[scdavis0]

Wow you are actually defending your math.. I can ensure you that you are embarassingly incorrect

Ahem.. to quote you

[ QUOTE ]
The difference is ((N/44) - 1)/86. If you somehow had > 44 outs
it would be +EV to draw twice (silly), and the less outs you have the worse it is. In the extreme case of having only 1 out,
you lose 1.1% of the pot in EV by drawing twice !!

[/ QUOTE ]

You say something about having greater than 44 outs (which is impossible with 44 cards left in the deck), then you provide this formula. You give no reasoning for why your math should break down with exactly one out.. in fact you point out with exasperation how bad of a deal it is if you are the one with one out.

I'll provide the general solution for any number of outs -- if that STILL doesn't satisfy you then I'll show you the error in your own calculations.

Then if that is no longer enough, I'll agree to meet you and we can deal out a scenario where we run it twice and I have two outs. Just give me a 0.1% edge on the payout. Bring your whole bankroll!

EV of running once = S*x/44

S = size of the pot
x = number of outs

4 scenarios:
1. miss twice
2. hit 1st / miss 2nd
3. hit 2nd / miss 1st
4. hit twice

I won't bother calculating the probability of scenario 1 since you have zero EV in this case.

2. hit 1st miss 2nd

(probability hit 1st)*(probability missing 2nd given that you hit 1st)

x/44 * (43 - (x-1))/43 = x/44 * (44-x)/43 = x/44 * (44/43 - x/43) = x/43 - x^2/(43*44)

3. I'll spare the math as it should be obvious the answer is equivalent to scenario 2

4. Hit twice

(probability of hitting 1st) * (probability of hitting 2nd given that you hit 1st)

x/44 * (x-1)/43 = x/44 * (x/43 - 1/43) = x^2/(43*44) - x/(43*44)


Total EV of running twice:

let 'term x' = result for above calculation for scenario x

EV = S*term2*(1/2) + S*term3*(1/2) + S*term4

= S*(1/2)*(x/43 - x^2/(43*44)) + S*(1/2)*(x/43 - x^2/(43*44)) + S*(x^2/(43*44) - x/(43*44))

= x/43 - x^2/(43*44) + x^2/(43*44) - x/(43*44)

= x/43 - x/(43*44)

= (44*x)/(43*44) - x/(43*44)

= (43*x)/(43*44)

= x/44 = EV of running once