Jewish Poker

For quite a while the two of us sat at our table, wordlessly stirring our coffee. Ervinke was bared. All right, he said. Let’s play poker.

No, I answered. I hate cards. I always lose.

Who’s talking about cards? thus Ervinke. I was thinking of Jewish poker.

He then briefly explained the rules of the game. Jewish poker is played without cards, in your head, as befits the People of the Book.

You think of a number, I also think of a num­ber, Ervinke said. Whoever thinks of a higher num­ber wins. This sounds easy, but it has a hundred pit­falls. Nu!

All right, I agreed. Let’s try.

We plunked down five piasters each, and, leaning back in our chairs began to think of numbers. After a while Ervinke signaled that he had one. I said I was ready.

All right, thus Ervinke. Let’s hear your number.

Eleven, I said.

Twelve, Ervinke said, and took the money.

I could have’ kicked myself, because originally I had thought of Fourteen, and only at the last moment had I climbed down to Eleven, I really don’t know why. Listen. I turned to Ervinke. What would have happened had I said Fourteen?

What a question! I’d have lost. Now, that is just the charm of poker: you never know how things will turn out. But if your nerves cannot stand a little gam­bling, perhaps we had better call it off.

…

Jewish Poker by Ephraim Kimshon

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I never liked mathematics in school. I mean, I did not really like school in general, but math in general was boring and uninspiring. Of all the classes, really only one stayed with me in any form, and that was social sciences. In the model UN I was Israel, it was hilarious. And perhaps prophetic.

But honestly the thing I liked most was the economics part, which the teacher spent most time on. Or at least I remember most of it. I took a book from the local library, and it was the origin of game theory itself by Morgenstern and von Neumann. And I remember that I fell in love with the beautiful results, in particular the minimax theorem. It was simply amazing. I was ready to build my own casino.

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Lets consider the following case: Assume it is late at night, you are at the bar. You are a bit tipsy already, but a talking, agitated cricket tries to get your attention. Finally you give in. It wears a white suit, after all. Some credibility, after all. (Loved the new Pinocchio btw.)

Anyway, he challenges you to a game. With a thick Texan accent, it slurs the rules, but you are to drunk to understand. But you see that you have a set of actions A. Those are your moves. The cricket has a set of moves B.

Let’s say both sets are finite. Now for every a in A and every b in B, f(a,b) is 0 if you won the round, and 1 otherwise.

Now, you both make your decisions, choosing, simultaneously, a or b (like in stone-paper-scissors-lizard-spock). You try to choose a so that there are few choices for b that win. But you are smart, and know that if you always choose stone (i.e. the same a), the cricket will just choose paper and always win.

So you do it randomly, according to a distribution P. You choose this so that whatever strategy Q the cricket chooses, your chances of winning are maximized.

In other words, you are trying to find P so that whatever strategy Q chooses, your choice is optimal. The best you can hope for is then a strategy attaining Image may be NSFW.
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The cricket, crafty as it is, does the opposite: It wants to maximize this expected value, that is it wants to choose its strategy preventing you from doing well. It chooses its strategy according to Image may be NSFW.
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Now the amazing fact: Even though you are going at it from opposite ends, you have

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This is the minimax theorem. Amazing.

But let us go back to the Jewish Poker. You see, this isn’t true. Whatever strategy the protagonist chooses, Ervinke can best him. What is the issue? Well, the situation is not finite, you see. That is not so cool.

My great love is the Einstein Institute. Only there you can hear a talk that started with online learning and end up hearing about one of your favorite theorems, because it all mixes and matches and is all just passion for science and math.

Hence, it ends up that I learn there that in the infinite case, the only thing that can go wrong is exactly Jewish Poker! And that whenever minimax is not true in an infinite situation, it must be Jewish Poker at fault. Thanks Jerusalem, and congratulations Roi, Shay and Steve.

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