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Risk of Ruin in blackjack

Introduction

Risk of Ruin in blackjack

Certain sources delve into the likelihood of doubling a bankroll before a loss occurs in the context of card counting. One notable reference is Ken Uston. This section will not revisit that topic. However, I frequently receive inquiries about what size a basic strategy player’s bankroll should be relative to the number of hands they intend to play. This becomes particularly relevant when players are required to complete a specific number of hands to qualify for an online casino bonus. Million Dollar Blackjack The following parameters were assumed for these tables: six decks are used, the dealer stands on a soft 17, players can double with any two cards, doubling after a split is allowed, players can resplit their hands up to three times, surrendering is not an option, and the dealer will check for blackjack. Based on these conditions, the house edge stands at 0.4140%.

Let's illustrate how to effectively use this table. For example, if a player deposits $1000 into an online casino and must wager a total of $5000, playing through 500 hands would mean an average bet of $5000 divided by 500, which equals $10. This results in 100 betting units as $1000 divided by $10 equals 100. According to the table, the risk of going broke is just 0.01% for 102 units, meaning it would be slightly above 0.01% for 100 units. If this seems a bit too cautious, the player might consider playing 200 hands instead. With this configuration, the average bet becomes $5000 divided by 200, translating to $25. Consequently, the number of units translates to $1000 divided by $25, yielding 40 units. Consulting the table, we see that the risk of ruin would be around 1.5%.

The tables provided were generated through random simulations. I've been asked on numerous occasions to supply a general formula applicable to other circumstances. Unfortunately, to my knowledge, no such formula exists. Risk of ruin scenarios are typically mathematically intricate. Conducting a random simulation tends to be simpler and more effective.

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

Strategies and statistically reliable information for various casino games including blackjack, craps, roulette, and many others available for play.

Written by: Michael Shackleford