o - outs
o/47 + (47-o / 47) * (o/46)
13 outs is:
13/47 + (34 / 47) * (13/46) =48.1%
that's on the flop
simply 13/46 on the turn
the formula can also be written as
o/47 * (1 + [{47-o}/46])
or
o/47 * (93-o) / 46
so if you know what the chance of making it by the turn is, subtract outs from 93 and divide by 46 and multiply by that chance
do not attempt this during the game unless you're sklansky though
the shorter way:
the amount you multiply the outs by is 4.3
BUT take away from that amount outs times 0.046
so for 13 outs the multiplier is 4.3 - (13 * 46) / 1000 - around 3.7
3.7 * 13 = 48.1
It's correct to 3 decimal places and doable in your head


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