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standard deviation

Winning at Blackjack - Edges


Our immediate interest here is in using a bigger advantage over the house to cut your fluctuations. Employing S-l, the counter using this strategy would win only 16 units for every 10,000 hands played, but one standard deviation on these hands would be about 110 units. That win rate of 0.11% is so small that even with 100,000 hands played, and an expectation of 156 units, the standard deviation, 348 units, is still more than twice the expectation.

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With this small of an edge, whether or not you win or lose is a crap shoot, even over a period of years. One of the main goals of the pro player is to raise his expectation of winning so that it's higher than the standard deviation as soon as possible. If your expected unit win is still less than one standard deviation after 100,000 hands, you may have the edge on the house, but you're still just gambling.

If you use S-3, however, with a win rate of 1.26%, your unit expectation is 126 after 10,000 hands played, with a standard deviation of only 110 units. (Note: the standard deviation numbers are not in the chart above, which has been condensed from the charts in the 6-deck report.) So, with S-3, you're more likely to be in the black after 10,000 hands played than you would be after 100,000 hands played with the S-l betting strategy. That higher win rate really pays off if you're trying to get past those initial short-term losses.

But there are other problems with the S-3 betting strategy, some of which we've mentioned already. Since we're only playing 26 hands per 100 seen, it's going to take a hell of a lot longer to play 10,000 hands in real-world hours, with most of our time spent circling around the pit like a buzzard just watching for a decent betting opportunity. It's not a practical solo approach to beating the game.

So, let's look at S-8, playing the same number of hands per hour (69) as S-l, but spreading from 1 to 8 units as the count increases. Let's say that we spread from $25 to $200 in order to get this 1 to 8 spread. The average bet is 2.23 units, which—with a $25 unit—translates to $55.75. It's a significantly smaller average bet than the one used by the S-l player, who is flat betting $100, even though we are playing the same number of hands, and bet twice as much ($200) on the best situations.

So, playing S-8 our Hourly Unit expectation is 1.62, and with a $25 unit, this comes to $40.50, significantly higher than any of the flat-betting strategies, despite the smaller unit size and smaller average bet. Finally, even though using S-8 we play the same number of hands as the S-1 bettor, and are sometimes betting twice as much as the S-l bettor, after 10,000 hands the S-l bettor's standard deviation (with a $100 betting unit) is $11,000, while ours (with a $25-$200 betting spread) is only $8,950. So, S-8 outperforms S-l by winning almost 4 times as much per hour, with an average bet almost half the size of S-l, and has significantly reduced fluctuations.

Although casual players who have outside income can seriously consider playing with very small edges in order to obtain comps and other amenities, pros must always do whatever possible to get as big of an edge over the house as possible in order to cut the flux. Table-hopping to avoid betting when the house has any significant advantage is one way to do this.

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