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This article was originally published in the Blackjack Insider, a Blackjack e-mail newsletter edited and published by Henry Tamburin, author of "Blackjack: Take the Money and Run". The article was written by Dan Pronovost, President of DeepNet Technologies.
The unbeatable card-counter myth
In our continuing series of articles on blackjack, we've gone from simplified basic strategy to uniform card-counting practices. In this installment, we talk about the amount of money you should bring to the blackjack tables if you want to last!
A common mistake even experienced card counters make is to play with an insufficient bankroll. Your bankroll is the upper limit of losses you will accept before stopping.
Once a player has learned how to count cards in blackjack and successfully apply those skills at the tables, it is easy to fall prey to a feeling of invulnerability. Even though a player may have a positive edge in a game, that does not mean he is guaranteed to make a profit. In fact, the 0.5% to 1.5% expectation you can achieve in blackjack (percentage of each bet you expect on average to win) is low enough such that luck can cause completely natural and significant fluctuations in your earnings.
To understand the consequences of playing with an insufficient bankroll, consider the following practical gambling example. You decide to play a standard six-deck blackjack game with a 1 to 10 bet spread, and $15 minimum bet. Let's give you the best possible advantage and assume that you are using the full High-Low count system, which yields a positive expectation of about 0.6% in this game. You decide the most you can afford to lose is $1,000, so you play for a fixed amount of time, leaving if at any point you lose $1,000.
In the analysis below, we usedBlackjack Audit, a blackjack simulator from DeepNet Technologies to collect all data. We ran a minimum of 500,000 blackjack sessions in its unique Risk of Ruin analysis tool. Each session played up to 400, 800, and 1200 hands of blackjack respectively (for the 4, 8, and 12 hours columns below). Our concept of a session here is identical to a single blackjack trip or outing. Note that to emulate the conditions above, a session was terminated prior to playing the specified number of hands if the bankroll was lost (i.e., a gambler would have to stop playing after he exhausted his allowed cash reserves).
The following table shows the results for different lengths of playing time:
At first glance, the table seems to show that the more you play, the more often you lose! Yet, the average winnings are positive and the earning rate per hour is constant, as is expected statistically (the expectation does not vary for each column). This surprising result is caused by the fact that you are using a very small bankroll and relatively large bets, but you are continuing to play without an upper limit (only a time limit). Although you leave the game when you are down at most a modest amount of money (in proportion to the minimum bet and bet spread), you do not do the same when you are up an equal amount. The result is that your fewer winning sessions will be more profitable than expected statistically, but you will have more losing outings overall. Notice also that the average rounds/hour goes down with the longer sessions: this is caused by the fact that you are more likely to exhaust your small $1,000 bankroll as the length of your time limit increases.
Suppose you repeat the same playing conditions with an initial $5,000 bankroll. Hence, you will leave the tables prematurely only if you lose $5,000:
Once again, the results are very surprising. Adding $4,000 to your bankroll reduces your chances of having a losing session in 12 hours to virtually zero.
Next upů choosing the right bankroll
So, what is the right amount of bankroll you should play with? This will depend on your minimum bet size, your bet spread, the game rules, and your count system (pretty much in that order). To analyze bankroll requirements, experts talk about risk of ruin (ROR). This is the chance that playing blackjack will exhaust a bankroll amount, under some set of fixed conditions. Typically, resources quote ROR values that represent a percentage chance of losing a specific amount of money, given an infinite amount of play. This is different from trip bankroll, which is intended to qualify risk of ruin for a limited amount of playing time.
In our next article, we will explore risk of ruin and bankrolls in detail, along with popular equations, software, and other methods for computing these values. For those curious about blackjack risk of ruin and other aspects of the game, we highly recommend Don Schlesinger's book Blackjack Attack: Playing the Pros' Way, published by RGE Publishing (and many thanks to Mr. Schlesinger for his review and contributions to this series of articles on risk of ruin).