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by Guide Bill Burton

The casinos make their money by paying off bets at less than the true odds.This is the House Edge. Lets take a look at how this effects you and yourbankroll.

The money it cost us to play a game in relation to the house edge is calledthe Expected Value or EV. The EV is actuallythe average outcome determined by multiplying the average Bet timesthe number of Hands Per Hour (HPH) times the House Edge. Basedon our Chart we can figureout the EV of any game for each hour we play. For this example we will usea $5 bet. The figure is what it costs you to play the negative expectationgames, (i.e. games with a house edge).

Roulette: $5 x 50 HPH x 5.26= $13.15
Craps: $5 x30 HPH x 1.4 = $ 2.10
Caribbean Stud : $5 x 40 HPH x 5.3 = $10.60
BlackJack: $5 x 60 HPH x 0.5 = $ 1.50

Now, the first time I saw these figures years ago, I thought there must bea misprint. I knew that I had lost more than $1.50 playing Blackjack forand hour and sometimes I won money so how could it be?

The answer to this question is a thing the mathematicians call StandardDeviation. Lets flip a coin 100 times. The EV should be 50 headsand 50 tails but it doesn’t happen this way every time. Most of thetime you get more heads than tails or the opposite. The amount we stray fromthe EV is the Standard Deviation. You will be one standard deviation awayfrom the EV about 68 % of the time and will be within 2 standard deviations95 % of the time. There is an equation for figuring this:

Lets say we played 100 hands. The square root of 100 is 10. we divide 1.1by 10 and come up with 11% or 11 units (11% of 100 hands). If we are playing$5 per hand one unit would equal $5. so our standard deviation would be $55.

If we are playing Blackjack , we figure that the EV is minus $2.50 for 100hands. We find that the range for one standard deviation (68% of the time)is between: -$56.50 and +$52.50

Doubling the standard deviation will give us a 95% accurate range between:-$112.50 and +$107.50.

This is a pretty wild fluctuation for our bankroll. It also shows how badthings can get when we lose and what we can realistically expect towin. Because we are playing against the house edge ourLOSES will always be greater than our WINS in the long run. The chart belowshows a Bell Curve of the single and double standard deviation

Knowing this, our best bet is to walk away from the table when we find ourselvesin the positive range. The longer we play the more chance of getting closerto the EV which we know is negative. Now we know thePrice We Pay To Play.

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