Wait for the turn for more equity or not? - Page 3

Paxosmotic · #21 08-01-2005, 01:50 PM

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But how do I know I'll win more than 33%. Certainly there is the possibility that someone has a made flush, a set or two pair. So were I have the problem is in knowing if I indeed have an equity edge. Knowing that sure helps in deciding how to play the hand.

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Odds of flopping a flush are 1 in 119. So conversely, anyone holding a suited hand was 1 in 119 to hit this flop. Even if everyone stay saw the flop stays in that's still only 7 in 119, 5.88%.

Odds of flopping two pair is slightly less than 3%, I can't remember right now, we'll say it's 2.8%. Times all 7 people is 19.6% chance that someone just flopped two pair.

Odds of flopping a set is the chance that someone had a pair (1 in 17) times the chance of flopping a set (1 in 8.5) times the number of people (7): 4.84%

So the combined chances of someone holding a flush or a set or two pair in this hand is 30.32%. That should give you a pretty good idea.

chief444 · #22 08-01-2005, 01:52 PM

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Odds of flopping a flush are 1 in 119. So conversely, anyone holding a suited hand was 1 in 119 to hit this flop. Even if everyone stay saw the flop stays in that's still only 7 in 119, 5.88%.

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Not after you see a monotone flop.

I'm not saying we should be concerned about a flush yet. Just pointing out your math mistake.

W. Deranged · #23 08-01-2005, 01:54 PM

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.

Paxosmotic · #24 08-01-2005, 01:55 PM

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Odds of flopping a flush are 1 in 119. So conversely, anyone holding a suited hand was 1 in 119 to hit this flop. Even if everyone stay saw the flop stays in that's still only 7 in 119, 5.88%.

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Not after you see a monotone flop.

I'm not saying we should be concerned about a flush yet. Just pointing out your math mistake.

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Yeah, that's why it took me so long to post the math. I think the logic of my working backwards could be slightly flawed. But the chances of flopping a flush are 1 in 119 for everyone at the table, and the only way to do that is with a monotone flop, so that means everyone at the table has exactly a 1 in 119 chance of flopping a flush if they hold a suited hand. I'm still not sure I'm approaching the math problem itself correct, but the above statement is correct.

Paxosmotic · #25 08-01-2005, 01:56 PM

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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.

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I wouldn't go so far as to put our equity at >69% (the chances of those things not happening), but it's important that hero understands the possibility of these things. It's like looking at a flop of T98 and saying "does villain have QJ?" the answer is the vast majority of situations is "probably not." I was just trying to put some numbers to it.

W. Deranged · #26 08-01-2005, 02:01 PM

Paxo,

I definitely commend the effort of trying to get some numbers and I think that's a good place to start. We should note, though, that if hero is dodging something like 15 cards on both streets, we need to discount hero's equity by something like 60% or so. So if we start with your 69% number, we are down at 41% or so already, and I think that there's a lot we haven't factored in.

I think this problem is mathematically quite complex. I think hero may be the most likely winner of this hand, but I think I can say with a fair amount of confidence that he does not have majority equity and is hence going to lose this hand the majority of the time.

About the only more solid conclusion I can come to is that hero's flop equity has very, very high variance based upon the distribution of hands for villains. It is for this reason I think that arguments for waiting until the turn have some merit, as on the turn the variance on hero's equity has reduced a lot more, and, if for no other reason, on the turn we are more likely to make a correct decision.

Does everyone see what I mean by this? Let me know if I've confused myself.

mdob · #27 08-01-2005, 02:04 PM

You're right that we may not have an equity edge. I got caught up in arguing that we should raise if we have an edge that I neglected that part.

That being said, I think we probably do have an edge, just a very small one. I can certainly see us not having an edge, so I won't argue that and, of course, agree that we don't want to raise without one.

Paxosmotic · #28 08-01-2005, 02:05 PM

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Odds of flopping a flush are 1 in 119. So conversely, anyone holding a suited hand was 1 in 119 to hit this flop. Even if everyone stay saw the flop stays in that's still only 7 in 119, 5.88%.

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Not after you see a monotone flop.

I'm not saying we should be concerned about a flush yet. Just pointing out your math mistake.

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Here's a better and frankly the correct way of doing the math. It just took me a bit longer than I'd like to realize it.

The flop came all of one suit with the J93[img]/images/graemlins/spade.gif[/img] If we remove those from the 1,326 preflop hands we're left with 1,176 possible hands. Of those 1,176 starting hands that are possible if this is the flop, the 45 remaining combinations of spades just flopped a flush. Thus, the correct odds of someone holding any two cards having a flush is...

3.8265% (nowhere near the figure I pulled out of my ass in the last post)

Multiplying it times the five players left in the hand when it's hero's time to act gives us...

... a 19.132% chance that someone holds a flush (theoretically)

Fair enough? Those numbers could come in handy, I like what we've done here.

W. Deranged · #29 08-01-2005, 02:06 PM

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.

W. Deranged · #30 08-01-2005, 02:12 PM

Pax,

FWIW it's going to be more correct to take that 3% number and then use it to calculate the odds no one has a flush. It will be more accurate than multiplying that number times 5.

Using that slightly more correct approach yields:

1 - (1-.038265)^5 = 17.72%

which is a better number.

It is still not the correct number, as it doesn't account for the fact that the hands of various villain's aren't independent trials; the odds one opponent has a flush goes up if we know that another one doesn't, and so forth.