Mathematical discard comparison

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meppii
Posts: 6
Joined: Mon Dec 26, 2022 10:04 am

Mathematical discard comparison

Unread post by meppii » Mon Dec 26, 2022 10:42 am

Please help me. I am the dealer in seat 4:
I hold 10D, KD, 10C, QC, and AS
I turn up AD, seat one, two, three pass, and I pick up the AD.
Let us say 10,000 hands, what is the difference between my team getting euchred mathematically speaking if I discard the 10D vs discarding AS?
Assume all players are experienced players and equally skilled.
Your help would really be appreciated.
Thanks,
mepii



jblowery
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Unread post by jblowery » Mon Dec 26, 2022 6:10 pm

Always keep the ace.

irishwolf
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Unread post by irishwolf » Tue Dec 27, 2022 12:10 am

I don't get it, you say, "Let us say 10,000 hands, what is the difference between my team getting euchred mathematically speaking if I discard the 10D vs discarding AS.

Why would you ever consider with the hand you posted, discarding the 10D or AS? Those are needed to win tricks! Your only choice is the 10C to discard.

IRISH

meppii
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Joined: Mon Dec 26, 2022 10:04 am

Unread post by meppii » Tue Dec 27, 2022 7:52 am

Oh my. My mistake. I meant to ask if I discard the 10C or the AS. I apologize for the confusion. I still wonder if Clearing the suit with the AS might work better. I have played it both ways and both make our point over half the time, but I was wondering if someone could give me the mathematical data. Sorry for the error. Any help would be appreciated.
mepii

irishwolf
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Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Tue Dec 27, 2022 11:19 am

Okay, that makes more since, NoP!

However, no way will you have better results discarding the AS vs 10C.
WHY?

Because saving the Club doubleton and creating a void in Spades (NO bower) makes you hand significantly weaker. AS is a winning Boss card in Spades. True you now have two voids (with a weak hand). So what, you have no bower with a weak doubleton off suit.

Suppose you did discard AS and Eldest led a spade. You trump a Spade lead - now have two trumps. What are you going to lead to trick 2? You have to lead trump for any hope of winning a point. You could have won that trick with AS and have 3 trumps, lead one with two back. In addition if a heart is led and your partner wins it with AH or trumping hearts, you can void your hand in clubs. Having a club played early in any manner, tells your opponents you most likely will have another club. If your opponents have AC doubleton or KC doubleton it can put you in a squeeze more often than you can win a club trick. So many more things can happen that are bad having that club doubleton.

Same goes for having a KC dbltn the dealer might have with AS.

Bottom line is you discard the AS your euchre rate will be over 50%. (all hands considered - estimating) Because if you did discard the AS, your partner would have to win the Club trick and have JD or JH to boot. Or AH with bower. Slim chance - less than 10% (AC) or 14% (AC or AH). EV will be negative.

Compare that with discarding a club your you will make a point 75% + (euchre rate about 25 - 30% - EV will be positive.

Never discard a winning card to save a King/Queen doubleton off suit.

If in doubt and want confirmation, you could actually find the answer yourself by dealing out hands. Give S4 that hand - six known cards, discarding and playing out hands all combinations with 18 cards. Eliminating those that hands S1/S2 or S3 might order. All combinations played both ways. But you have to have a minimum of 100 hands just to see which way this leans (or a simulator).

IRISH

meppii
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Joined: Mon Dec 26, 2022 10:04 am

Unread post by meppii » Tue Dec 27, 2022 7:59 pm

Hello,
I do appreciate your reply. I was hoping someone with a simulator might run it for me. Either way, I have played euchre a little and I have discarded the AS and at times the 10C. There is not a big difference in the success rate either way.
To follow up on your comment, if I discard the AS and spades is led, as you said I trump it for my first trick unless my partner had the AS. YOU DO NOT LEAD TRUMP back. You must, and I mean must lead back the 10C. You hope your partner takes it, but the more likely fallback is that the AC comes out so your KC is now boss. If the AC comes out, and it normally does, you are in an okay spot. Often the heart is lead next and you trump in. If you take a second trick, leading the KC is the move with you holding the AD. Granted, if your partner has either bar or if they take a trick, especially using a trump, this hand works. Don't get me wrong, it gets euchred about (estimate) 25 to 30 percent. But holding the AS is seemingly not much different, That is why I was wondering about the actual mathematical difference. Thanks again for your comments, I have learned a lot reading your stuff through the years (talking to Irish, but could be talking to a bunch of you).
mepii

P.S. A side question might be does this change your discard if we put the AH as a substitute for the AS. I wonder how much difference the ACE of next vs a green ACE, mathematically...

irishwolf
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Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Tue Dec 27, 2022 8:36 pm

I will strongly disagree with your gut analysis. But hopefully Ray will run his simulator on both ways on this to resolve.

IRISH

sdu754
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Unread post by sdu754 » Fri Dec 30, 2022 3:04 pm

You would always keep a singleton Ace, even if it means holding an extra suit. A singleton Ace is as likely to take a trick as the Queen in the Trump suit. Remember that you might be able to slough off the other Club after discarding the 10 when picking up the Ace of Diamonds.

meppii
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Unread post by meppii » Sun Jan 01, 2023 10:52 am

Would it make a difference to you if the singleton ACE was the AH (ACE In next) instead of the AC (Green ACE)? I believe the differences are very slight, however, I am aware there is a best choice statistically.

raydog
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Unread post by raydog » Sun Jan 01, 2023 9:38 pm

I simulated 3 different hands over 100,000 deals:
1) S4 holds AS + K-10D + Q-10C (AD turned)
2) same, but AH turned
3) S4 holds AS + K-10D + K-QC (AD turned)

These six cards fixed, all other cards random; only counted hands where S4 bid, R1.

1) 76,409 hands counted
discard 10C: (5,286 / 55,195 / 15,929) [sweep / +1 pt. / euchred] EV = +0.44
discard AS: (3,789 / 48,054 / 24,566) EV = +0.09
Much better to discard the 10C - euchre rate is much lower. Note that the euchre rate I found is quite different from what Irish predicted, probably because of the almost 25% of hands I DIDN'T count, which would include the cases where S1 and S3 had such strong hands that they bid.

2) 75,001 hands counted
discard 10C: (5,370 / 54,092 / 16,139) EV = +0.50
discard AH: (3,845 / 47,642 / 24,114) EV = +0.09
Same results (difference is hardly significant given the sample size)

3) 76,700 hands counted
discard QC: (5,708 / 56,188 / 14,804 ) EV = +0.50
discard AS: (4,980 / 50,130 / 21,590) EV = +0.22
Discarding the A is not quite as bad (because you are keeping a K rather than a Q), but still far better to discard a C. I only tested this scenario to check Irish's generalized rule of not discarding an A to keep a K/Q doubleton.
Last edited by raydog on Wed Jan 04, 2023 9:50 pm, edited 1 time in total.

irishwolf
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Unread post by irishwolf » Mon Jan 02, 2023 12:19 am

RAY, Thanks for running the simulation(s). No real surprise, except maybe the sweeps.

What's important tho is the difference in EVs of discarding that AS or AH singleton ace and keeping a weak doubleton.

As far as the Euchre rate - several variables impacting that but I accept your simulator on the magnitude of the differences in the euchre rates. Not close a statistically significant difference. Notice that at a euchre rate of 32% for discarding the AS/AH your are just short of Parity.

CONCLUDE: Discarding the low Club you make a point over 75% of the time as predicted.

IRISH

meppii
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Joined: Mon Dec 26, 2022 10:04 am

Unread post by meppii » Mon Jan 02, 2023 10:59 am

Thank you Ray,
Thank you to all the euchre players. This is a really cool site for euchre lovers. I am a euchre lover, and I appreciate your time discussing this specific situation. With that said, I admit my gut estimate is significantly off. While this is a simple game to learn, it is not a simple game to excel. I am experienced, but I still have a lot of situations to learn, and reading this site has helped me. I do have a follow-up.
The two hands above need to be played very differently. In the situation of holding the singleton off-suite ACE, if the dealer takes a trick and still holds the off-suite ACE, they need to lead back trump in order to strengthen the off-suite ACE. If the dealer takes a trick holding the weak doubleton suite, they need to lead back the lower card of the doubleton suite. I guess my question is, does the simulation program play these hands differently? I thank all of you again.

mepii

Tbolt65
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Location: Las Vegas

Unread post by Tbolt65 » Tue Jan 03, 2023 12:16 am

meppii wrote:
Mon Jan 02, 2023 10:59 am
Thank you Ray,
Thank you to all the euchre players. This is a really cool site for euchre lovers. I am a euchre lover, and I appreciate your time discussing this specific situation. With that said, I admit my gut estimate is significantly off. While this is a simple game to learn, it is not a simple game to excel. I am experienced, but I still have a lot of situations to learn, and reading this site has helped me. I do have a follow-up.
The two hands above need to be played very differently. In the situation of holding the singleton off-suite ACE, if the dealer takes a trick and still holds the off-suite ACE, they need to lead back trump in order to strengthen the off-suite ACE. If the dealer takes a trick holding the weak doubleton suite, they need to lead back the lower card of the doubleton suite. I guess my question is, does the simulation program play these hands differently? I thank all of you again.

mepii
Irish sums it up pretty good and Ray with his simulator is nice to see from a statistical value. Feel free to bring up any questions, we have some good discussions here, some get heated at times but we are all here to share ideas and our experiences and to perhaps gain new perspectives. So never shy away from asking a question or making a comment or suggestion on plays or ploys.

Tbolt65
Edward

raydog
Posts: 260
Joined: Thu Sep 16, 2021 6:56 pm

Unread post by raydog » Fri Jan 06, 2023 10:28 am

Sorry for the delayed response, meppii. I ran into some coding errors in my simulator and it took me a little while to correct them - it's a work in progress, but slowly getting better thanks to the analysis of hands on this site. I should also add that I re-ran the original scenario and there was no significant change to the results I found earlier. While my simulator has its flaws, all the ones I have corrected over the past 18 months or so have led to very small incremental differences and improvements. I only trust the results of my simulator if the difference between two plays is significant.

When S4 holds the AS and KC and 3 trump:
1) win 1st trick with AS: lead best trump [your strength in this hand is your long trump suit; draw trump!]
2) win 1st trick by trumping a H lead: lead worst trump [have only 2 trump left; hope to draw out bower(s) and also give AS a better chance of winning]
3) win 1st trick with KC: lead best trump [similar to 2), but have 3 trump, so angling for possible sweep; I tested leading lowest trump here - similar results (no significant difference)]

When S4 holding the K-QC and 3 trump (having discarded AS):
1) win 1st trick by trumping H or S: lead KC [I tested this, and better than leading AD]
2) win 1st trick with QC: lead AD [AC is clearly buried, KC is now boss C; draw trump to potentially make that KC a winner]

Ray

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