Wait for the turn for more equity or not?

[chief444]

Yeah, that's better. Obviously it's never 100% because not everyone plays any 2 suited.

[Paxosmotic]

[ QUOTE ]
I think we should put out some kind of bounty for someone to deliver a correct calculation showing that hero does in fact have an equity edge. At this point my intuition suggests he does have a slight edge but if someone could stick in some ranges for villains and produce some kind of average number I think that would be an extremely useful contribution to the forum.

[/ QUOTE ]
I'm doing it, I just gotta know. [img]/images/graemlins/laugh.gif[/img] Gimme a while, this could take days.

[Paxosmotic]

I can't seem to get PokerStove to accept that many hands. I enumerated every possible hand for villain to have and it doesn't like that many entries.

[VBCurtis]

Deranged already fixed it, but I want to explain some math:
Paxo logic:
If each player is 1 in 5 to have something, a field of 5 players is then 5 in 5 to have it.
Deranged logic:
If each player is 1 in 5 to have something, they are 4 in 5 to not have it. The probability someone has it is then 1 minus the 4 out of 5 for each of 5 players: 1-(.8)^5, since by def'n someone has it only when it's not the case that nobody has it. Find Pr(nobody has it), subtract that from 1.

Paxo, if you wish to combine probabilities of independent events, you have to be a little more precise than just multiplying.

As for calculating equity, what range are we putting the flop bettor and caller on? What hands other than 2 pair, a spade (or flush), or top pair would someone call with? (bettor is noted to be capable of bluff, so his range must be very wide). If we decide this, calculating equity seems pretty easy.
If you want to calculate actual mathematical chance of spades in villain's hands, we need to make assumptions about spades in the folders' hands. 4 people folded; clearly none of them had two spades. How big a naked spade would a SS player need to call here? Ten? 8? Decide on this cutoff, and we can calculate prob of spade lower than T or 8 in folded cards, and then find actual prob of spades in each hand.
I can apply as much prob theory as you wish, but if you want accurate equity, we have to make more precuse assumptions about what was folded/called.
-Curtis

[W. Deranged]

I really doubt we can come up with a number by direct calculation that anyone is going to be confident with.

I would really like to know one thing (which I should know how to do based on all that damn contest math.....)

How exactly do we calculate the exact number, without any exceptions as to what hands do and do not get played, that some player among 8 (or whatever number) is holding two spades?

Calculating the number that no one has 1 spade is quite easy, but two spades becomes quite small because we have to start accounting for the fact that different villains might have 1 but not 2 spades in their hands, and that affects the likelihood others will have spades.

I haven't given the calculation much thought but I'd like to figure it out.

[crunchy1]

[ QUOTE ]
I really doubt we can come up with a number by direct calculation that anyone is going to be confident with.

[/ QUOTE ]
Nor should you need to. There are other factors at work besides equity that need to be factored into the equation.

I'm not trying to dissolve what is an interesting discussion. I think it deserves attention that there is more to this problem than just factoring the equity (specifically since from what I've seen most of those calculations are being based on 5 players where there could in fact be only 3 - regardless of Hero's flop action).

[Paxosmotic]

[ QUOTE ]
If each player is 1 in 5 to have something, they are 4 in 5 to not have it. The probability someone has it is then 1 minus the 4 out of 5 for each of 5 players: 1-(.8)^5, since by def'n someone has it only when it's not the case that nobody has it. Find Pr(nobody has it), subtract that from 1.

[/ QUOTE ]
I like it. You'd never know I have credits in statistics. I need to read more on the subject and stop getting lost.

Deranged said: [ QUOTE ]
I think it is basically impossible to make any calculation of hero's equity edge here by only considering pre-flop distributions of opponenent's hands.

Hero's hand is extremely vulnerable and is laying big reverse implied odds. Hero could be dodging in the neighborhood of 15 - 20 cards or even more when he is ahead, so just figuring out how often he won't be against a set, two pair, or a made flush is really not an accurate rendering of hero's equity.


[/ QUOTE ]

Yessss.

My blind ass guess is that if Hero is not against a made flush then it's at least 90% I'm against a flush draw. So minimum is .33 * .90 = 30% of the possible equity is gone for flush draws say another 17% for a made flush or 47% gone. So even if hero has 50% of remaining equity that is only 24% pot equity. That's my guess which puts the hero on shakey ground as far as pushing the pot goes - at least on the flop.

And one more comment,

This discussion and all your replies are awesome. I'm learning.

Thanks.

[W. Deranged]

Fep,

Good job on coming up with an interesting hand for one of your first posts. This one is pretty thought provoking, in my opinion.