Greyjack, An Easier Model of Blackjack

[RayDonaldPratt]

Homework Statement

Work at Home, But Not Homework: Decades ago I read a book about card counting in blackjack, and the author had created a game called 'greyjack' for training purposes where the highest hand was 11, aces counted as 1 or 6, and number 5 cards were the highest number of card. I thought it was one of Ken Uston's books, but I cannot find 'greyjack' as a simpler model game of blackjack by searching through google.

I want to create a javascript program that logically iterates through every possible shuffle and starts card play at each and every possible beginning card in a given shuffle and does it all again for increasing numbers of players, and then tallies the results for every possible hand play. I want the progressive algorithm for shuffling to be human understandable.

My first question is whether I should add one or more face cards as 'fives.' I want greyjack to have a similar ratio of high and low cards as in a regular blackjack game. My guess is that each suit should only have a five and a jack. Has anyone read about 'greyjack'?

Relevant Equations

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See above.

 

[pbuk]

I want to create a javascript program that logically iterates through every possible shuffle.

For a 4 suit deck of cards { A, 2, 3, 4, 5 }, i.e. 20 cards, there are $20! \approx 2.4 \times 10^{18}$ permutations. For Blackjack the suits don't matter so you can reduce this by a factor of $(4!)^5$ to give $\approx 3 \times 10^{11}$ permutations which is just within the bounds of practical computability (if you can process a million permutations a second it will take 3.5 days to process them all).

The standard algorithm for generating lexicographic permutations works with repeated values, see e.g. https://en.wikipedia.org/wiki/Permutation#Generation_in_lexicographic_order

and starts card play at each and every possible beginning card in a given shuffle and does it all again for increasing numbers of players, and then tallies the results for every possible hand play.

You are not going to be able to do all that a million times a second.

I want the progressive algorithm for shuffling to be human understandable.

The algorithm referred to above is certainly that (it has been known for over 500 years).

 

[RayDonaldPratt]

Pbuk, thank you for letting me know just how astronomical the number of permutations are. I feared that, and I don't know if my potato laptop could even summarize the results in any readable form, much less in a memorable form. I'm probably looking for something more general than iterating through every possible permutation. As I understand the term "pattern," it means some discernible order with some degree of reliablility that can be expressed without laying out the exact sequence of cards in a deck. If a sequence of cards can only be stated by laying out the exact sequence of cards, then the sequence is effectively random, even if only because the observer cannot divine and state a description of the pattern. I will play with some ideas about generating patterns, tallying wins and losses, etc., and then increasingly randomizing general patterns to see when they break down from indicating favorablility or unfavorability.

Unfortunately, a modern variation of blackjack with a side bet ("Match the Dealer") makes suit important, so 20! even for greyjack is still a problem. Thank you for the heads up.

 

[pbuk]

I'm probably looking for something more general than iterating through every possible permutation.

Indeed.

I would start by learning what others have done. This paper and its references might be a good start: https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/4/

I will play with some ideas about generating patterns, tallying wins and losses, etc., and then increasingly randomizing general patterns to see when they break down from indicating favorablility or unfavorability.

Game theory is quite a well developed science: you might be better off studying the existing techniques rather than playing with your own ideas.

Unfortunately, a modern variation of blackjack with a side bet ("Match the Dealer") makes suit important

Only when there is more than one deck in the shoe, and by this time you have lost all hope of enumerating permutations.