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Euchre Column of the Month – May 2005

By Joe Andrews

Forced Loner Calls - Partner is Dealer and the Right is Turned

In some circles, there is a rule which requires the partner of the Dealer to go Alone whenever he orders trump to his partner. There is some logic for this, as there are hands in which it is essential to play the Loner from that side of the table in order to avoid a blocking position. And there are other times when the Dealer has a sure-fire Loner, only to have his partner order trump and thus steal his Loner! When the Right is turned, the position is always dynamic. A lot of live event directors do not enforce the mandatory Loner rule if a partner orders trump to his partner. And finally, there are times when the Dealer does not want to have his/her partner ordering trump. How can one be sure?

Now we must look at those situations in which the Right is turned, and the Dealer has no other trump and must decide what to do if three passes come to him. How many times have you heard the old adage "Turn down a Bower and lose every hour?" You may rest assured that if he turns down the Right, the player on his left will go Alone in the next (same color) suit. It truly is amazing how many times this happens. Some players have an agreement to never turn down the Right when they are Dealer. It is a convention, of sorts. This agreement comes in mighty handy when the Dealer's partner is sitting on two or three trump, perhaps a side Ace, and wants to order. Now, if this player knows that his (Dealer) partner will never reject the Right, he/she can pass with confidence and feel good about having a nice supporting hand.

This approach also allows for the Dealer's partner to go Alone if his hand warrants this choice. (He holds the Left, two other decent trump, and a good side suit, and wants the Right knocked out of the hand.) Of course, the Dealer might wind up picking the Right with a totally useless hand and no other trump card. What the heck; you can't have it both ways! At least the opponents won't be trying Loner of their own. However, there are only so many times during the course of Match when you can give up 2 points. If you are going to use this convention, be sure that your partner knows what's going on, and accept the fact that you will get burned occasionally.

Euchre Math, part 1 of 2
(Excerpted from Joe’s "The Complete Win At Euchre", copyright 2004.)

You might find this "exercise in numbers" rather interesting!

Questions

1.       What are the odds of being dealt Right Bower, Left Bower, A - K - Q of a suit and having either the nine or ten turned as the up card?

2.       What are the odds of having Right Bower, Left Bower, and three other NON-TRUMP cards in your hand? (Assume that the color of the suit of the upturned card is the same as the color of the two Jack in your hand.)

3.       Just how many different five-card Euchre hands are possible?

4.       What are the odds that you will be dealt:

        a. One Jack (any Jack)

                b. Two Jacks (any two Jacks)

                c. Three Jacks (any three Jacks)

                d. Four Jacks (all four Jacks)

Answers

1.       There are two possible "perfect" hands in spades, two in hearts, and so on, or a total of eight perfect hands. But it's not 8/42504 = 0.134%, because that doesn't take the cut into account. There are actually only four perfect hands, one in each suit, each with two possible cuts. Suppose you have the perfect hand in spades (probability 1/42504 or 0.00235%); the odds of a perfect cut is 2/19, or 0.105%. So your chances of getting a perfect hand in spades is (1/42504)(2/19) = 0.0000248%. If you'll settle for a perfect hand (and cut) in any suit, it's four times that, or 0.0000991%. In rough terms, it's one out of a hundred thousand.

2.       There are seventeen non-trump cards. Suppose spades are trump. There are 17C3 hands consisting of Left Bower, Right Bower, and three non-trumps, or 680 hands. Divide by 42504, for a probability of 1.600%. But wait! We haven't yet turned up a trump. There are five cards that will set the right trump, out of nineteen cards. So multiply by 5/19, and it drops to 0.421%. Multiply by 4, since there are an equal number of hands with hearts, diamonds, and clubs trump, and we're up to 1.684%.

3.       42504 hands.

4.       a. 4C1*20C4, or 19380 hands, contain one Jack. 19380/42504 = 45.596%
b. 4C2*20C3, or 6840 hands, contain two Jacks. 6840/42504 = 16.093%
c. 4C3*20C2, or 760 hands, contain three Jacks. 760/42504 = 1.788%
d. 4C4*20C1, or 20 hands, contain three Jacks. 20/42504 = .0473%

Of course, there's one remaining possibility:
4C0*20C5, or 15504 hands, contain no Jacks. 15504/42504 = 36.477%

Special thanks to Richard Freedman of Billerica, MA.

See you in June!