Risk Of Ruin Blackjack
How To Trade Multiple Time Frames Like Professional Traders (The Triple Screen System) - Duration: 10:06. The Secret Mindset 170,038 views. While many blackjack authors have written extensively about the subject and described it in terms of complex mathematical equations, risk of ruin can be simply described as your chance of doubling your bankroll versus busting out during a blackjack session. The Kelly Criterion and Blackjack. The Kelly Criterion is a method of betting for blackjack players who have a mathematical edge in a wager. The Kelly Criterion maximizes your profit while eliminating your risk of ruin. The Kelly Criterion is most often used by card counters. The probability of a 6-loss streak in fair coin flip is 1/64 (or 1/45 in blackjack), and a streak can begin on any hand. So, it will take only 50 fair coin flips or 36 hands of blackjack to provide a 50% risk of ruin with 6-step martingale. A 10% risk of ruin is reached in a mere 10 hands.
US Players and Credit Card, BitCoin Deposits Accepted!
The Kelly Criterion is a method of betting for blackjack players who have a mathematical edge in a wager. The Kelly Criterion maximizes your profit while eliminating your risk of ruin.
The Kelly Criterion is most often used by card counters. The better a player's chances of winning based on the card count, the more the player bets. The size of this bet is determined according to the Kelly Criterion, sometimes known as the Kelly Formula. If the house has an edge in a game, then the Kelly Criterion is useless.
Calculating Risk and Applying the Kelly Criterion
The Kelly Criterion is a mathematical formula used to maximize the growth rate of serial gambling wagers that have a positive expectation. The Kelly Criterion is a model for long-term growth rate.It does not predict automatic short-term success, but the Kelly Criterion does maximize profits by setting the percentage of a player's bankroll which should be bet at each stage of play.
Basically, the Kelly Criterion can be boiled down to this: you should bet a percentage of your bankroll equal to the edge you have at the game. When you raise the size of your bet based on how good the count is in a blackjack game where you're counting, you're putting the Kelly Criterion into action.
What the Kelly Criterion Does Not Do
- The Kelly Criterion doesn't assure you will make a profit. It maximizes your profits when you do win.
- Conversely, the Kelly Criterion doesn't assure you won't lose money. The criterion minimizes the chance you will lose all your money.
- The Kelly Criterion does not help gamblers defeat a house edge. It is meant to help those playing with a positive expectation. It really has no use when playing most casino games, because the house has the edge in most casino games..
The History of the Kelly Criterion
The Kelly Criterion was developed by John Larry Kelly, Jr. J.L. Kelly worked at Bell Labs in Texas, and was born in Corsicana, Texas.
Kelly began to develop investing strategies according to probability theory. These theories also applied to gambling strategies, too, and these investing strategies are part of what is now called game theory.
John Kelly's friend and colleague, Claude Shannon, made a visit to Las Vegas in the 1960's. Shannon and his wife used the Kelly Criterion to win at blackjack. Claude Shannon and another colleague eventually applied the Kelly Criterion to the stock market, eventually collecting a fortune.
By this time, John Kelly was dead of a stroke. His theory has been applied to gambling with increasing frequency over the years.
The Kelly Formula
The Kelly formula is meant to determine the fraction of your bankroll which you should bet at any given times. The idea is that you find that fraction which maximizes the amount of money you expect to win.
Here is the basic equation for the Kelly Criterion:
f = (b times p minus q) divided by b
There are several portions of the formula which need to be described:
f = The fraction of a player's bankroll which should be wagered. This is the number someone is looking for when using the Kelly formula.
b = This is the odds the player is receiving on the wager.
p = The probability the player will win the wager.
q = The probability the player will lose the wager, which is easily determined in a simple bet as 1 - p. For example, if the probability of winning (p) is 0.50%, then the probability of losing (q) would be 1 - 0.50 or 0.50%.
This would imply an even-money bet. In such an even-money bet, the Kelly Formula can be simplified to f = 2p - 1.
To use the Kelly Criterion, then, a player must be able to estimate the odds, the probability of winning and the probability of losing the bet.
Drawbacks to Using the Kelly Criterion
The Kelly Criterion cannot guarantee a win on gambling. What the Kelly Criterion does is guarantee you will not lose all of your money. It also maximizes your profits when you are winning. The Kelly Criterion is supposed to accumulate a compound interest of 9.06% when used correctly.
The problem with the Kelly Criterion is that it can lead to highly volatile results. You have a 33% chance of losing half of your bankroll before you double your payroll. There have been many attempts to modify the Kelly Criterion to make it less volatile. This led to the creation of Half-Kelly techniques.
The Half-Kelly Criterion
The Half-Kelly Criterion is often used by players who don't entirely trust the Kelly Criterion or their implementation of it. In a casino setting, it is easy to miscalculate the formula. If this leads to over-betting, the formula becomes counter-productive and the player can lose a large amount.
To safeguard against this, some people simply half the bet the Kelly Formula requires. This is called the half-kelly. This eliminates the chances of mistaken over-betting. Of course, the Half-Kelly undermines the original purpose of the Kelly Criterion, which was to maximize the amount won at a casino.
See also:
US Players and Credit Card, BitCoin Deposits Accepted!
- Appendices
- Miscellaneous
- External Links
Introduction
Risk Of Ruin Blackjack
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
Blackjack Risk Of Ruin Chart
| 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.