Book "Small Stakes Hold 'em" mistake? - Gambling and Probability

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Book "Small Stakes Hold 'em" mistake?

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11-07-2018 , 01:24 PM

yapyap

stranger

Join Date: Nov 2018 Posts: 2

Hi,

my name is Peter, I live in Cologne and I am trying to learn Poker, starting with small limit games. I got the book Small Stakes Hold 'em by Miller, Sklansky and Malmuth yesterday and got confused with a formula for calculating the EV at Roulette when you bet 100$ on a single number where you are paid 1:35 if you win.

The formula in the book (page 26):
(1/38)(3,500$)+(37/38)(–100$)=–$5,26

As I have to bet 100 $ to win 3,500 $, shouldn't the formula say either

(1/38)(3,400$)+(37/38)(–100$)=–$7,89

or

(1/38)(3,500$)+(38/38)(–100$)=–$7,89

Thanks for your answers!
Peter

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11-07-2018 , 01:59 PM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 4,987

EV can be defined as the change in your stack as a result of the betting decision.

For your roulette example, if you hit, you get back 35 for each dollar bet plus your bet. So the stack change for a 100 bet is +3500. On a 38 pocket roulette wheel, you win 1/38 of the time, so the expected change is +3500/38.

If you don’t hit your roulette number, your stack diminishes by the bet size, 100, so the expected loss is (37/38)*100.

Adding the expected gain and expected loss is the same as the book’s equation

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11-07-2018 , 02:59 PM

yapyap

stranger

Join Date: Nov 2018 Posts: 2

Hi Statmanhal,

thanks for your quick and helpful answer. I didn't know that I get my bet back if I win, that's what I got wrong. So you can consider it as a pot where you put 100$ and the casino puts 3500$, and if you win you take the pot. Makes sense.

Peter

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