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Practical Poker Math

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On average, over the course of 13 such bets you will lose 12<br />

for a loss of $1,200 and win 1 worth $1,500, for a net profit<br />

of $300 over 13 tries.<br />

12 losses @ $100 ea = $1,200 loss<br />

1 Win @ $1,500 = $1,500 profit<br />

Net Profit = $300<br />

With a profit of $300 over 13 tries, you can anticipate an<br />

average profit of $300 / 13 = $23.08 per trial. The value or<br />

expectation of each draw is +$23.08.<br />

The sum of all expectations in any proposition must be zero.<br />

You, as the player, have a positive expectation of +$23.08 per<br />

draw and the person who laid the bet has a negative expectation<br />

of -$23.08.<br />

Fluctuation is short-term.<br />

After 20 draws it would not be unusual for you, as the taker<br />

of such a wager, to be down $2,000 and your opponent, who<br />

made the proposition, up $2,000 — a fluctuation. While<br />

after a small number of tries you might be down, it is almost<br />

a 100% certainty that after 100,000 tries you will be up over<br />

$2,000,000 and your opponent will be down over<br />

$2,000,000 — an expectation.<br />

Expectation is long-term.<br />

The same applies to every bet or raise you make or take<br />

playing poker. As long as all of your bets, calls and raises<br />

carry greater money odds than risk odds, you will be a<br />

long-term winner.<br />

21<br />

Money Odds & Expectation

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