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The Price We Pay To Play

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"I have seen many people drinking very heavily while gambling"
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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 your bankroll.

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

Roulette:              $5 x 50 HPH x 5.26 = $13.15
Craps:                 $5 x 30 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 be a misprint. I knew that I had lost more than $1.50 playing Blackjack for and hour and sometimes I won money so how could it be?

The answer to this question is a thing the mathematicians call Standard Deviation. Lets flip a coin 100 times. The EV should be 50 heads and 50 tails but it doesn’t happen this way every time. Most of the time you get more heads than tails or the opposite. The amount we stray from the EV is the Standard Deviation. You will be one standard deviation away from the EV about 68 % of the time and will be within 2 standard deviations 95 % of the time. There is an equation for figuring this:

Standard Deviation = 1.1 divided by the square root of the number of hands played.

Lets say we played 100 hands. The square root of 100 is 10. we divide 1.1 by 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 100 hands. We find that the range for one standard deviation (68% of the time) is between:  -$56.50 and +$52.50

-$2.50 + plus $55 = plus $52.50
-$2.50 + minus $55 = minus 57.50

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 bad things can get  when we lose and what we can realistically expect to win. Because we are playing against the house edge our LOSES will always be greater than our  WINS in the long run. The chart below shows 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 ourselves in the positive range. The longer we play the more chance of getting closer to the EV which we know is negative. Now we know the Price We Pay To Play.

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