Blackjack: Myths vs. Reality

1. Group K Andrew Kerr Andrew Phillips Sven Skoog Woj Wrona Blackjack: Myths vs. Reality

2. Agenda • Blackjack: The Game • Assumptions • Simulation • Data Findings • Decision Tree • Descriptive Analysis • Question & Answers

3. Blackjack: The Game • Each player is dealt two cards and is then offered the opportunity to take more. • The hand with the highest total wins as long as it doesn't exceed 21; a hand with a higher total than 21 is said to bust. Cards 2 through 10 are worth their face value, and face cards (Jack, Queen, King) are also worth 10. • An ace's value is 11 unless this would cause the player to bust, in which case it is worth 1. A hand in which an ace's value is counted as 11 is called a soft hand, because it cannot be busted if the player draws another card.

4. Assumptions • $100 bet / hand • No splitting, double down, insurance • Samples with blackjack bonus and without bonus

5. Simulation

6. Percentage of Blackjack Assumption: 10,000 Hands Mean: 0.0454 or 4.5%

7. Percentage of Bust Assumption: 10,000 Hands Mean: 0.2803 or 28.03%

8. Normality of 1, 2 and 3 CardTotals Face card probability = 30% Approaching Normality as Card Count Increases

9. Why Dealer Stays at 17? Values derived from 10,000 card simulation

10. 2 Card Total Confidence Interval Probability of achieving a 2 card total 18 ≤ 2 cards ≤ 21 is 20.9%

11. 3 Card Total Confidence Interval Probability of achieving a 3 card total 18 ≤ 3 cards ≤ 21 is 37.1%

12. Regression of Aces vs. Wins • Do Aces result in Wins? • Many players assume that an Ace increases the odds of winning a hand • Regression model confirms that Aces lead to a very slight player edge • Any edge is likely attributable to the flexibility of the Ace (1 or 11) but not the fact that the Ace gives you an 11 ( no more powerful that any other pairing, i.e. 8,3 or 7,4 that leads to an 11).

13. Regression of Aces vs. Wins Four Card Play Two Card Play Three Card Play

14. Player=15, Dealer shows 7

15. Player=17, Dealer shows 8

16. Player=11, Dealer shows 7

17. Player=15, Dealer shows 7 18 16 19 17 20

18. House Edge (and Sensitivity) …many complicating factors… • Play on Hunches (ex: “stop on 17”), no Split, no Double 5%-15% • ‘Educated Hunches’ (modified basic strat.), Split + Double 3%-5% • Basic Strategy (perfect play), 8-decks, blackjack pays 3:2 0.5% • Basic Strategy (perfect play), 1-deck, blackjack pays 3:2 ≈ 0% (not typical) • Basic Strategy (perfect play), 1-deck, blackjack pays 6:5 ≈ 1.4% • Basic Strategy plus variable-bet card counting ≈ 1.0% (plus broken kneecaps) • How much difference does splitting/doubling-down make? ± 3.5% • How much difference does blackjack payoff make? ± 1.3% • How much difference does surrender make? ± 0.8% • How much difference from deviations/slip-ups? 1 slip/hr ≈ 1% (basic strategy becomes hunch)

19. Two, Three, and Four Card Game Payout Over Time • House has distinct advantage over the player as additional cards are played. • The house edge results from the fact that the player acts first and risks busting before the dealer.

20. Two, Three, and Four Card Game Payout Over Time

21. The End