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# A simple blackjack variant

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### #21 Prime

Prime

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Posted 20 December 2012 - 06:36 AM

The analytical solution for the probability of win for each hand is as following:

1st hand = .342538484

2nd hand = .318676316

3rd hand = .338785200

A recursive program, which would traverse the entire game for 3 hands, would be simple enough to code. However, I did not chance it fearing unmanageable number of iterations. After all, given the infinite deck, a single hand in this game can be as large as 18 cards.

Instead of writing a program, I built a spreadsheet table with probabilities of win/bust/continue for a single player for each round. From that probabilities of winning a “sudden death game” for each seat among 3 players may be derived. It’s a tedious solution, but I had some similar tables from my own projects with BJ probabilities, so it did not take too much of my time.

I could not see any simple and elegant solution, which would avoid calculating actual probabilities.

Some more trivia from the table if you play this game without partners, by your lonesome:

Probability to bust = .621058

Probability to get 21 = .159379

Probability to get 20 = .219563

Probability to finish the game with a hand of 6 cards or less = .996315

• 0

Past prime, actually.

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