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Old 10-23-2007, 05:37 PM
br.bm br.bm is offline
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Join Date: Jul 2006
Posts: 601
Default Re: Help me with this math...

the first 100 is villians complete stack
and the second 100 is wrong and should be OS (before the push)
EV = 0 = F% * [pot] + (100%-F%) * [Oeq * VS - Veq * OS]
We want to isolate Oeq
use this equation to eliminate Veq:
100% = Veq + Oeq
Veq = 100% - Oeq
0 = F%*Pot + (100%-F%)* [Oeq*VS - (100%-Oeq)*OS]
100% = 1

0 = F*Pot + (1-F)*[Oeq*VS - (1-Oeq)*OS ]
0 = F*Pot + (1-F)*[Oeq*VS - OS + Oeq*OS]
multiply 1-F with the last bracket:
0 = F*Pot + Oeq*VS - OS + Oeq*OS -Oeq*VS*F + F*OS + Oeq*OS*F
build a bracket to isolate Oeq:
0 = F*Pot - OS + F*OS + Oeq(VS+OS-VS*F+OS*F)

Oeq = [OS-F(OS-Pot)] / (VS+OS-VS*F+OS*F)
F=0,6
Pot = 15,5
OS = 100-3,5 = 96,5
VS = 100
Oeq = [96,5 - 0,6(96,5-15,5)] / (100+96,5 - 100*0,6+ 96,5*0,6)
Oeq = 24,6%


I'm not sure if this is right ... maybe I use pen and paper tomorrow and do it again.
24% pot equity seems pretty low ... but hey villian folds 60% of the time.
So if we do it 100 times:
we make 12*60 when he folds = 720
How often do we have to win his 100 to make it 0 EV?
If Oeq is 50% we don't loose or win anything on the other 40 hands. so we are very +EV
If he wins 75% and we 25% then he wins
75% * 40 * 100 = 3000
and looses
25% * 40 * 100 = 1000
-------------------------
-2000 for us

looks like 24% is wrong
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