WHAT TO LEAD

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

WHAT TO LEAD

Unread post by irishwolf » Sat Apr 23, 2022 10:49 am

Test you knowledge:

The upcard (Card_K-H) and you are in 1st seat (S1) and order up the Dealer. Assume the score is 6 to 6.
This is your hand: (Card_A-H) (Card_Q-H) (Card_10-H) (Card_9-H) (Card_Q-S)

What card are you going to lead to the 1st trick?

Please justify why?

IRISH



Tbolt65
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Unread post by Tbolt65 » Sat Apr 23, 2022 3:16 pm

I can see this being as a trick question but honestly, I am leading Ace of hearts. I can see a possible argument it doesn't matter what trump you lead but I'm still leading the ace of hearts for those situations where might still march if both bauers are down and my queen of spades is either good or my partner takes it. You are going to be set regardless if Seat 4 has J-J-K. Say if dealer has Left-King or Right-King. Your not out of the woods yet but you at least push the left or right out of the hand with your ace or make them make a mistake but putting the king on it. Funny things happens in euchre. Make your opponent make a mistake. That goes with the rest of the hand even if they play the Left or the right. There are many hands secnario's to go into but the main reason. In times that both bauers are in the discard/kitty. Lead the Ace. If your partner has the right or Left in Third seat all the better. If trump is split say s2 has bare Left or bare right. It can get dicey and with this hand for a large portion of scenario's you will need your partner to take one, just because of the bauer situations. He's going to do that either by having the bare right, bare left and taking the trick. Or taking with some Off suit if you allow him to either by throwing off or him naturally taking it with the king or Ace of your suit Queen. There could be times your queen is good on it's own due to circumstances but in the end. Your play will dictate a larger majority of the time on how you manufacture that 1 point or possible two here. Like I said when the cards are clearly all in S4 with J-J-Kh you are euchred/set no matter what you do.


Tbolt65
Edward

justme
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Unread post by justme » Sat Apr 23, 2022 6:23 pm

A trump lead is absolute here, but rather than lead the Ace to the first trick I suggest leading the Q T or 9 of trump (a heart). If your partner has either one of the bowers to play , win or lose that trick, playing after the dealer you will then control the hand at trick 2 with the boss heart (Ah) in your hand. 3 of the last 4 tricks will be yours. If your partner does win the first trick you will hope he has an ace to lead back for a shot at a march, praying the other bower is buried.

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

Unread post by irishwolf » Sat Apr 23, 2022 8:48 pm

Well, two interesting and somewhat opposing comments.

I am going to comment once we get more 'votes' on this. Need more input. Don't be shy this is a learning exercise (not trickery).

And welcome back Justme!

P.S. - If you are listening Ray. Don't Post your Simulator results. I would tho like you to do that after I comment. If you would run results for Leading AH, QH (same as 9h/10h) and QS.

IRISH

raydog
Posts: 205
Joined: Thu Sep 16, 2021 6:56 pm

Unread post by raydog » Sat Apr 23, 2022 10:21 pm

Well, Irish, I cheated and already did the simulation. I then went back and was able to justify the results quite clearly. I'll hold off posting until you post your answer.

irishwolf
Posts: 1237
Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Sat Apr 23, 2022 10:57 pm

Ray,

Good, should be straight forward.
But also do going alone with this hand. Just for fun!

IRISH

Richardb02
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Location: Florida

Unread post by Richardb02 » Sun Apr 24, 2022 3:25 pm

I would lead the Ah. The probability of then knowing the location of the Bowers is extremely strong. Then armed with the knowledge of the location of the Bowers and extremely strong trump S1 will have clear direction on how to handle the rest of play.

jockosaurus
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Joined: Sun Jan 16, 2022 11:18 pm

Unread post by jockosaurus » Sun Apr 24, 2022 8:56 pm

I can't think of any distribution of the two bowers which would justify leading the 9, 10 or Q. There might be one I missed, but A is clearly the superior lead for the vast majority of cases.

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

Unread post by irishwolf » Sun Apr 24, 2022 9:52 pm

THE ANSWER:

Others may post on this but I think time to put this to rest. Of the comments made, IMO that Justme correctly said, " A trump lead is absolute here, but rather than lead the Ace to the first trick I suggest leading the Q T or 9 of trump (a heart). If your partner has either one of the bowers to play , win or lose that trick, playing after the dealer you will then control the hand at trick 2 with the boss heart (Ah) in your hand. 3 of the last 4 tricks will be yours. If your partner does win the first trick you will hope he has an ace to lead back for a shot at a march, praying the other bower is buried. "

Clearly, you will get in a lot of trouble not leading trump. Reason is that this gives the opponents their Best opportunity to win the Spade trick with AS or by trumping.

Trump MUST be led. And it's not a bad lead by leading AH as when both bowers are buried, S1 AH wins the KH. However, that both bowers being buried is a mear 2% probability.

So lets dwell on leading a low trump, and any will do as they are 'touching'. Leading low trump in the event that the Dealer has JH/KH and his partner, Pone, at S3 now forces the JH. Now S1 in most cases win his KH with his AH. This is about a 8 - 9% advantage over leading the AH. So in summation, there is about a 8 - 9% difference in Euchre rates here. Look for Ray to run his 100,000 both ways to confirm my statement.

Other than these two particular situations & probabilities, the Euchre rates and Sweeps are pretty much equal (the same for leading AH or Low, QH). I could bore you with the math but no need, IMO.

Ed pointed out the Dealer with both Jacks + KH is a euchre. However, consider unless the QS is led and dealer has a void and S3 trumps. Then S1 can 'might' escape a euchre with S3 over trump or if the Dealer plays a Bower to S3 lead. But overall, its a very bad lead, QS.

Here the Bonus Part II.
What if the score is not tied, like 9 to 4 and you are way behind. Should S1 swing for the fence? It's a long shot. But consider Both Bowers being with S3 and/or the Stock - a whopping 26% void in bowers for S2/S4. But the Loner success rate will NOT be 26% because S1 has the QS trailer. What the chance it makes it? That also is another 26% - AS & KS ARE BURIED OR WITH S3.
So that successful loner rate will be 6 to 7%. We await Ray's results on that too. And that euchre rate jumps to about 55% and flips to a Negative EV. So carefully decide but if you are going to lose anyway, why not swing for the fence?

Fee free to challenge any part of this post.

IRISH

raydog
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Unread post by raydog » Mon Apr 25, 2022 11:28 am

I fixed the cards in S1 + the turn card, randomized the distribution of all the other cards, then ran the simulation 100,000 times, comparing different leads. Here's what I found:

lead AH: (17,236 / 53,179 / 29,585) [sweep / 1 pt / euchred] EV = +0.28
lead QH: (16,296 / 59,430 / 24,274) EV = +0.43
lead QS: (6,424 / 64,130 / 29,446) EV = +0.18

note that leading the AH results in 0.9% more sweeps and 5.3% more euchres than leading the QH.

Analysis: (same as what Irish said, but with a bit more detail)
Obviously the whereabouts of those two bowers are key. There are two bowers which can be in 4 different "hands" (S2, S3, S4 and kitty), so 4x4 = 16 permutations. Of these, 14 yield situations where the outcome is the same no matter which trump card is led. It is the 2 remaining cases which are critical.

1) both bowers in the kitty (buried):
In this case, it is possible to sweep by leading the AH, whereas leading the KH will always result in just 1 point. This situation will arise 3/18 x 2/17 = 2.0% of the time. But leading the AH will not guarantee a sweep in these cases; the opponents still need to win that last trick, when you lead the QS. How often will that happen? Well, the most common instance of losing that trick is when S2 or S4 holds the AS, which we would expect 9/16 = 63% of the time. This is not exact, as there are 2nd order (less likely) scenarios - the person who holds the AS may also hold another A, and discard the wrong one on trick 4; the KS may be a winner (if the AS is buried AND the KS is held to the end; etc. - but it's a good approximation. So you really only gain 2% x (1-63%) = 0.74% sweeps (approx.) by leading the AH and capturing these sweeps. From the simulation, we see 0.9% - the difference is the effect of the 2nd order scenarios. Looks good so far.

2) S3 holds JD (L) and S4 holds JH (R):
In this case, leading the QH draws out the two bowers and leaves the AH in S1's hand as boss trump. It's irrelevant if the QS wins the last trick, we will win 3 or 4 tricks and get a point. But if we lead the AH, S4 wins the first trick and has the boss trump (KH), giving the opponents 2 trump tricks. If they can win the final trick, they will euchre us. This scenario (positioning of L and R bowers) arises 5/18 x 5/17 = 8.2% of the time. But the opponents do need to win that last trick as well to euchre us. How often does that happen? In the previous scenario, it seemed to actual occur 55% of the time (2.0% - 0.9%). Here, it seems to occur more often - 5.3% / 8.2% = 65%. Why? Because S4 wins 2 trump tricks early, and has a decent chance of leading either the K or AS (if they hold it) or a low S to partner's K or A (if they hold it), and so there is less chance of one of the opponents discarding the potentially critical card early. Once again, the simulation seems reasonable.

So it appears that even if there are only a couple of outlier (low percentage) situations which are important, and even if they oppose each other (one advantageous, the other disadvantageous), they may still steer the correct decision.

As for leading the QS on trick 1, that just removes any guesswork from the opponents' play, and so can't help us. Winning that final trick - when S1 leads the QS - is critical in the deciding scenarios (getting a sweep or avoiding a euchre). And we increase our chances of winning that trick if we play it last.
_____________________________________

On to the addendum. You're way behind in score and so want to shoot for the fences and go alone! Is that advisable?

I did a fresh run of 100,000 hands to see the results:

lead AH: (7,464 / 50,831 / 41,705) EV = -0.03
lead QH: (0 / 58,295 / 41,705) EV = -0.25

Of course in this scenario you will lead the AH; leading the QH means relinquishing a trick, so no 4 pts. Going back to the 16 possible permutations of bower placement, there are several where partner's holding will change the outcome [I haven't bothered examining in detail - the simulation results support mine and Irish's intuition], the extra 4 pt wins come nowhere near compensating for the extra euchres. Don't go alone!

irishwolf
Posts: 1237
Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Mon Apr 25, 2022 12:20 pm

Ray,

Yep, in total agreement, all aspects thereof.

What I like is that your simulator (and this pretty much straight forward thinking by all positions) is that it agrees with my calculations. Confirming I can do the math that will equal any simulator. I wanted to Post the results such that no one would say, you just copied Ray, lol. I hope it confirms, I don't blow SMOKE.

I did no hands because this would require an excessive and needless amount of time and effort.
:lol:

IRISH

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