Last Updated: January 21, 2019

Risk of Ruin in blackjack

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% 7 11 14 16 18 20 22 24 25
40% 9 14 17 20 23 25 27 29 31
30% 12 17 21 25 28 31 33 36 38
20% 15 21 26 31 34 38 41 44 47
10% 19 27 34 39 44 48 53 57 60
5% 22 32 40 46 52 58 62 67 71
4% 23 34 42 49 55 60 65 70 75
3% 25 36 44 51 58 64 69 74 79
2% 27 38 47 55 62 68 74 79 84
1% 29 42 52 61 68 75 82 88 93
0.5% 32 46 57 66 74 82 89 95 101
0.25% 35 50 61 71 80 88 96 102 109
0.1% 38 54 67 77 87 95 104 111 118
0.01% 45 64 79 91 102 112 122 131 139

Number of Hands to Play

Risk of Ruin 1000 1200 1400 1600 1800 2000 2500 3000
50% 27 30 32 35 37 40 45 50
40% 33 37 40 43 46 49 56 62
30% 41 45 49 53 56 60 68 75
20% 50 55 60 65 69 73 83 92
10% 64 70 76 82 88 93 105 116
5% 76 83 90 97 104 110 124 137
4% 79 87 95 102 108 114 129 143
3% 83 92 100 107 114 121 136 151
2% 89 98 107 114 122 129 145 161
1% 99 108 118 126 134 142 160 177
0.5% 107 118 128 137 146 154 174 192
0.25% 115 126 137 147 156 166 187 206
0.1% 125 138 149 160 170 180 202 223
0.01% 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.

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