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by Henry Tamburin

Henry Tamburin is the author of the "Ultimate Blackjack Strategy Guide," (, editor of the Blackjack Insider Newsletter, and host of He also teaches blackjack and video poker courses in Las Vegas.

"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 you'll see). Most likely you'll wind up with more, or less, than 50 heads and it's unlikely 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 a SD of 10. 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 10 (1 SD) or between 40 to 60 heads. How probable is probable? One SD implies that in 68.3% of the trials you will wind up 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).


Expected result

Possible Result


40 to 60 range (1SD or 68.3% of the time)


30 to 70 range (2SD or 95.4% of the time)


20 to 80 range (3SD or 97.7% of the time)

Now let's bet a buck on each coin flip. At the 2SD probable outcome, your result will be somewhere between 30 and 70 heads, 95% of the time. If heads comes up 70 times, you would be a winner by $40 (win one dollar on 70 flips and lose one dollar on 30 flips). If instead heads only came up 30 times, you'd wind up in the red by $40. In fact 95% of the time you would end up winning or losing between +$40 to -$40 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


30 to 70 heads

-$40 to +$40

What happens if you were to wind up losing $70 after 100 coin flips? I'd look carefully at the coin because it is highly unlikely that you would be outside the 2SD lower boundary of -$40 if the game is fair. In other words "something is rotten in Denmark" (e.g., maybe someone slipped a coin with two tails into the game).

So let's get back to our frustrated blackjack player. In her email she mentioned 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.

Our player estimated she played 25 hours of blackjack and averaged $10 per hand. We'll assume she was dealt a standard, 100 hands per hour. This means she played 2,500 hands of blackjack over the three weekends and made $25,000 worth of bets (you didn't think it would be that much did you). We'll also assume that she played perfect basic strategy with a casino's edge of 0.5 percent.

With the above assumptions we can calculate the SD and determine how much money she should have won or lost with 95% certainty (i.e. 2SD).

First let's calculate her expected result based on the fact that even though she played perfect basic strategy, the casino still has a tiny 0.5% edge. To determine her expected result you simply multiply the total amount wagered by the casino's edge ($2500 x 0.5%). In other words her expectation was to lose $125 simply because the casino had the slight mathematical edge. However, rarely will she lose exactly $125. The calculated 2SD is $1,100 therefore, the most likely outcome is that she will wind up winning or losing between +$975 to -$1,225. This result will occur 95% of the time or 19 out of 20 twenty five hour playing sessions.

2500 BJ Hands at $10 per hand

Expected Result

Possible Result @ 2SD


+$975 to -$1225

If you compare her actual result - losing $500 - with the projected 2SD outcome of +$975 to -$1,225, you see that losing $500 is within the range. This means her $500 loss was not abnormal. In fact she had just as much chance to win up to $975, or in the absolute worst case, lose $1,225.

What happens if she plays more blackjack? Will she ever get a shot at recouping her loss? It's possible but the chance diminishes the longer she plays. Just look at her 2SD probable outcome as she plays more hands (see below). Notice the more hands she plays the more the range of the probable outcome is skewed more to the losing side and eventually at 200,000 hands she has virtually no chance of showing a profit. So even though luck plays a big part in your outcome in the short term, over time the casino's edge will prevail and you will come closer to the expected outcome (which in this case is a net loss).

# Hands Played

Expected Result

Outcome @ 2SD



+$975 to -$1225



+$1700 to -$2700



+$2230 to -$4730



+$2420 to -$7460



+$1960 to -$11960



-$160 to -$19,840

So what's the lesson learned in all this?

  • First, experiencing losing sessions as a basic strategy player is quite normal and should come as no surprise. The reason you have some winning and some losing sessions is due to the natural variation in the game (i.e. SD).
  • Secondly, in the short term you could experience many consecutive winning or losing sessions because luck has a lot to do with your outcome.
  • Thirdly, the longer you play the more likely your final outcome will be a net loss because the casino math will ultimately prevail over "luck".

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