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Proportional Betting Schemes
 

Hence the average bet at this level (remember, many of the bets are zero, when the deck is bad) will be .2377 per cent of $10,000, or $23.77.

To find the average earning i must first determine how often the deck is favorable. On page 91 i find the normal curve area to the right of z = .54 is .5000 - .2054 = .2946 which is also the fraction of the 130 card remainders that are favorable to the player. (Note that the average bet, when one is made, is $23.77/.2946 = $80.69, although this number plays no role in our calculations.) The average earning will be given by the formula
m X average perceived advantage + b2 X probability of favorable deck Plugging in our figures i crank out an average profit of -.70 X .2377 + (1.28)2 X .2946 = .3163 which is in percent of percent of our bankroll. Thus our average earning per hand is $.32. Our percentage advantage on money invested would be .32/23.77 - 1.33%.

What is a trifle unrealistic here is the notion that the player can diagnose his advantage perfectly. if a card counting system with betting correlation p = .96 ire used, i would multiply the original value of b by p and get a revised b = 1.28 X .96 = 1.23 and repeat the calculations, getting:
z = .70 = .571.23 1770 from page 87 1770 X 1.23 = .21771%), giving an average bet of $21.77

Area to the right of z = .57 from page 91 is .5000 - .2157 _ .2843
Average earning of -.70 X .2177 + (1.23)z X .2843 = .2777 (% of %), or $.28 with a percentage advantage on money bet of .28/21.77 = 1.28%
Naturally, to assess total performance throughout the shoe one would repeat these calculations for various values of n one expected to encounter, and not just for n = 130.

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Lending Money in Nome Games
 
Despite these reasons, lending money in such situations is fraught with peril. You don't have to be a poker player to know how many friendships break up over the stresses that loaned money can create. Regular losers may appreciate a loan in the moment, but if it helps them lose far more in an evening than they originally were prepared to lose, they may be unhappy the next day ("Why did you lend me money when I was throwing it away so foolishly?!?"). Someone who loses a truly huge sum may decide he can't pay it back and quit the game owing it all. Watching someone use money you lent him to come back and beat you is almost as bad.
 
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