# Probability of Blackjack

2190 Words Mar 23rd, 2013 9 Pages
Mathematical Studies Project

Probability of Blackjack

Content Page

Page

Introduction 3 - 4

Data collection 5 - 6

The four Blackjack strategies 7 - 15

Conclusion 16

Bibliography 17

This project aims to investigate how mathematics works in one of the most popular card games in the world - Blackjack. It examines the probability in the Blackjack and how the use of mathematics can be
Blackjack strategies

Strategy I Hit when the sum of the first two cards is less than the dealer’s upcard

Let x be the player’s sum of card values of the first two cards.

Let D be the dealer’s upcard(the second card).

If x < D, the player should always hit.

When x < D, it is obvious that x must be less than the dealer’s final value (covered card + upcard), given that the sum of the first two cards of the dealer is[pic]- no busting. Therefore, under this situation, the player must hit. Otherwise, his probability of winning is 0.

Strategy II Hit or Stand

If the hard total is 11 or less, the player should always hit. This is because no matter what card the player is getting, the total hand value will not exceed 21. By using the Hit ot Stand strategy, the house edge can be cut to as low as 2%.[1] Fig. 1 is the decision making chart when using this strategy.

Card | |A |2 |3 |4 |5 |6 |7 |8 |9 |10 |J |Q |K | | |Real value |1 |11 |2 |3 |4 |5 |6 |7 |8 |9 |10 |10 |10 |10 | |A |1 |2 |12 |3 |4 |5 |6 |7 |8 |9 |10 |11 |11 |11 |11 | | |11 |12 |22 |13 |14 |15 |16 |17 |18 |19 |20 |21 |21 |21 |21 | |2 |2 |3 |13 |4 |5 |6 |7 |8 |9 |10 |11 |12 |12 |12 |12 | |3 |3 |4 |14 |5 |6 |7 |8 |9 |10 |11 |12 |13 |13 |13 |13 | |4 |4 |5 |15 |6 |7 |8 |9 |10 |11 |12 |13 |14 |14 |14 |14 | |5 |5 |6 |16 |7 |8 |9 |10 |11 |12 |13 |14