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can you explain where you get "Notice that (1-x)/(x-a) = 2" ?
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since x is the minimum for your opponent's optimal calling range , this means he will be calling 1-x of the time .
Likewise , a is hero's minimum for his optimal betting range. X-a are the numbers that hero would be losing to when villain calls .
So , since villain is getting 2:1 pot odds , he should be calling with any hand with any equity greater than 1/3 . This is equivalent to (1-x)
x-a) = 2:1