Blackjack: Myths vs. Reality

1
Blackjack Myths vs. Reality

• Group K
• Andrew Kerr Andrew Phillips
• Sven Skoog Woj Wrona

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
Mean 0.0454 or 4.5
Assumption 10,000 Hands
7
Percentage of Bust
Mean 0.2803 or 28.03
Assumption 10,000 Hands
8
Normality of 1, 2 and 3 CardTotals
Face card probability 30
Approaching Normality as Card Count Increases
9
Why Dealer Stays at 17?
Dealer Stays at.. 16 17 18
Blackjack 4.7 4.6 4.9
Bust 20.42 28.23 37.53
Dealer Beats 17 17.74 27.85 23.33
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

• Two Card Play

Four Card Play
Three Card Play
14
Player15, Dealer shows 7
Win Push Lose
30.7 7.7 61.5
15
Player17, Dealer shows 8
Win Push Lose
23.0 7.7 69.2
16
Player11, Dealer shows 7
Win Push Lose
53.8 7.7 38.4
17
Player15, Dealer shows 7
16
18
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 32 0.5
• Basic Strategy (perfect play), 1-deck, blackjack
  pays 32 0
• (not typical)
• Basic Strategy (perfect play), 1-deck, blackjack
  pays 65 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.

Head to Head 2 card 3 card 4 card
Player 45.70 40.47 21.16
Dealer 47.48 55.90 77.92
Push 6.82 3.63 0.92
20
Two, Three, and Four Card Game Payout Over Time
21
The End
22
Normality Test
Face card probability 30
Approaching Normality as Card Count Increases
23
Player vs. Dealer Odds
Winner 2 card 3 card 4 card
Player 45.70 40.47 21.16
Dealer 47.48 55.90 77.92
Push 6.82 3.63 0.92
Percentages based on 10,000 card games