# Beat the Dealer: A Winning Strategy for the Game of Twenty-One

@inproceedings{Thorp1962BeatTD, title={Beat the Dealer: A Winning Strategy for the Game of Twenty-One}, author={Edward O. Thorp}, year={1962} }

New York Times Bestseller В Edward O. Thorp is the father of card counting, and in Beat the Dealer he reveals the revolutionary point system that has been successfully used by professional and amateur card players for two generations. From Las Vegas to Monte Carlo, the tables have been turned and the house no longer has the advantage at blackjack. В В В В В В В В В Containing the basic rules of the game, proven winning strategies, how to overcome casino counter measures and spot cheating. Beat…

## 82 Citations

Real Valued Card Counting Strategies for the Game of Blackjack

- MathematicsICONIP
- 2020

Card counting is a family of casino card game advantage gambling strategies, in which a player keeps a mental tally of the cards played in order to calculate whether the next hand is likely to be in…

Card Counting in Continuous Time

- MathematicsJ. Appl. Probab.
- 2012

We consider the problem of finding an optimal betting strategy for a house-banked casino card game that is played for several coups before reshuffling. The sampling without replacement makes it…

Finding Blackjack's Optimal Strategy in Real-time and Player's Expected Win

- Mathematics
- 2004

We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the…

Intelligent Agent for Playing Casino Card Games

- Economics, Computer Science
- 2010

This paper lays out a method of creating an intelligent gambling agent capable of playing blackjack using learning, utility theory and decision-making to maximise the expected probability of winning the game.

ec 2 00 4 Finding Blackjack ’ s Optimal Strategy in Real-time and Player ’ s Expected

- Computer Science
- 2008

We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player’s expected win given that he follows the…

Determination of Profit Quantification on Kelly Betting Based on Relative Entropy

- Computer Science
- 2021

It is demonstrated that the logarithm of the return of a game when bidding the optimal fraction (corresponding to the difference between the player’s belief probability of the event occurrence and the proportion of real outcomes) for finite-time steps is achieved.

A Markov Chain Analysis of Blackjack Strategy

- Mathematics
- 2004

A collection of Markov chains used to model the play of a single hand are developed and used to compute the player’s expected advantage when playing according to a basic strategy.

Keep That Card in Mind: Card Guessing with Limited Memory

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2021

The case of a memory bounded Guesser that has m < n memory bits is considered, and it is shown that no Guesser with m bits of memory can score better than O( √ m) correct guesses against a random Dealer, thus, the above Guesser is optimal.

Optimal Betting in Casino Blackjack III: Table-Hopping

- Economics
- 2008

The casino blackjack technique usually called back-counting, or ‘wonging’, consists of beginning play (‘entry’) at a table only after an indicator of favourability exceeds a certain threshold. The…