Fold Equity

Well I came across some high stakes player today as he was instructing a low limit player on fold equity. The amateur asked how to calculate the probability to win, should the fold equity be 50% and the equity to win the pot at showdown be 25%. The pro said that you get it from 50%+50%*25%. Now this seemed outrageous to me! Generally when you see a '+' in the probability calculations, you can be quite certain to be wrong. Now I pointed this out and studied it a bit further, only to find that it is correct - but for a bit different reasons than I thought at the first glance.

The formula is actually win% = FE + (100%-FE) * EQ. So the fact that it happened to be 50% and 50% confused me at first, but should FE be 60%, the numbers would be 60% and 40% which would make more sense.

So I started to think how you properly calculate and came to the conclusion that it's done by substracting the probability of losing from 100% (reasonable assumption) and with the formula:
W% = 1-(1-FE)*(1-EQ)

Okay so, to prove whether he's right or wrong, I went right on to get that equation open and well surprise surprise, it eventually does go to the pro's (who apparently didn't come up with that himself) formula - liek this:

F1. W% = FE+(1-FE)*EQ
F2. W% = 1-(1-FE)*(1-EQ)

F1. W% = FE+(1-FE)*EQ
=> W% = FE + EQ - FE*EQ
=> W% = FE + (1-FE)*EQ

F2. W% = 1-(1-FE)*(1-EQ)
= 1-(1-EQ-FE+FE*EQ)
= 1-1 + EQ + FE - FE*EQ
= FE + EQ - FE*EQ
= FE + (1-FE)*EQ

Proof positive! \o/

So they go into the same format, effectively making my bitchin' to be in vain, but at least I managed to spend some time at work, thinking it out. So now you know easyish way to approximate your W% with a given fold equity that should help you with your analysis. You probably knew all this beforehand, but if you didn't, well I hope that taught you something!

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And well I did play a bit, not much, but just enough to get my confidence even higher. I played around 400 to 500 hands total of full and short-handed Omaha Hi (PLO50@PokerStars) and won around 4 buy-ins. People just felt like going broke with overpair or top pair and who am I to stop them. Here are a few gems from the session:
Better than average flop for 99xx
I wonder what they were expecting to see
Perhaps the safest board for AAxx in a while... Oh wait!
It wasn't all uphill though... quite bitter.

Yea well that's all for now, I might play a bit today and I'll keep posting stuff here in the coming days. Also my plan now is to get the Stars $100 promotion done, then move to Boss network for some bonii, then go to UB and/or Full Tilt and after I'm done with those, it should be lookin' pretty good for even as high as NL200, so I'll see if I'll stick to it. I have yet to get my schmuck out of MansionPoker as well since they have quite secure system with the cashouts - which of course is good, but a bit of a pain in the ass.

I feel very confident and I really think it's very hard for me to get into the bad play/tilt mode with the current session system I have. I hope it stays that way, but I believe I can control myself pretty well and not have that bi-weekly blow up. Above and Beyond! _o/