Total Number of Possible Combinations
June 8th, 2013 at 9:16:25 PM
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For a given set of blackjack rules and basic strategy, is it possible to compute the total number of possible combinations that can occur between a player and the dealer ?
June 8th, 2013 at 9:37:31 PM
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Yes. The first step would involve figuring out the maximum number of cards needed in the worst-case scenario, such as splitting to 4 hands and having the most cards possible in each hand, and the dealer also having the maximum cards possible in his hand. Then, as you iterate through every possible outcome, weigh its combination count appropriately to put it on equal footing with the worst-case scenario.
To illustrate this with a simple example, consider baccarat. Sometimes you need 4 cards, sometimes you need 5 cards, sometimes you need 6 cards. So 6 cards is the worst-case scenario for baccarat. If only 5 cards are needed, multiply the 5-card combination count by the number of cards left, as if a sixth card that we don't care about had also been dealt. If 4 cards were needed, weigh the 4-card combination count as if two extra cards that we don't care about had been dealt.
If you do this with blackjack the combination counts will be very large, far beyond what a 64-bit integer can hold. You would need some type of BigInteger class to accumulate the results.
To illustrate this with a simple example, consider baccarat. Sometimes you need 4 cards, sometimes you need 5 cards, sometimes you need 6 cards. So 6 cards is the worst-case scenario for baccarat. If only 5 cards are needed, multiply the 5-card combination count by the number of cards left, as if a sixth card that we don't care about had also been dealt. If 4 cards were needed, weigh the 4-card combination count as if two extra cards that we don't care about had been dealt.
If you do this with blackjack the combination counts will be very large, far beyond what a 64-bit integer can hold. You would need some type of BigInteger class to accumulate the results.
June 8th, 2013 at 9:49:57 PM
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Thanks for your reply. I have a program can compute the total combinations for baccarat but not blackjack
For example, 2 deck BJ game, what is the total possible combinations ?
For example, 2 deck BJ game, what is the total possible combinations ?
June 8th, 2013 at 9:51:45 PM
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I have no idea. You'd have to figure it out for yourself.
June 8th, 2013 at 10:46:16 PM
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Also another niche situation, using double deck as an example... if you're working with 60% penetration, the last hand could go out with about 42 cards remaining. Unless my math is way off, you have the potential of 6 spots, each splitting to 4 hands, resulting in 48 cards being distributed (6 spots*4 hands*2 cards per hand), plus whatever gets hit on top of that.
I have no idea what the policy is regarding running out of cards, but I suspect this is another headache that may have to be accounted for in the pursuit of every possible combination.
I have no idea what the policy is regarding running out of cards, but I suspect this is another headache that may have to be accounted for in the pursuit of every possible combination.
