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Actually, I think both boris and razvan are right, in a sense.
The confusion comes from the subtle difference between EV/required equity calculations and pot odd calculations.
As far as I understand it, in calculating pot odds, we are not risking call for call + pot. Pot odds are expressed as ratio current pot size to call. Therefore pot odds should be calculated as risking .20 for pot of .68 or .68 to .20. or roughly 2.5 to 1 in original example. This agrees with Boris
To calculate required equity for the call, THEN the required equity is the ratio of .20/.88. This is not the risk for gain ratio. This is actually derived from the following math:
EV = P(win) * potsize - P(lose) * callsize >= 0
P(win) * potsize - (1-P(win) * callsize)) >=0
P(win) * potsize -callsize + P(win)*callsize >=0
P(win)(potsize +callsize) - callsize >=0
P(win) >= callsize/(potsize+callsize)
As you can see, although the required expectation is .20/.88 this is NOT
risking .20 for .88. This is risking .20 for potsize which is .68
Finally, what Boris is saying reduces to what Razvan is saying anyway.
For example, an example he gave was 2 to 1 pot odds requires winning 1 in 3
to break even, which is correct and also is the same as the result from
the expectation formula: callsize = 1, pot size is 2, P(win) must be 1/1+2 = 1/3.
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