Poker Maths: Simple Calculations

Expected Value (EV)
-the profit of an outcome weighted by its probability
eg. 20% chance to win $100 then our EV is 20% x $100 = $20


Simple EV Calculation
eg. Coinflip for $1
Heads = 50% = Net profit = $1
Tails = 50% = Profit = -$1

EV(total) = P(A)xEV(A) + P(B)xEV(B)

EV(total) =(0.5x$1)+(0.5x-$1)= 0

Poker Scenario:
$100 in the pot, Villain bets $100 on the river
-> we need to call $100 to win $200
-> we estimate to have 38% equity against the betting range of villain (from calculating bluff/value ratio)
therefore: EV(call) = (0.38*$200) + (1-0.38)*(-$100) = +$14 (we should always call)


Scenario: Semibluff flop with nut flush draw
Pot: $100, Villain bets $75, we shove $450
We estimate to have 55% fold equity; against his calling-range we got 20% equity.

What's our EV?
EV(total)= P(Vf)* $175 + P(Vc) *-$450+ P(Vc)*550
=(0.55*175) + (0.45*(0.8*-450)+(0.45*0.2*550) = -16.25

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