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### EUCHRE HAND - TEASER

Posted: **Tue Dec 04, 2018 5:54 pm**

by **irishwolf**

FOR ALL:

Below is a real hand. Put yourself in the dealerâ€™s situation. What will you play on trick 3. What are you odds of winning the trick?

Score is 9 to 8, JC UP: Its been a see-saw game, playing a best of three with each team winning one game a piece. This is the third and final game, the score is 9 to 8 to the dealerâ€™s advantage.

(You) The Dealer pick up the JC and discards the 10D. Opponents have just won two tricks. The dealer is holding JC, JS, KC and his partnership must win the next three tricks to win the game and rubber. 3rd seat has just won the 2nd trick with the Ace of spades and now puts the dealer in a squeeze with QS lead. [Assume all players are experienced with equal skill.] Eldest wins the first trick with the AH. He now leads 9s and Pone wins the trick with the AS. Pone now leads the QS:

You are the dealer, what will you play on trick #3?

Tricks: 1 2 3 4 5

1st Seat AH 9S

2nd Seat TS 9D

3rd Seat 9H AS QS

4th Dealer KH KS ??

irishwolf

### Re: EUCHRE HAND - TEASER

Posted: **Tue Dec 04, 2018 6:50 pm**

by **RedDuke**

So you have both bowers and the king of trump and you need all three tricks?

You're going to want to Trump with something that your opponents won't be able to stop on the off chance that one of them is holding the A-Clubs so pick either of the jacks. Spades has already been led once so you know that somebody else is probably void and will trump in. So what you do here is use one of the bowers to take the trick, then lead back the other bower to try and pull the Ace-Clubs. On the final trick, you lead the king and hope it walks or that your partner has the Ace.

### Re: EUCHRE HAND - TEASER

Posted: **Fri Dec 07, 2018 11:41 am**

by **irishwolf**

RedDuke;

To break this problem down - the Dealer holds the JC JS & KC. Consider the facts of using a bower vs KC on trick 3:

1) Five spades have been played and JS is trump. Thus the dealer (you) are in a squeeze and eldest can trump or slough;

2) There are four unknown trumps that include the AC, the only trump that can over trump you KC if play the AC;

3) If the dealer uses a bower, then what is probability of eldest having his AC guarded by the 9c 10c and/or Qc?

4) And if the AC is with 3rd seat (Pone) what is the chance it is guarded vs not-guarded?

5) There are only 8 cards that really matter of which 4 are trump, your partner at 2nd seat has already demonstrated by not trumping trick one that he/she has no trumps (or is an idiot);

6) What is chance that the AC is buried in the Stock which has 3 unknown cards to the dealer?

I hope the dealer does not quickly play without fully grasping the complexity of the situation.

Does any of this RedDuke make you think a little more about the predicament the dealer (you) are in, and the game is on the line? This is the last hand of this game - score 9 to 8 in the dealer's favor.

Irishwolf

### Re: EUCHRE HAND - TEASER

Posted: **Fri Dec 07, 2018 12:04 pm**

by **RedDuke**

If first seat has A-C, then you're euchred if you play the K-C and it's game over. If your partner has it or if it's in the stock, then you've won the game no matter what you do.

Realistically then, the only way you can win this game is to have either you or your partner take this trick. Your partner can't take it because they've already demonstrated that they have no trump. The only way that you can ensure that you take this trick is to use a bower. Thus, the best bet to my mind is still the original advice. Take this trick with one of the bowers then lead the other jack next hand and hope you can pull the A-C.

You make reference to eldest having a guarded A-C. That's a possibility. If they have that, you're euchred regardless because they'll just slough off if you play a bower here or overtrump your king if you play that. They'll then play the 9-C or 10-C on the next trick and then overtake your king on the final one.

If A-C is with third seat, then yeah, it's best to play the K-C here, but you don't know that. The odds are probably highest if you take it with a bower but that's only because first seat has three cards that you don't know and third seat only has two so first seat is the bigger threat to your king. One of your opponents at least probably has two trumps, one of which is the Ace. There's slightly higher odds that first seat has it than third (but the same chance that it's in the stock as it is that first seat has it).

Then again though, if we assume that one of the opponents has the A-C guarded, then you can win if it's third seat that has it but you have no chance of winning if it's first that has that. It might be worth it just to take the gamble and play the king and pray that eldest doesn't have the ace.

However... keep in mind that the reason that third seat led the same suit again might mean that he does not have the Ace-Clubs and he's leading through you hoping that his partner can take it by overtrumping you... He knows that you have the right but doesn't know what else you have. He's probably hoping that his partner has either the left or the ace to overtrump you for the euchre.

### Re: EUCHRE HAND - TEASER

Posted: **Fri Dec 07, 2018 7:14 pm**

by **irishwolf**

I was hoping more people would tackle the hand proposed. Anyway, you did RedDuke. I can see you have given it good effort. Here the answer to:

1. The Dealer is in a pickle if you trump with a bower, yes you win the trick but then it boils down either opponent having the AC but it also has to be guarded by one of the three low trumps (9c, 10c, and/or QC).

2. If the dealer trumps with the KC eldest can over trump if he has the AC. It won't matter in this situation if he has more trump.

3. And it will not matter which card the dealer uses if the AC is buried in the Stock of 3 unknown cards.

It has already been established that the dealer's partner did not trump the 1st trick, nor did he trump the 2nd trick. So safe to assume his hand of 3 unknown cards are irrelevant to the hand. There are 3 cards in the stock and 3 with eldest leaving 2 unknown cards with 3rd seat (Pone). 8 cards in total. There are 56 hand combinations possible to the 1st seat opponent, 4 trumps and 4 off suit cards. We only care about the trump cards.

The expected probability calculated (this requires many hands played to come close to the statistical calculation - 400 hands to be 95% accurate). Out of 56 hands the AC can be expected at eldest position 20/56 for 35.7% (lets round this to 36%). So if the dealer uses the KC to trump he will be euchred on the average 35.7%(400 hands).

Now if the dealer uses a bower, he will win trick 3 but can now get euchred if 1st seat or 3rd seat has the AC guarded. That number is (drum roll .....) 42.9% basically rounded to 43%. You will be Euchred on the average 43% if you use a bower on trick 3. Thus approximately a 7% difference. Not big difference but would you not want to gain any advantage possible. 7% is significant in my book. Thus the answer is use the KC on trick 3, and hope the AC is not with eldest. It could be in the stock or with 3rd seat. Doing 20 hands on the kitchen table will be no help in this situation.

There is one more thing you might do to sort out which player, Eldest or Pone has the AC - hesitate and look at each player for "body language" that may assist you. There is no rule that you can't turn to one or the other, and ask Do You have the AC? If you are good at reading, sensing, it may help your situation!

Irishwolf