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Blackjack table odds // Blackjack

Blackjack table odds

Risk of Ruin in blackjack (Appendix 12)
December 24, 2012 – 05:49 pm
Casino Table Odds of Winning
Wizard of Odds Approved

Introduction

There are some sources that address the question of the probability of doubling a bankroll before losing it, in a card counting situation. Ken Uston's Million Dollar Blackjack, to name one. This appendix shall not recover that issue. However, I am often asked about how much the basic strategy player's bankroll should be, given a targeted number of hands to play. This is especially practical if the player must play a certain number of hands to earn an online casino bonus.

The rules assumed for these tables are six decks, dealer stands on soft 17, player may double on any two cards, player may double after splitting, player may resplit to three hands, no surrender, dealer peeks for blackjack. Under these rules, the house edge is 0.4140%.

Let's look at an example of how this table can be used. Assume that the player makes a deposit of $1000 to an online casino, and is required to bet through $5000 in action. If the player is to willing to play through 500 hands, then his average bet size would be $5000/500 = $10. The number of betting units would be $1000/$10 = 100. The table shows the risk of ruin is 0.01% for 102 units, so would be just over 0.01% for 100. Perhaps this is too conservative, so the player considers playing 200 hands. The bet size is now $5000/200 = $25. The number of units is $1000/$25 = 40. Interpolating the table shows the risk of ruin would be 1.5%.

Number of Hands to Play

Risk of Ruin 100 200 300 400 500 600 700 800 900
50% 11 14 16 18 20 22 24 25
40% 17 23 27 29 31
30% 12 21 28 33 36 38
20% 15 26 34 41 44 47
10% 19 39 48 53 57 60
5% 32 40 46 52 58 62 67 71
4% 42 49 55 65 70 75
3% 51 64 69 74 79
2% 68 84
1% 61 82 88 93
0.5% 66 89 95 101
0.25% 35 50 80 96 102 109
0.1% 54 77 87 104 111 118
0.01% 45 91 112 122 131 139
1000 1200 1400 1600 1800 2000 2500 3000
30 37
43 56
73 83 92
76 105 116
90 97 110 124 137
108 114 129 143
100 107 121 136 151
98 145 161
99 126 134 142 160 177
128 146 154 174 192
115 147 156 166 187 206
125 138 149 170 180 202 223
148 162 175 188 198 212 236 261

Methodology

The tables above were created by random simulation. I have been asked several times for a general formula for other situations. Unfortunately there isn't any that I know of. Risk of ruin problems are mathematically usually very complicated. It is easier and more convincing to run a random simulation instead.

Source: wizardofodds.com
Interesting facts

Blackjack Switch is a casino gambling game invented by Geoff Hall and patented in 2009. It is based on blackjack, but differs in that two hands, rather than one, are dealt to each playing position, and the player is initially allowed to exchange ("switch") the top two cards between hands. Natural blackjacks are paid 1:1 instead of the standard...

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