An alternative method of EOR calculation

Most of the time effect of removal is calculated by running sims with one card of a rank removed each time and measuring the change in advantage.

While monkeying around with my combinatorial analysis code recently I made an observation. Sometimes the advantage can change dramatically and in an unexpected direction as cards are removed, especially late in the shoe. So I hypothesized an alternative way of generating EORs: by running a simulator through a shoe, counting the total number of cards removed by rank and normalizing after each hand, and multiplying those normalized values by your win or loss on that hand. Compiling the data over a billion shoes should produce the relative EOR of each card.

The interesting thing about this is that it should work exactly the same way for any game: blackjack, sidebets, baccarat, red dog, anything dealt from a shoe. In particular some of the sidebets involve complicated interactions between cards and this method might be more accurate than removing one card at a time, because in reality we are never playing that way. The EORs would be integrated over the normal distribution of decks we can expect to be playing from.

I was wondering if anyone is aware of this work already being done.

Automatic Monkey,

Your idea sounds intriguing. Can you expand upon your concept of "normalizing after each hand"? I'm not sure quite what you mean.

Dog Hand

If you remove two fives and three sixes and then note the deflection in e.v., how do you know how much of that to ascribe to each rank?

Don

I'm not going to be measuring EV other than winning or losing that hand, and the only other data I have is the percentage of the dealt cards that consists of each rank. Over a very large set of data there will be a correlation between cards having been dealt, and winning.

It may be that the result is exactly what you get when you do the usual method of EOR calculation. But I think it could be possible to find EOR's that are hidden with the usual method. An absurd example is a shoe consisting only of 8's, where the player would always win and a lot. That would never happen, but there may be some other combinations that actually do happen and this method would pick them up. Only question is if it could be reduced to a count that a player could use at the table rather than something like a combinatorial analysis routine.

It's mostly interesting to me because of the universality of it. With certain sidebets some cards are only valuable to the player when other cards are present, which is also true for straight BJ but the effect is much stronger with sidebets. Or again it could be just like the other way. When you do it the usual way you get different result when you deal all the way through the shoe to a realistic penetration depth and when you just deal one hand off the top of each shoe with the target card removed, and that might be what I'm neglecting resulting in overthinking, and the usual simulator method will do the same as what I'm proposing.

You really didn't answer my question. If you remove two fives and three sixes and you win the hand a lot, was it because of the fives, the sixes, or both? How do you know? And what was the contribution of each? If you want to devise a point count for each rank, you need to know that, no?

Don

Good point. Come to think of it, it probably wouldn't work any better than the usual method for EOR just because of this, the information would only be usable by a CA but then you could just use a CA which doesn't need any other information. The theory was that there will be some hands with mostly 5's removed and other hands with mostly 6's removed and by comparing the two you would get the relative EORs, but running a full-shoe regular sim with one card removed will also average those two different situations into the result and give the same answers.