a low probability event in most cases and doesn't outweigh the loss of two points with the euchre.

Given your holding and what your partner likely has, you can probably prevent the enemy from making march if they call. This will limit them to 1 point. I'd pass here and then play as best you can on defense if they call. The idea being to keep them to 1 point.

Wes (aka the legend)
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Joined: Wed Jun 13, 2018 3:03 pm

Post by Wes (aka the legend) » Thu May 09, 2019 5:51 am

Richardb02 wrote:
Wed May 08, 2019 6:17 am
We have (Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)
Would you call next with this hand down 0-5 or up 9-7?
RedDuke wrote:
Wed May 08, 2019 5:41 pm
Up 9-7, you absolutely have to call something here.


First, let's ignore the fact that we can never be up 9-7 in that spot with that holding due to the fact that we would've donated with that holding. That's boring, unfun and gets us nowhere. What's immediately more interesting to me is that we can use an EV argument that's very strong (unlike the one I've used in this thread) that supports calling up 9-7 in this spot with that weak hand.

Ok here we go: Assume if we call Next we win the game 35% of the time and thus we get euchred 65% of the time. The 65% of the time we get euchred we still get the deal at 9-9 with roughly 65% equity (according to this site it's 70% but let's be conservative).

Ok now assume that if we pass with this hand up 9-7 we will lose roughly 1 point on average. So passing with this hand up 9-7 is mathematically equivalent to having the deal up 9-8. I think this is a conservative assumption since passing may easily cost us more than a point on average given that we blocking nothing. Ok well what's our equity up 9-8 with the deal. According to the probability chart below it is around 72%.

http://members.tripod.com/borf_books/euchprob.htm

So now we have enough to do a simple and compelling EV analysis:

EV of calling = (.35) + (.65 x .65) = .7725 or 77.25% win equity

EV of passing = 72% win equity


77% is greater than 72% therefore we should always call with this hand up 9-7.

Notice we already have a super compelling logical argument for always calling up 9-7 from seat 1, 2nd rd. By calling you guarantee your team 2 chances to win, including 1 chance as the dealer with roughly a 2-1 edge, and you can never lose to a hail mary loner. If you pass you aren't even guaranteed one chance to win. Now we also have a super compelling EV argument to back this up too.

Now the question is can we expand this compelling logical/EV argument further. I think so, and here's how. If it is correct to always call up 9-7 from 1 seat, 2nd round, then it necessarily follows that it's correct to always call up 9-6, up 9-5, etc, all the way down to up 9-0. And if it's correct to always call up 9-7 from seat 1, 2nd round then it's also correct to always call ANYTIME our team is up 2 points or more from seat 1, 2nd round.

For clarification: Am I saying to always call up 2 points or more from Seat 1, 2nd rd with this weak Next holding or better or am I saying always call something with your entire range in this spot. Well I think it's the latter. Yes if we call with a hand weaker than 1 trump and an off ace we will get euchred more often, but that's probably offset by the fact that passing with a weaker holding costs us more too. The weaker the hand we pass the more likely Seat 2 gets a 4 point sweep, makes a 2 point call, and a 1 point call. All those probabilities go up and conversely the probability of Seat 2 getting euchred goes down accordingly also.

Of course we are not gonna make weak calls if we have suits blocked. So that leads us to this formulation: From seat 1, 2nd round, up 2 points or more, always call something if you don't block reverse next.

Now if you block reverse next but don't block next, I think it actually depends on the exact hand and situation. With this holding we should still always call up 9-7/9-6 imo. At those scores I'm deploying a "no loners" offense.

But should we really feel compelled to call something up say 2-0, with a hand like this:

Dealer just turned down a (Card_9-S)

We have (Card_A-C) (Card_K-C) (Card_K-S) (Card_J-D) (Card_10-H)

We have approx 2 tricks vs a reverse next call and the probability that Seat 2 is sitting on a loner sweep in Next is pretty low given that he already passed on a black upcard and we have AcKc which takes out a lot of loner combos and our partner also has a strong chance of having at least 1 black bower given the action in the first round. I would pass in this spot and feel good about it.

But if I had a hand like this up 2-0...

Dealer turns down a (Card_9-S)

We have (Card_K-S) (Card_Q-S) (Card_J-D) (Card_10-H) (Card_9-H)

I'm calling hearts. Not cause I love my holding. I don't. It's just that I get awfully nervous in this spot when I have not one card in Next. Now I'm way more worried that the 2 seat will make a Next call and if he does it's a pretty devastating call for our team since we would then have a completely dead hand, let alone the devastation caused if Seat 2 has a loner sweep in Next.

Let me know if you guys agree/disagree with any arguments in this post. If there's a weak spot in my thinking I want it exposed.

Wes (aka the legend)
Posts: 269
Joined: Wed Jun 13, 2018 3:03 pm

Post by Wes (aka the legend) » Thu May 09, 2019 3:14 pm

mekane wrote:
Fri May 03, 2019 11:55 am
My guess is probably 90% of the games where they get that 14% rate is of players who pass a lot not like you guys, and you have to modify that number drastically. What is your personal rate of getting Euchred? I would use that as your base value then adjust for the weak hand from seat 1.
My personal euchre rate is around 27%. If I gave seat 2 a euchre rate of 20% to account for the fact that Seat 1 is passing a hand that blocks nothing, would that be acceptable to you? (others can chime in here too).

Also, what do you think about my other numbers for Seat 1 calling Next. Are there any of those you disagree with?

Wes (aka the legend)
Posts: 269
Joined: Wed Jun 13, 2018 3:03 pm

Post by Wes (aka the legend) » Thu May 09, 2019 3:35 pm

Richardb02 wrote:
Sun May 05, 2019 4:44 pm
First, I will answer Wes with my percentages:
I complete a loner sweep 3% of the time, get euchred 15% of the time, score 1 point 67% of the time, and score 2 points 15% of the time.

The math:
(.03 x 4) + (.15 x -2) + (.67) + (2 x .15) = 0.79
Ok looks good. I like different numbers from you guys!
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
So the model now says every time we pass our opponents average 0.79 points, whereas if we Donate we lose 1.05 points.
No, my model said we lose .9 points if we "donate" (I'm fine with calling it that). Of course that .9 is based on subjective guesses that you still have to approve of.
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
(I created 2 more complex models, the least conservative projecting 0.36 points and the conservative model 0.70 points. I got a headache making these models. So I don't want to get a migraine explaining them)! Having said all of that I am happy with 0.79, even rounding to 0.80 for this post.

So let's simplify even more to discuss the strategy:
If you call you can expect to lose 1 point.
If you pass you can expect Opponents to gain 1 point.
Based on your numbers and assuming you accept my calling numbers, we now lose .9 on a call and .79 on a pass. Calling therefore costs our team a net of .11. Everytime we call our team loses .11 on average.
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
Let's build a strategy based on this 1:1 simplification:
Calling locks in a 2 point loss vs passing a 1 point loss. Net -1
But passing carries a risk of losing 4 points to a successful Loner.
You pay a 1 point premium to eliminate a potential 4 point loss. Net -3

I am willing to pay the premium to eliminate the 4 point loss when:
Opponent will end up with 5 points or less.
So not only 0-0 but 0-1, ,0-2, 0-3, it makes sense to call.
I am siding with Wes, based on his Advanced Quiz answers and explanations.
I am also defining an edge point of Donating when working with a low Opponents' score.
I don't like the simplification but I like the logic or at least the idea of it. We don't need to oversimplify here becuz we have a real estimate to work with now. We now can assume based on your Seat 2 numbers and my Seat 1 calling numbers that the premium we are paying to block Seat 2 loners is .11.

BTW, a technical note that is relevant: In real life, We are not just paying a premium just to block Seat 2, we are actually also paying a premium to block Seat 4 too, as it is actually Seat 1's job to block loners from both spots in theory. I.E. in theory one should never feel compelled to order thin from 3rd seat, 2nd rd to block Seat 4 loners. That's still Seat 1's job too. Seat 1 is the gatekeeper. Seat 1 decides what loners get through. But this is a needless digression since the model has Seat 2 always calling if we pass, a necessity to keep the model simple--and a decent approximation of reality in many game textures. Either way, the value of Seat 1 blocking a Seat 4 loner is marginal due to the fact that it takes a parlay to get that far. I.E. both Seat 2 and Seat 3 have to pass. Plus the value of blocking Seat 4 may be offset by the times we block our partner when they have a loner or a good calling hand. That said, I've certainly lost more games than I'd like having to pass a nothing hand from Seat 3, 2nd rd, and then watching the dealer make a 4 point sweep in reverse next that never should happen....in theory ofc.
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
If the score is in my favor by 2 points or more and Opponents have 5, 6 and even 7 points it makes sense to call. Making sense = I think my odds of winning the game has improved.
At 9-7 donating makes the score 9-9 and I have a 70% chance of winning as dealer on the next hand.
Why risk losing to a 4 point Loner when you have a 70% chance of winning the game?
At 8-6, and 7-5, the concept is the same

Everyone, what are your thoughts?
I'm not sure our opponents exact score is relevant. Maybe I'm missing something but why not just say, "if the score is in my favor by 2 points or more.....it makes sense to call."

RedDuke
Posts: 267
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Post by RedDuke » Fri May 10, 2019 3:52 pm

BTW, a technical note that is relevant: In real life, We are not just paying a premium just to block Seat 2, we are actually also paying a premium to block Seat 4 too, as it is actually Seat 1's job to block loners from both spots in theory. I.E. in theory one should never feel compelled to order thin from 3rd seat, 2nd rd to block Seat 4 loners. That's still Seat 1's job too. Seat 1 is the gatekeeper. Seat 1 decides what loners get through. But this is a needless digression since the model has Seat 2 always calling if we pass, a necessity to keep the model simple--and a decent approximation of reality in many game textures. Either way, the value of Seat 1 blocking a Seat 4 loner is marginal due to the fact that it takes a parlay to get that far. I.E. both Seat 2 and Seat 3 have to pass. Plus the value of blocking Seat 4 may be offset by the times we block our partner when they have a loner or a good calling hand. That said, I've certainly lost more games than I'd like having to pass a nothing hand from Seat 3, 2nd rd, and then watching the dealer make a 4 point sweep in reverse next that never should happen....in theory ofc.
While you are technically correct, I can't remember the last time I had a partner that knew how to play Seat 1 correctly. In practice, pretty much everybody passes there unless they have a solid call in their own hand (ie. not considering what their opponents or partner has). Thus, there are times when we frequently want to call thin from third seat just in case the dealer has a loner. The odds that the dealer has a loner are pretty high if all three of the other players have nothing so if you're in a game with a partner that doesn't play Seat 1 correctly then you may want to call next from third seat unless you block all suits.

Wes (aka the legend)
Posts: 269
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Post by Wes (aka the legend) » Fri May 10, 2019 5:49 pm

RedDuke wrote:
Fri May 10, 2019 3:52 pm
While you are technically correct, I can't remember the last time I had a partner that knew how to play Seat 1 correctly. In practice, pretty much everybody passes there unless they have a solid call in their own hand (ie. not considering what their opponents or partner has). Thus, there are times when we frequently want to call thin from third seat just in case the dealer has a loner. The odds that the dealer has a loner are pretty high if all three of the other players have nothing so if you're in a game with a partner that doesn't play Seat 1 correctly then you may want to call next from third seat unless you block all suits.
This is true. That's why I made sure to say "in theory". The question of course is how thin do we go. On that I'm not sure, but I will go as thin as Right + 1 in next with nothing else.

Interesting to note. If we have a strong partner who's 1st seat, 2nd rd pass signals that he has reverse next blocked but not necessarily next blocked, then some apparently too thin calls become correct:

E.G. dealer turns down a (Card_9-S) and the actions on us 3rd seat, 2nd rd:

(Card_A-D) (Card_K-D) (Card_9-D) (Card_10-S) (Card_10-C)

Knowing that our partner has a sure trick in diamonds and knowing that it's possible he doesn't have Next blocked makes this an easy call that will almost surely net our team 1 point.

Another example, assume again the dealer turns down a (Card_9-S)

(Card_Q-H) (Card_J-H) (Card_A-C) (Card_10-C) (Card_10-S)

This should be another easy point for the same reasons if we call Hearts.

And conversely if our partner plays Seat 1, 2nd seat well, then we would not call Next with this hand:

(Card_A-C) (Card_J-C) (Card_A-S) (Card_10-D) (Card_10-H)

We already know our partner has reverse next blocked, so our team now has a great chance of setting the dealer. In real life that hand is a MUST call imo becuz virtually no one plays Seat 1, 2nd round well, and it's not becuz people aren't smart enough.

The problem with playing Seat 1, 2nd round well is you have to embrace getting euchred a lot and most people can't deal with that. Every time I play euchre in real life (at my tournament) at least 2 or 3 people get mad at me. I've had people scream at me, others just fume. One guy had a hissy fit calling me totally reckless. One person even threatened me. Not a physical threat, he just said that he's gonna make sure to lose on purpose any time we are partners in the future. Luckily he calmed down by next week. Most people don't wanna deal with this crap. Most don't want others to think they are stupid, dumb, crazy, etc. So they play tight, try not to get euchred, gracefully pass to a loss and blame bad luck for the outcome. For me, it's the same approach for when I played poker semi-pro from 2005-15, or when I was counting cards playing Blackjack in my younger days. I don't care what others think of me. I just wanna make the right play.

Richardb02
Posts: 171
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Post by Richardb02 » Sun May 12, 2019 4:40 pm

Wes (aka the legend) wrote:
Thu May 09, 2019 3:35 pm
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
First, I will answer Wes with my percentages:
I complete a loner sweep 3% of the time, get euchred 15% of the time, score 1 point 67% of the time, and score 2 points 15% of the time.

The math:
(.03 x 4) + (.15 x -2) + (.67) + (2 x .15) = 0.79
Ok looks good. I like different numbers from you guys!
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
So the model now says every time we pass our opponents average 0.79 points, whereas if we Donate we lose 1.05 points.
No, my model said we lose .9 points if we "donate" (I'm fine with calling it that). Of course that .9 is based on subjective guesses that you still have to approve of.
This is getting complicated. I read this post 3 times and misinterpreted your point. I stand corrected. Your EV model projects a loss of 09 points if we call from S1.
I agree with your S1 EV model based on my simplified approach. My simplified approach is, I don't have any cards, therefore there is a 1 in 3 chance that my partner has the cards, the 3 uncovered cards are neutral, therefore there s a 1 in 3 chance that my partner will win the hand, so we will be euchred 2/3 of the time or 67%. Your projection of 65% is close enough. Your split between Partner taking 1 point or 4 points is reasonable enough. So your EV for Seat 1 at -0.90 is fine with me.
Wes (aka the legend) wrote:
Thu May 09, 2019 3:35 pm
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
(I created 2 more complex models, the least conservative projecting 0.36 points and the conservative model 0.70 points. I got a headache making these models. So I don't want to get a migraine explaining them)! Having said all of that I am happy with 0.79, even rounding to 0.80 for this post.

So let's simplify even more to discuss the strategy:
If you call you can expect to lose 1 point.
If you pass you can expect Opponents to gain 1 point.
Based on your numbers and assuming you accept my calling numbers, we now lose .9 on a call and .79 on a pass. Calling therefore costs our team a net of .11. Everytime we call our team loses .11 on average.
OK. I agree.
Wes (aka the legend) wrote:
Thu May 09, 2019 3:35 pm
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
Let's build a strategy based on this 1:1 simplification:
Calling locks in a 2 point loss vs passing a 1 point loss. Net -1
But passing carries a risk of losing 4 points to a successful Loner.
You pay a 1 point premium to eliminate a potential 4 point loss. Net -3

I am willing to pay the premium to eliminate the 4 point loss when:
Opponent will end up with 5 points or less.
So not only 0-0 but 0-1, ,0-2, 0-3, it makes sense to call.
I am siding with Wes, based on his Advanced Quiz answers and explanations.
I am also defining an edge point of Donating when working with a low Opponents' score.
I don't like the simplification but I like the logic or at least the idea of it. We don't need to oversimplify here becuz we have a real estimate to work with now. We now can assume based on your Seat 2 numbers and my Seat 1 calling numbers that the premium we are paying to block Seat 2 loners is .11.

BTW, a technical note that is relevant: In real life, We are not just paying a premium just to block Seat 2, we are actually also paying a premium to block Seat 4 too, as it is actually Seat 1's job to block loners from both spots in theory. I.E. in theory one should never feel compelled to order thin from 3rd seat, 2nd rd to block Seat 4 loners. That's still Seat 1's job too. Seat 1 is the gatekeeper. Seat 1 decides what loners get through. But this is a needless digression since the model has Seat 2 always calling if we pass, a necessity to keep the model simple--and a decent approximation of reality in many game textures. Either way, the value of Seat 1 blocking a Seat 4 loner is marginal due to the fact that it takes a parlay to get that far. I.E. both Seat 2 and Seat 3 have to pass. Plus the value of blocking Seat 4 may be offset by the times we block our partner when they have a loner or a good calling hand. That said, I've certainly lost more games than I'd like having to pass a nothing hand from Seat 3, 2nd rd, and then watching the dealer make a 4 point sweep in reverse next that never should happen....in theory ofc.
OK. I agree.
Wes (aka the legend) wrote:
Thu May 09, 2019 3:35 pm
Richardb02 wrote:
Sun May 05, 2019 4:44 pm
If the score is in my favor by 2 points or more and Opponents have 5, 6 and even 7 points it makes sense to call. Making sense = I think my odds of winning the game has improved.
At 9-7 donating makes the score 9-9 and I have a 70% chance of winning as dealer on the next hand.
Why risk losing to a 4 point Loner when you have a 70% chance of winning the game?
At 8-6, and 7-5, the concept is the same

Everyone, what are your thoughts?
I'm not sure our opponents exact score is relevant. Maybe I'm missing something but why not just say, "if the score is in my favor by 2 points or more.....it makes sense to call."
OK. I agree. In my defense, I over-complicated the comparison because I expected more debate about the finer points. So your simplification, "if the score is in my favor by 2 points or more.....it makes sense to call," is an excellent simplification.

Wes (aka the legend)
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Post by Wes (aka the legend) » Wed May 15, 2019 6:25 pm

Richardb02 wrote:
Sun May 12, 2019 4:40 pm
OK. I agree. In my defense, I over-complicated the comparison because I expected more debate about the finer points. So your simplification, "if the score is in my favor by 2 points or more.....it makes sense to call," is an excellent simplification.
Now the question is can we expand this argument further. In my OP numbers (which admittedly were not accepted), my EV analysis gave making a Next call with 1 trump + an off ace a value of +.15. Your EV analysis based on your 2 seat numbers gives this Next call a value of -.11. This leads me to the following assertion:

The EV of calling with 1 trump + an off ace is close enough to zero to warrant us always calling with this hand when we don't block reverse next no matter what the score [barring the obvious exception when we're up 9-8, and perhaps other scores (8-8, 8-7, 7-8, 7-7)]. The logic being: this weak call doesn't really hurt our team, it's close enough to EV neutral, but it does benefit our team by smoothing out some of the variance of the game, I.E. we never allow Seat 2 to get that devastating 4 point loner sweep.

And if the above argument is accepted it extends further to always calling with our whole range when we don't block reverse next since the additional cost of calling with a hand weaker than 1 trump + an off ace will be roughly offset by the higher cost of passing with this hand.

IOW:
RedDuke wrote:
Sun May 05, 2019 9:50 pm
In the end then, you aren't giving up much of anything by calling. However, what you do is stop them from making the four point loner sweep.
Which means, yes to the below question. I would call with this hand down 5-0.
Richardb02 wrote:
Wed May 08, 2019 6:17 am
The score is 0-0, we're in seat 1 and the dealer just turned down the (Card_9-S)

We have (Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)
Would you call next with this hand down 0-5 or up 9-7?
What about other scores? (8-8, 8-7, 7-8, 7-7)

Does this argument break down at these scores? After all we no longer gain the mathematical value of stopping a 4 point loner sweep. Well unfortunately I'm currently running out of time at the moment. But the clue to answering that question involves making the same kind of assumptions backing up my thin Next call, but then referring to this probability chart to fill in the blanks:

http://borf_books.tripod.com/euchprob.htm

Example of analyzing calling Next with 1 trump + an off ace at the score 7-7:

Based on OP numbers if we call we go set 65% of the time and thus end up with the deal down 9-7 with 23% equity. 30% of the time we score a point and end up with the deal up 8-7 with 66% equity. 5% of the time we hit our partner hard enough to score 2 points and now have the deal up 9-7 with 81% equity.

If we instead pass that hand we can conservatively estimate that this will cost our team 1 point on average. I suspect it's probably more than 1 point on average given that we block nothing but it's hard to know without that aforementioned mythical euchre simulator. Ok so if we pass, on average we end up with the deal down 7-8 with 40% equity.

Ok now multiplying and adding up the equities in the call scenario gets us to 38.8%....

(.65 x .35) + (.30 x .66) + (.05 x .81) = 38.8%

....vs the equity of passing = 40%.

40% is greater than 38.8%, suggesting that passing is marginally better than calling. However I think it's close enough to still warrant a call, but I can't prove that. It certainly wouldn't take much assumption tweaking to justify a call. Just assume that passing costs us more than 1 point, a plausible assumption given that we block nothing. Or we could challenge my OP numbers in a more non-conservative direction: Are we really getting euchred 65% of the time on this Next call? We are calling to hit our partner's range after all. Maybe it's only 55%? Bottom line, I think it's close enough, with enough uncertainty to err on the side of aggression.

However if Seat 2 donates, that could swing this close play to a pass at 7-7 becuz now in our worst case scenario when we call and get euchred and now have the deal down 9-7 we won't get to realize our full equity suggested in that probability chart (23%). All our game winning loners will be blocked.

I'll look at other scenarios 8-8, 8-7, 7-8 later, but the key to analyzing them is using that probability chart. Gotta go for now.

Wes (aka the legend)
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Post by Wes (aka the legend) » Thu May 16, 2019 3:09 pm

Wes (aka the legend) wrote:
Wed May 15, 2019 6:25 pm
Now the question is can we expand this argument further. In my OP numbers (which admittedly were not accepted), my EV analysis gave making a Next call with 1 trump + an off ace a value of +.15. Your EV analysis based on your 2 seat numbers gives this Next call a value of -.11. This leads me to the following assertion:

The EV of calling with 1 trump + an off ace is close enough to zero to warrant us always calling with this hand when we don't block reverse next no matter what the score [barring the obvious exception when we're up 9-8, and perhaps other scores (8-8, 8-7, 7-8, 7-7)]. The logic being: this weak call doesn't really hurt our team, it's close enough to EV neutral, but it does benefit our team by smoothing out some of the variance of the game, I.E. we never allow Seat 2 to get that devastating 4 point loner sweep.

And if the above argument is accepted it extends further to always calling with our whole range when we don't block reverse next since the additional cost of calling with a hand weaker than 1 trump + an off ace will be roughly offset by the higher cost of passing with this hand.


Let's go back to the OP where the score is 0-0 and the actions on us in the 1 seat, 2nd after the dealer turned down the (Card_9-S)

We have (Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)

My claim is that the EV of this thin Next call is close to Zero. Let's test this out using that probability chart: http://borf_books.tripod.com/euchprob.htm

Win Equity of calling: (.65 x .38) + (.30 x .57) + (.05 x .64) = .45

To translate the above numbers. If we call 65% of the time we get euchred and have a win equity of 38% down 0-2 with the deal. 30% of the time we score a point and have a win equity of 57% up 1-0 with the deal. 5% we score 2 points and have a win equity of 64% up 2-0 with the deal. Multiply and add the probabilities and calling here gives us a win equity of 45%.

Now assume that passing costs us 1 point and thus on average puts us down 0-1 with the deal. What's our equity in that spot? Guess what, it's also 45%

So using my numbers in the OP or Richard's updated numbers we get an EV of calling close to Zero. And when we utilize that probability chart we get an EV of exactly zero.

Thus supporting my assertion:

The EV of calling with 1 trump + an off ace is close enough to zero to warrant us always calling with this hand when we don't block reverse next no matter what the score, barring a few exceptions, which I'll talk about in my next post.

Wes (aka the legend)
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Post by Wes (aka the legend) » Thu May 16, 2019 3:42 pm

Wes (aka the legend) wrote:
Thu May 16, 2019 3:09 pm
The EV of calling with 1 trump + an off ace is close enough to zero to warrant us always calling with this hand when we don't block reverse next no matter what the score, barring a few exceptions, which I'll talk about in my next post.
Ok, first we have update something. The EV model I started with in the OP is now obsolete. We don't need it. Incorporating that probability chart into our EV model is simpler and better. We now no longer have to waste time guessing at Seat 2 probabilities. And we no loner have to sweat it about the assumption of Seat 2 always calling to prop up the model. Although we still have to assign probabilities to Seat 1 calls to get things going. Other than that, to incorporate the probability chart all we need is two key assumptions:

1) The probability chart is approximately accurate

2) The cost of passing is roughly 1 point.

Ok, Just for fun let's look at calling with Next with:

(Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)

When the score is 9-8 in our favor.

Win equity of calling = (.65 x 0) + (.30 x 100) + (.05 x 1) = 35%

Win equity of passing = 65%

65% is way better than 35%. Calling with this thin hand up 9-8 would be egregiously wrong and suicidal. No surprise so far.

Ok Let's do 8-8:

Win equity of calling = (.65 x 0) + (.30 x .72) + (.05 x 1) = 26.6%

Win equity of passing = 36%

36% is significantly higher than 26.6%. Passing clearly dominates calling with this hand. Again, not a surprise. We have to tighten up in this spot.

What about when we're up 8-7:

Win equity of calling = (.65 x .36) + (.30 x .81) + (.05 x 1) = 52.7%

Win equity of passing = 54%

54% is greater than 52.7% suggesting passing is marginally better, but it's close enough to be debatable becuz small tweaks in any assumption could easily support calling.

Ok now let's do down 7-8:

Win equity of calling = (.65 x 0) + (.30 x .54) + (.05 x .72) = 19.8%

Win equity of passing = 23%

23% is greater than 19.8% suggesting that passing is better than calling. But that's still not a large enough difference to be clear.

For example, Here's how little we'd have to tweak our assumptions to justify calling: Assume we get euchred 60% of the time instead of 65% of the time:

(.60 x 0) + (.35 x .54) + (.05 x .72) = 22.5%

That one tweak almost gets us to even with passing. This is close enough that the only real way to decide this issue would be to run this spot a million times or whatever amount is necessary to really know what our euchre, 1 pt, 2 pt probabilities really are. IOW only that mythical euchre simulator can really decide this issue.

Conclusion:

Up 9-8, clearly pass.
8-8 clearly pass.
Up 8-7, it's debatable
Down 7-8, it's debatable

Edit: And based on my other post 7-7 is also close/debatable

Wes (aka the legend)
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Joined: Wed Jun 13, 2018 3:03 pm

Post by Wes (aka the legend) » Thu May 16, 2019 4:04 pm

Richardb02 wrote:
Wed May 08, 2019 6:17 am
The score is 0-0, we're in seat 1 and the dealer just turned down the (Card_9-S)

We have (Card_A-D) (Card_K-D) (Card_K-S) (Card_10-H) (Card_10-C)
Would you call next with this hand down 0-5 or up 9-7?
http://borf_books.tripod.com/euchprob.htm

What's cool about this probability chart is we can use it to figure out our EV of calling vs passing at any score. Again assume passing costs us 1 point on avg.

For fun let's do down 0-5:

Equity of calling: (.65 x .08) + (.30 x .23) + (.05 x .29) = 13.55%

Equity of passing: 13%

13.55% is greater than 13% suggesting this is a marginal call. This is basically a tie, but remember a tie supports a call becuz we still get the benefit of controlling some of our variance by never allowing Seat 2 to pull off a loner sweep.

What about 6-6:

Equity of calling: (.65 x .30) + (.30 x .61) + (.05 x .74) = 41.5%

Equity of passing: 42%

Again, a virtual tie. When it's close I err on the side of aggression for aforementioned reasons.

What about when we're down 0-7:

Equity of calling: (.65 x .01) + (.30 x .11) + (.05 x .14) = 4.65%

Equity of passing: 4%

Calling is marginally better than passing, but again, it's a virtual tie given how little we could tweak assumptions to get an answer we like. But like I said before, a tie favors a call.

Wes (aka the legend)
Posts: 269
Joined: Wed Jun 13, 2018 3:03 pm

Post by Wes (aka the legend) » Thu May 16, 2019 8:38 pm

Wes (aka the legend) wrote:
Thu May 16, 2019 3:42 pm
Conclusion:

Up 8-7, it's debatable
Down 7-8, it's debatable

Edit: And based on my other post 7-7 is also close/debatable
I forgot to look at the "down 6-8 spot". Assume same assumptions hold with same 1 trump plus off ace hand. And we're still using that chart: http://borf_books.tripod.com/euchprob.htm

Ok here we go

Equity of calling: (.65 x 0) + (.30 x .40) + (.05 x .54) = 14.7%

Equity of passing: 18%

Passing appears better than calling as 18% is greater than 14.7%. Out of curiosity, I wondered how much would I have to tweak my model to force a tie. By tweaking the model I'm just gonna mess around with our euchre rate which will necessarily impact our 1 point rate. I'm gonna keep our 2 point rate constant.

It turns out in order to force a virtual tie our euchre rate would have to be approx 57% or 56%

Equity of calling: (.57 x 0) + (.38 x .40) + (.05 x .54) = 17.9%

Equity of calling: (.56 x 0) + (.39 x .40) + (.05 x .54) = 18.3%

This gives us some insight. If we think a 57% euchre rate is wildly unrealistic (I.E. we think our call would get euchred significantly more) that can give us more confidence that passing is indeed correct. I personally don't have a strong conviction on this. Like, if the euchre god(s) came down and told me that the real euchre rate in this spot was 50% I would not be surprised at all, but if he said it was 70% I wouldn't be surprised either.

Either way, passing down 6-8 with this hand is defensible, but I'm not convinced that calling isn't defensible also. Another monkey wrench to throw in the mix: If Seat 2 donates we should be more likely to call becuz even if we pass and likely end up down 6-9, we will never get to realize our full equity share becuz Seat 2 will block all our loners. Although with that said, if seat 2 donates and we're playing in a tournament where points matter more than winning, we should be more apt to pass becuz we would gladly accept that donation down 6-9 for hopefully 2 more points.

Conclusion: Either down 6-8 is a pass or it's debatable.

Wes (aka the legend)
Posts: 269
Joined: Wed Jun 13, 2018 3:03 pm

Post by Wes (aka the legend) » Thu May 16, 2019 8:51 pm

Let's look at the rest of the spots when our opponents have 8 points:

Down 5-8:

Equity of calling: (.65 x 0) + (.30 x .30) + (.05 x .40) = 11%

Equity of passing: 10%

Calling edges out passing.

Down 4-8:

Equity of calling: (.65 x 0) + (.30 x .22) + (.05 x .30) = 8.1%

Equity of passing: 8%

Calling barely wins, a virtual tie. Ties go to the side of aggression, so call.

Down 3-8:

Equity of calling: (.65 x 0) + (.30 x .16) + (.05 x .22) = 5.9%

Equity of passing: 5%

Calling edges out passing.

Down 2-8:

Equity of calling: (.65 x 0) + (.30 x .11) + (.05 x .16) = 4.1%

Equity of passing: 3%

Calling beats passing.

Down 1-8:

Equity of calling: (.65 x 0) + (.30 x .08) + (.05 x .11) = 2.95%

Equity of passing: 2%

Calling beats passing

Down 0-8:

Equity of calling: (.65 x 0) + (.30 x .06) + (.05 x .08) = 2.2%

Equity of passing: 1%

Calling beats passing

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