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Black Jack Appendix 11
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 it comes up often how much the basic strategy should bankroll given a targeted number of hands to play. This is especialy 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 .4140%.

Let's look at an example of how this table can be used. Assume the player makes a deposit of $1000 to an online casino and is required to bet through $5000 in action. Assume the player is willing to accept a 5% risk of ruin and wishes to play only 500 hands. How much should the player bet every hand? My table shows the player should purchase 52 units. $1000 divided by 52 is $19.23. So by betting $20 a hand the risk of ruin should be just over 5%.

Risk
of Ruin		 Number of Hands to Play
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

Risk
of Ruin		 Number of Hands to Play
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

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