"What Went Wrong?" by Henry Tamburin
I received this email from an agitated blackjack player: "I went to Las Vegas last weekend and played blackjack using the basic playing strategy in your book. I played every hand exactly the way your books says to, and I wound up losing $500. The least you can do is refund the money I paid for your stupid book." If you had received this email, how would you have responded? Here's what I did. First, I contacted the weekend warrior (WW) to find out a little more about his playing session. Here's what he told me. - He was betting from $10 to $50 using a progressive betting system (meaning he increased his bet following a win, and decreased it following a loss).
- He played a 6-deck game where the dealer stands on soft 17 (s17).
- He played roughly 16 hours of blackjack over the weekend.
- He played the basic strategy, as described in my book, "flawlessly" (his word).
- He always played with at least two or more other players, and never alone.
- He is not a card counter.
With the above information, I calculated what his expected loss should have been after his 16 hours of play (this is also known as his theoretical loss). This is simply the total amount of his wagers multiplied by the house edge. I assumed his bets averaged $20 per hand (which is about right for the type of betting progression that he was using. The precise value, obtained through simulations by Norm Wattenberger, is $19.70). I also assumed he played 100 hands per hour, which is roughly what you will be dealt at a three-player table. By multiplying the 100 hands played per hour by the 16 hours that he played, you arrive at the fact that he played a total of about 1,600 hands. His average bet on each of those hands was about 20 bucks, so over the weekend our WW made a total of about $32,000 worth of bets (surprised by this number?). The house edge against our WW was about 0.5 percent (again I'm assuming he played flawless basic strategy). This means the house stood to win 0.5 percent of all the money that he wagered, which amounts to $160. In other words, our WW's expected result was to lose $160 after 16 hours of playing. But the reality is that he lost $500, not $160. Does this mean the basic strategy is flawed? Nope, and here's why. Suppose I ask you how many times you would expect heads if I flipped an honest coin one hundred times? You probably answered "50." But you rarely will get Applying similar mathematics to our WW's 16-hour playing session yields this result: His expected weekend result will lie somewhere between a loss of $2,287 and a win of $1,967, and he'll get that result roughly 19 out of 20 weekend trips to Sin City. Even though his expected loss was $160, he shouldn't be a bit surprised over the fact that he lost $500, because such losses or greater not only fall within the calculated range of results but actually occur a whopping 37% of the time. In fact, 5% of the time, he could have won $1,967 or more, or, alas, lost $2,287 or more, just as easily. His $500 loss wasn't because of the "stupid strategy" in my book, but rather it was due to the standard deviation, or variance, that is inherent in the game of blackjack (meaning your session results will often be more or less than your expected result). So what's the moral to this story? Even though you may be playing perfect basic strategy, your results on a session-by-session basis will fluctuate widely from the expected result. In some sessions you will win, in others you will lose, but the results will always be skewed toward the losing side (because the house has the edge over a basic strategy player). Over time your losses will equal half a percent times the total amount of your wagers. That, my dear readers, is a mathematical fact about the game of blackjack, and no betting system or other voodoo is going to change it. I emailed the above results to my reader, and encouraged him to consider learning a simple card counting system because then the range of his session results will be skewed toward the positive side, and over time he'll
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