Fluctuations and Your Blackjack Bankroll
FROM ET FAN:
Waiting for the Long RunBy Arnold Snyder
(From Blackjack Forum , Vol. X #3, September 1990)
© Blackjack Forum 1990
Usually, I take this opening space to fool around with some inane concept that has no serious bearing on anyone's strategic attack on the game. You may find occasional snippets of information herein, usually tied to some moral or message, but nothing really meaty you can sink your teeth into. Certainly not negative fluctuations at blackjack. I like to have a couple pages in each issue of this mag where I can dish out some of the screwball ideas that pop into my head without having to proofread charts and tables and figures and quotes and formulas.
This Sermon, however, is going to be different. I've come up with a way to deal with one of the most common queries I get from my readers, which I could paraphrase thusly: "The table conditions were great; I know I was playing my system well; I lost my shirt. What happened?"
Why is it that so many smart players still believe that negative fluctuations at blackjack are something that happens to the other guy? In order to demonstrate what can happen to you in the short run in a great blackjack game, even when you're using your system perfectly, I've run 100 consecutive computer simulations of 1000 hands each. Each simulation represents about 10 hours of play in a great blackjack game: single deck, Vegas Strip rules with double after splits, 80% dealt out.
The player is using the Zen Count with all published indices, and spreading his bets from $25 to $100. His long run advantage in this game is 2.1%, which translates to about $105 per hour. I ran a 10-million hand simulation to come up with this expectation. Since you probably won't play any 10-million hand sessions, let's look at what happens in your real world 10-hour sessions.
Of these 100 10-hour sessions, you won at least some money on 76 of them, but lost on 24 of them. That sounds great. You'll lose on less than one out of four 10-hour playing sessions.
However, these wins and losses do not distribute themselves evenly. The longest series of consecutive winning sessions, not interrupted by a single losing session of any amount, was 18. During this simulated 180 consecutive hours of real time play, you won an average of $198.50 per hour, almost twice your actual expectation!
In dollars and cents, after 180 hours of play in this game, you would expect to be ahead by $18,900; due to normal fluctuation, however, in this run you were ahead by $35,640! Your single best playing session, in fact, during which you had an expectation of $1050 after 10 hours of play, you actually won $6,200, which translates to a win rate of 11.76%!
What a marvelous game!
But wait a minute. If your wins are fluctuating and clumping so wildly, doesn't that mean your losses are also? You better believe it. On your worst losing session, instead of winning your expected $1050, you lost an even $4000. And on your worst two consecutive losing sessions, instead of winning your expected $2,100, you lost $7,675!
Your worst 10 consecutive sessions contained 7 losing sessions and 3 winning sessions. At the end of this simulated 100 consecutive hours of play, you would expect to be ahead by $10,500; instead, you were behind by $8,175!
And what was the longest series of consecutive sessions in which vou still failed to show a net win at the end? Nineteen. One hundred and ninety consecutive hours of blackjack play at an excellent edge, and still in the red. Now that's a negative fluctuation.
The series contained 11 losing sessions and 8 winning sessions. Your expectation after 190 hours at this game is to be ahead by $19,950. Instead, you were still behind by an even $2,000.
Mercifully, there was no series of 20 consecutive sessions in which you did not show at least some small win. So, in this game, if we define "long run" to mean approximately how long you must play before you're more or less assured of being ahead, the answer is about 200 consecutive hours.
Bear in mind that this simulation study is based on only 100 consecutive 10-tour sessions. If I ran 1000 consecutive sessions, I would expect to come up with even more radical swings on both the positive and negative series.
Normal fluctuation is what makes and breaks most card counters. You can't get away from it. No system, no betting method, no "money management" strategy, no "stop loss" limit will have any effect whatsoever on normal fluctuation.
In the unrealistically marvelous game described above, in which you ultimately won on 76 out of 100 playing sessions, and in which you ultimately won a total of $101,400 (within .1% of your actual expectation), look what you had to go through to get there! Had you been playing 8 hours per day, 5 days per week, you would have had to withstand one series of playing sessions of almost 5 consecutive weeks still showing a net loss!
Even more sobering is the thought that you will never find a game this great that lasts this long! Most counters are happy to play at half of this 2.1% win rate. Most players can expect to experience fluctuations far more drastic than those I recorded in this simulation. With a 1% advantage, you'll only win on about 60 out of 100 10-hour sessions. You can expect to show a net loss sometimes after 30 to 35 consecutive 10-hour sessions, up to 2+ months of full-time play!
I would guess I have some two dozen letters in my slush pile right now with some variation of: "It was supposed to be a great game, so how come I lost?" Many of these queries are from players who recently switched systems, tried a new game, or played in some casino they hadn't visited before. They want to know if their new counting system is no good, or if the dealers in such and such place are cheating, or if the shuffling routine is designed to foil card counters, etc., etc. (Incidentally, I used a random shuffle in all of my simulations.) I also have some letters which say: "I've won 9 out of 10 sessions for the past six months. Do you think it's because of my new system, or money management technique, etc., etc.?"
I've written this Sermon to answer these two dozen plus letters. You can't judge a game or a system on the basis of a weekend or a week or even a month of full time play. If you're playing for high stakes, you've got to have a large enough bankroll to withstand incredible negative fluctuations, plus cover your living expenses. Just hang in there. The long run is a long time, but it does come around. ♠
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||Bankroll Fluctuation and Losing Streaks in Blackjack Card Counting
Many practitioners of card counting take too much credit for their winning streaks and take too much to heart their losing streaks. But bankroll fluctuations, even with a winning gambling system like blackjack card counting, are inevitable. Arnold Snyder explains how to judge whether the results of your gambling are due to truly winning systems or merely bankroll fluctuations (winning or losing streaks).