Optimum Zero-Memory Strategy and Exact Probabilities for 4-Deck Blackjack

Manson, A. R.; Barr, A. J.; Goodnight, J. H.

doi:10.1080/00031305.1975.10477376

Cited by 3 publications

(7 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because of our restrictive rules on splitting, we need not concern ourselves with which cards are used for decisions about split hands. We follow the approach originated for blackjack by Manson et al [8] and used by Griffin [7, p. 172] and Ethier [3, Section 21.2], and we use the notation of the latter source. A completely different approach was taken by Werthamer [13, Section 7.2.1], who wrote (p. 74), ".…”

Section: Snackjack Basic Strategy Methodologymentioning

confidence: 99%

Snackjack: A toy model of blackjack

Ethier¹

2019

Preprint

View full text Add to dashboard Cite

Snackjack is a highly simplified version of blackjack that was proposed by Ethier (2010) and given its name by Epstein (2013). The eight-card deck comprises two aces, two deuces, and four treys, with aces having value either 1 or 4, and deuces and treys having values 2 and 3, respectively. The target total is 7 (vs. 21 in blackjack), and ace-trey is a natural. The dealer stands on 6 and 7, including soft totals, and otherwise hits. The player can stand, hit, double, or split, but split pairs receive only one card per paircard (like split aces in blackjack), and there is no insurance.We analyze the game, both single and multiple deck, deriving basic strategy and one-parameter card-counting systems. Unlike in blackjack, these derivations can be done by hand, though it may nevertheless be easier and more reliable to use a computer. More importantly, the simplicity of snackjack allows us to do computations that would be prohibitively time-consuming at blackjack. We can thereby enhance our understanding of blackjack by thoroughly exploring snackjack.

show abstract

Section: Snackjack Basic Strategy Methodologymentioning

confidence: 99%

Snackjack: A toy model of blackjack

Ethier¹

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In summary, these historic table are not particularly accurate, probably used the wrong approximate formula, and only provide results for one set of splitting rules. Manson et al [8], did calculations for a four deck game with resplitting allowed, doubling down allowed on any two cards, and dealer stands on soft 17. They estimated that exact calculations would take 100 times longer than their other calculations (an estimate that is off by about 9 orders of magnitude), and therefore did all splitting calculations by Monte Carlo simulations.…”

Section: Resultsmentioning

confidence: 99%

“…A hand with an ace that does not exceed 21 when the ace is counted as 11 is a "soft" hand (e.g., (A,8) is a soft 19). If all aces in a hand must be counted as 1 to avoid exceeding 21, it becomes a hard hand (e.g., (8,7,A) is a hard 16).…”

Section: Blackjack and Splitting Rulesmentioning

confidence: 99%

“…This paper is about an additional player option known as pair splitting. If the first two cards are matched (e.g., hands with (8,8), (4,4), or (10,Q); the last example indicates that any two ten cards can be split), the player can split the hand. When splitting, the two cards are separated into two hands and a second bet equal to the initial bet size in placed on the second hand.…”

Section: Blackjack and Splitting Rulesmentioning

confidence: 99%

See 1 more Smart Citation

Exact Calculation of Expected Values for Splitting Pairs in Blackjack

Nairn¹

2019

Preprint

View full text Add to dashboard Cite

Computer calculations for most exact expected values in blackjack have been available since the 1960's, but exact results for pair splitting and resplitting have previously been too computer intensive. This paper describes a new algorithm for exact pairsplitting. By using dealer probability caching methods and revising the method for recursively generating possible player hands, the estimated calculation time compared to standard methods was reduced by five orders of magnitude. The resulting algorithm was used to calculate the first exact and complete pair splitting results for a single deck game. The exact results were compared to prior approximate theories for resplitting. The prior theories are accurate for many calculations, but inaccurate for resplitting tens. A new approximation method was developed that is accurate for all resplitting calculations.

show abstract

“…See Werthamer (2018, Section 7.1) for a viable approach. The recursive algorithm mentioned above dates back to Manson et al (1975) and was used by Griffin (1999, p. 172). In the end it requires a rather elaborate computer program, which raises the question of whether this approach is suitable for a textbook.…”

Section: Blackjackmentioning

confidence: 99%

Teaching a university course on the mathematics of gambling

Ethier¹,

Hoppe²

2019

Preprint

View full text Add to dashboard Cite

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review but rather an essay offering advice about which topics to include in a course on the mathematics of gambling.

show abstract

Optimum Zero-Memory Strategy and Exact Probabilities for 4-Deck Blackjack

Cited by 3 publications

References 5 publications

Snackjack: A toy model of blackjack

Snackjack: A toy model of blackjack

Exact Calculation of Expected Values for Splitting Pairs in Blackjack

Teaching a university course on the mathematics of gambling

Contact Info

Product

Resources

About