The Reason Why We Sometime Still Lose

“I was a big loser playing blackjack so I took your advice and learned the basic playing strategy. I’m still a big loser. What gives?”

Yes, I know it’s frustrating to lose, especially when you play your hands perfectly.
But this player’s experience is not uncommon. Even the most highly skilled players suffer losing streaks (been there, done that). The reason has nothing to do with “faulty strategy,” or “the bad play of your fellow players,” or “a cheating dealer.”
No, the reason is due to what mathematicians call “standard deviation” (which I will refer to as SD).

If you’ve never heard of SD, don’t fret, because you are not alone. However, it is often the culprit that causes a player’s bankroll to swing wildly, so it’s important that you understand a little about SD. But I promise not to bore you with a lot of mathematical equations. Instead, I’ll show you how SD can be used to predict and understand the results of your playing sessions.

Basically, SD is a measure of the variance (or difference) between an actual result compared to an expected result. For example, how many heads would you expect if you flipped a coin 100 times? You probably said “50.” However, in the real world it’s rare that your outcome would be exactly 50 heads (try it, and you’ll see). Most likely, you’ll wind up with more, or less, than 50 heads, and it’s unlikely that you’ll get the same result on each 100-coin-flip trial.

If you want to know beforehand how far away you most likely will be from exactly 50 heads (i.e., the outer boundary) you need to calculate the SD.  In the case of our 100-trial coin-flip game, the math yields an SD of 5. This means that instead of ending up with exactly 50 heads as expected, you will probably end up in the range of 50 plus or minus 5 (1 SD), or between 45 and 55 heads. How probable is probable? For a large number of trials, one SD implies that in 68.3% of the trials you will wind up between plus and minus one SD from the expected result. If you want to know the probable result with more accuracy, you can calculate twice the SD, or 2SD (95.4% certainty), or 3SD (99.7% certainty).
(Note: Our 100-coin-flip example is not a very large trial, therefore, the percent probabilities will be slightly different than the above theoretical probabilities.)

100 COIN FLIPS
Expected result          Possible Result   
50            45 to 55 range (1SD)
50            40 to 60 range (2SD)   
50            35 to 65 range (3SD)

Now let’s bet a buck on each coin flip. At the 2SD probable outcome, your result will be somewhere between 40 and 60 heads, about 95% of the time.
If heads comes up 60 times, you would be a winner of $20 (win one dollar on 60 flips and lose one dollar on 40 flips). If instead heads came up only 40 times, you’d wind up in the red by $20.  In fact about 95% of the time you would end up winning or losing between +$20 and -$20, after 100 coin flips, and only 5% of the time would your final outcome be a win or loss outside this range.
The point is that by calculating the SD you can predict how much money you should expect to be ahead or behind in this 100-trial coin-flip game with a fair degree of certainty.

#Coin Flips    Probable Outcome at 2SD        Predicted Amount Won/Lost
      100             40 to 60 heads                  +$20 to -$20

What happens if you were to wind up losing $40 after 100 coin flips? I’d look carefully at the coin, because it is highly unlikely that you would be that far outside the 2SD lower boundary of -$20 if the game were fair.  In other words, “something is rotten in the state of Denmark” (e.g., maybe someone slipped a biased, weighted coin into the game).

So let’s get back to our frustrated blackjack player. In her email she mentioned that she lost “close to $500” after three consecutive weekends of play. Let’s use SD to determine what her most likely outcome should have been.

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