A thought Experiment to clarify the Cut-Card Effect

From Stanford Wong's BJ21

Posted by MathProf on 2 Feb 1999, 5:23 am, in response to Re: The Cut-Card Effect, posted by Border Crosser on 2 Feb 1999, 1:08 am

I agree with you that if the cut-card is placed such that the number of rounds dealt is usually three, then on those occasions when a fourth round is dealt it will be dealt from a 10-poor deck.

But on those occasions, the first three rounds will have been dealt from a set of cards rich in 10s (and other high cards).

That is right. But those three rounds that are rich in 10s are already reflected in the Basic Strategy (no cut-card) EV. That is, without a cut-card we are going to some rounds which are rich in 10s, and some which are lean. The average of all of these is reflected in the BS expectation.

Here is a though experiment which may help clarify. Imagine two players Me (M) and my Shadow(S) betting on the same spot. S is basically making "over-the-shoulder" bets on my box. The hands are played in accordance with BS and we both must put up more money when we split and double.

Suppose the games is dealt with the cut-card listed above. M flat-bets on all the rounds. S bets the same on the first three rounds, but never plays a 4^th round. Now S's EV should be that of Basic Strategy (full-deck). My EV is clearly less than S. The only difference between us is the money I lose on those negative 4^th rounds. So M is worse off with the cut-card.

Now when there is a 4^th round, the first 3 rounds are favorable to M. But they are also favorable to S. S gets all the benefits of those, but doesn't actually bet the negative 4^th round.