[binions]

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There is some missing information . How much does your opponent bet into the pot ? Does he make a pot size bet or a two thirds size bet ?

If he makes a pot size bet , then the amount of fold equity required is :

(3SPR-1)/(3SPR+9) = 8/18 = 44.444% so clearly 62% is too high .

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I over simplified my example calculation. W = the total amount you would win if called times your equity minus your initial stack size. So if your opponent bets into you and you have to call that bet first you have to factor that into the total amount you would win if called. Pot is the size of the pot after you match opponent’s bet.

Example:
You’re stack size is 250 (opponent has you covered).
Initial Pot size is 50.
Villain bets 50.
You call 50.
Pot = 150 = (50 + 50 + 50)
You’re equity if called is 20%.

W = ((Pot) +200 + 200) * .2 ) – 250 = -140
-140 / (-140 ) – Pot = -140 / -290 = .48275

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Therein lies part of the rub.

The formula derived by OP & JayShark figures the fold equity you need when you come over the top not when you call.

So, in your example, with 20% equity, a 50 final pot preflop, a pot sized bet into you, and 250 effective stacks going into the flop:

1. the SPR is 5 (250 to 50)
2. the 20% formula for a pot sized bet is 3SPR-1/3SPR+9

So, villain needs to fold at least 14/24 or 58.3% when you come over the top to break even for the times when he calls and you are drawing at 20%.

Let's see if it works.

14/24 he folds and you win 100 (the 50 in the pot and his 50 bet)
2/14 he calls and you win 300 (50 in the pot + his 250)
8/14 he calls and you lose 250 (the 250 in your stack on the flop)

1400 + 600 = 2000
8*250 = 2000

Yep, it works.