My background: I'm 70-something, math major in college, 40+ years in computer work of all sorts. I have been a BJ card-counting admirer for many years. I have read several books on it, but I have never tried card counting in a casino, although I can play basic strategy easily. I'm now ready to try card counting For Real.
Mostly as an exercise, I have written a casino blackjack simulator program. It's not a simple, demonstration program, but an attempt to do it right. It plays basic strategy against a dealer, flat bets, using typical Vegas strip rules. I have run tens of millions of hands through it, and am getting numbers that I think are pretty good, but I want to hear an expert's opinion. Recently, I have added keeping track of the true count, and varying my bet with the true count. The numbers I'm seeing here don't look right to me, but I haven't found a definitive source of truth, so I will ask (below) for an expert's opinion here, too. So there are two questions:
1. Do my flat-betting numbers look okay? Do they match what gold-standard BJ simulators show? (If not, then maybe #2 is irrelevant.)
2. Do my numbers for bet-spreading, but still using basic strategy look right to you?
Here are my results for 200 million hands, dealt in the following way:
5 players at the table
75% penetration
6 decks
Dealer hits S17
DAS allowed
max split hands 4
max split aces 2
no hitting split aces
later surrender
I think that should pin down all the variables. Let me know if it doesn't.
So, for 200 millions hands (40 millions rounds of 5 hands), my programs says the house edge is 0.51%.
QUESTION: How far off is that from The Accepted Value?
From what I can find, that number looks pretty reasonable.
But my numbers for bet spreading look suspect to me, because I have to go to more than a 4-1 spread to achieve ANY edge over the house. Details:
I configured the bet chooser to bet the true count in betting units, when the true count is positive, up to a maximum that was defined for each run of about 50 million hands. Of course, it bets one unit in zero or negative counts. First, I set the max bet to TWO; i.e., it would bet 2 units for true count of 2 or above. Then I set max to 3, 4, and 6, and re-ran the test. I was thinking that when max was 2 or 3, I would be even with the house, but that's not what I see.
Here are the results. Remember that when MAX is n, the bet is the true count in bet units, but is capped at n units. Remember, I am NOT doing any deviations from basic strategy.
MAX player edge
==== ===========
1 -0.51% (flat betting)
2 -0.26%
3 -0.15%
4 -0.03%
6 +0.05%
I skipped the max=5 case, but notice that even a 4-1 bet spread does not overcome the house edge! I felt sure that it should, but maybe I didn't research enough.
So, to anyone who really knows what he's talking about, I invite you to give me your thoughts, based on Real BJ sims, on my results. Are they pretty close?
Mostly as an exercise, I have written a casino blackjack simulator program. It's not a simple, demonstration program, but an attempt to do it right. It plays basic strategy against a dealer, flat bets, using typical Vegas strip rules. I have run tens of millions of hands through it, and am getting numbers that I think are pretty good, but I want to hear an expert's opinion. Recently, I have added keeping track of the true count, and varying my bet with the true count. The numbers I'm seeing here don't look right to me, but I haven't found a definitive source of truth, so I will ask (below) for an expert's opinion here, too. So there are two questions:
1. Do my flat-betting numbers look okay? Do they match what gold-standard BJ simulators show? (If not, then maybe #2 is irrelevant.)
2. Do my numbers for bet-spreading, but still using basic strategy look right to you?
Here are my results for 200 million hands, dealt in the following way:
5 players at the table
75% penetration
6 decks
Dealer hits S17
DAS allowed
max split hands 4
max split aces 2
no hitting split aces
later surrender
I think that should pin down all the variables. Let me know if it doesn't.
So, for 200 millions hands (40 millions rounds of 5 hands), my programs says the house edge is 0.51%.
QUESTION: How far off is that from The Accepted Value?
From what I can find, that number looks pretty reasonable.
But my numbers for bet spreading look suspect to me, because I have to go to more than a 4-1 spread to achieve ANY edge over the house. Details:
I configured the bet chooser to bet the true count in betting units, when the true count is positive, up to a maximum that was defined for each run of about 50 million hands. Of course, it bets one unit in zero or negative counts. First, I set the max bet to TWO; i.e., it would bet 2 units for true count of 2 or above. Then I set max to 3, 4, and 6, and re-ran the test. I was thinking that when max was 2 or 3, I would be even with the house, but that's not what I see.
Here are the results. Remember that when MAX is n, the bet is the true count in bet units, but is capped at n units. Remember, I am NOT doing any deviations from basic strategy.
MAX player edge
==== ===========
1 -0.51% (flat betting)
2 -0.26%
3 -0.15%
4 -0.03%
6 +0.05%
I skipped the max=5 case, but notice that even a 4-1 bet spread does not overcome the house edge! I felt sure that it should, but maybe I didn't research enough.
So, to anyone who really knows what he's talking about, I invite you to give me your thoughts, based on Real BJ sims, on my results. Are they pretty close?