I built blackjack card counting simulation software - interesting results

[autonymity]

Disclaimer – The results expressed here could be incorrect – I’ve testing my software and it lines up with CVCX results, however it’s always possible there is some bug I couldn’t find especially when it comes to simulating multiple players, as I have few statistical baselines to compare to. Nevertheless, I wanted to share these results in the hope someone could try to replicate them.


That out of the way, I built card counting simulation software to see if I could find out anything interesting about the game of blackjack. Here are some interesting results (200 million rounds were simulated in all sims):


Playing 1-2 hand spread alone vs. gamblers vs. with another counter:


Parameters:


Philly rules (6D, S17, DAS, nRSA, LS), 5D Pen, .5 deck estimation, (most) BJA extended deviations, 75 RPH


1x$25 (TC -3 and below), 1x$25, 1x$25, 1x$25, 2x$25, 2x$50, 2x$100, 2x$200, 2x$250, 2x$300 (TC 6 and up)


Alone:


EV: $76
SD: $1110
ROR: .20%
N0: 211


With 1 Gambler:


EV: $81
SD: $1098
ROR .12%
N0: 184


With 4 Gamblers:


EV: $86
SD: $1079
ROR: .06%
N0: 158


2 Counters:


EV: $66
SD: $1009
ROR: .15%
N0: 232


Discussion: It appears that if you are getting the same RPH in all situations (which you likely are not), then playing with basic strategy gamblers actually leads to a more optimal game than playing a 1-2 handed spread alone. This could be from the recently oft discussed issue of going 1-2 hands when solo (see Colin's BJA forum post on the new PBS). Additionally, there is a substantial decrease in gain when playing with a card counter (the tracked players position was first base).


1 Handed spread:


Same rules


1x$25 (TC -3 and below), 1x$25, 1x$25, 1x$25, 1x$50, 1x$100, 1x$200, 1x$400, 1x$500, 1x$600 (TC 6 and up)


Alone:


EV: $107
SD: $1564
ROR: 1.24%
N0: 212


With 1 gambler:


EV: $103
SD: $1469
ROR: .83%
N0: 201


2 Counters:


EV: $102
SD: $1474
ROR: .92%
N0: 209


Discussion: Again, there appears to be a marginal gain to playing with a basic strategy gambler. Additionally, the counters appear to impact each other less when playing on one hand…although still marginally.


2 handed spread:


Same rules


2x$25 (TC -3 and below), 2x$25, 2x$25, 2x$25, 2x$25, 2x$50, 2x$100, 2x$200, 2x$250, 2x$300 (TC 6 and up)


Alone:


EV: $91
SD: $1259
ROR: .32%
N0: 191


With 1 Gambler:


EV: $89
SD: $1218
ROR: .25%
N0: 189


2 Counters:


EV: $89
SD: $1196
ROR: .20%
N0: 182


Discussion: In this case the three different sims have only marginally different results.


Conclusion:


I hope these results are interesting to somebody. I hope to continue researching the different outcomes caused by having multiple players at the table, particularly the outcomes of the same spread when playing solo vs. with others.


Best of luck!

[DSchles]

Questions:

1. What's the bankroll? You give a ROR but no bankroll.
2. If your player is at first base, does he reckon the other players' cards to his left before he plays his own hand?
3. What is the standard error? If you simulated 200 billion rounds, instead of 200 million, I suspect some of the differences might disappear.
4. In your first set of results, the very poor outcome playing with two counters doesn't make any sense to me. I think something is wrong there.

Don

[autonymity]

Questions:

1. What's the bankroll? You give a ROR but no bankroll.
2. If your player is at first base, does he reckon the other players' cards to his left before he plays his own hand?
3. What is the standard error? If you simulated 200 billion rounds, instead of 200 million, I suspect some of the differences might disappear.
4. In your first set of results, the very poor outcome playing with two counters doesn't make any sense to me. I think something is wrong there.

Don

1. $50,000

2. Yes, the player takes into accounts all cards on the table (besides the dealer's hole card, of course). I'm working on some sims of different player positions, but have yet to find any difference between positions at the table in a face up game.
3. Do you mean the classic formulas for standard for s.e. of SD/sqrt(rounds)? In any case, yes I was curious about that myself. My runtime is not fantastic so I wanted to get some initial findings out of the way, but now I'm running some sims with 2 billion rounds to try to confirm the results.

4. To clarify, that is the result of one of the counters, not both combined. It made some sense to me that with another counter at the table (in particular one going 1-2 hands), that some EV would evaporate for both of them, due to the counters competing to eat the high cards at high counts. Perhaps I am wrong though. Do you have an idea of what another counter at the table should theoretically do to EV?

[DSchles]

2. Yes, the player takes into accounts all cards on the table (besides the dealer's hole card, of course). I'm working on some sims of different player positions, but have yet to find any difference between positions at the table in a face up game.

Well, it will make a difference if you're at first base or, say, the fourth seat with others to your right. You get to play your hand with knowledge of those other players' hit cards. In essence, you're increasing penetration each time you play. This is common knowledge.

3. Do you mean the classic formulas for standard for s.e. of SD/sqrt(rounds)? In any case, yes I was curious about that myself. My runtime is not fantastic so I wanted to get some initial findings out of the way, but now I'm running some sims with 2 billion rounds to try to confirm the results.

Yes. And yes, that's a good idea. But two billion may not be enough.

4. To clarify, that is the result of one of the counters, not both combined. It made some sense to me that with another counter at the table (in particular one going 1-2 hands), that some EV would evaporate for both of them, due to the counters competing to eat the high cards at high counts. Perhaps I am wrong though. Do you have an idea of what another counter at the table should theoretically do to EV?

Another counter doesn't do anything to EV. It makes no difference if another player is counting or playing BS. You may be confusing with win per hour, which, of course, is diluted if you add an extra hand. If you start with, say, three hands but then go to four, because the counter adds another hand, then, yes, that will matter for the hourly win, but not the EV or the SCORE.

Don