Re: \"ahead on the flop\"-equity?
 

[ QUOTE ]
OK, maybe i used the wrong word. So for clarification:

I have XX, villain has YY.

There are Z possible flops

on how many flops am i ahead (probability of winning >50%)
on how many flops am i behind (probability of winning <50%)

[/ QUOTE ]

So as not to spoil the atmosphere of challenge, I PMed you what I think you're looking for. It's not a complete solution because it won't do hand ranges, but I don't think it would be hard to write a script to do that.

I went looking for something to do this some time ago because it seemed to me that overall equity isn't quite as useful as knowing "where you're at". Normally we look at the board and guestimate how we think our equity has changed given our opponent's range, but a tool to do that accurately, at least away from the table, would be nice.

Re: \"ahead on the flop\"-equity?
 

[ QUOTE ]
Gonso, on what percentage of flops is 72o ahead of AA sharing both suits? I worked out the value myself, but the computation was tedious, and I'd like to see how to use PokerStove to do it instead. However, it doesn't look possible. If you can't come up with a figure using PokerStove, please admit it.

[/ QUOTE ]

Phzon,

This was a different question then the one posed by OP orgininally - I'd have sent him to you or Prob. forum if that is what was asked for from the get go

G

Re: \"ahead on the flop\"-equity?
 

[ QUOTE ]
[ QUOTE ]
Gonso, on what percentage of flops is 72o ahead of AA sharing both suits? ... If you can't come up with a figure using PokerStove, please admit it.

[/ QUOTE ]

This was a different question then the one posed by OP orgininally - I'd have sent him to you or Prob. forum if that is what was asked for from the get go


[/ QUOTE ]
You had a different interpretation, but as far as I (and others) can tell, this is what the OP asked all along.

Re: \"ahead on the flop\"-equity?
 

My answer was pretty clear to the question as it was posted, I answered it literally. If that wasn't what he meant, fine, it was later clarified.

Re: \"ahead on the flop\"-equity?
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Gonso, on what percentage of flops is 72o ahead of AA sharing both suits? ... If you can't come up with a figure using PokerStove, please admit it.

[/ QUOTE ]

This was a different question then the one posed by OP orgininally - I'd have sent him to you or Prob. forum if that is what was asked for from the get go


[/ QUOTE ]
You had a different interpretation, but as far as I (and others) can tell, this is what the OP asked all along.

[/ QUOTE ]

I have to admit I was (and may still be) confused by the way the question was phrased and it took me a while to see that. This is the tool I pointed the OP to:

http://people.ucsc.edu/~tbabb/programs/pokerodds/

Hopefully that is in fact what he wanted.

Re: \"ahead on the flop\"-equity?
 

[ QUOTE ]
This is the tool I pointed the OP to:

http://people.ucsc.edu/~tbabb/programs/pokerodds/

Hopefully that is in fact what he wanted.

[/ QUOTE ]
I think that's a good start. From the description, I don't think it recognizes that a draw may be a favorite over a made hand.

Re: \"ahead on the flop\"-equity?
 

[ QUOTE ]
From the description, I don't think it recognizes that a draw may be a favorite over a made hand.

[/ QUOTE ]

You are right. I sent the programmer an email and he confirmed it. As I understand it, it just evaluates the hands on a specified street and declares the best hand at that point the winner. It calculates the percentage of times a hand is a winner in this sense over a large number of randomly generated boards.

But this means I'm still confused! Let's see. The total equity, Et, can be written

Et= (NE1 + NE2 + ... + NEn + PE1 + PE2 + ... + PEm)/(n+m)

where NE is equity for the specified hand on a flop when the equity is negative for the specified hand against a second specified hand, n is the total number of such negative equity flops, PE is equity for the specified hand on a flop when the equity is positive for the specified hand, and m is the total number of positive equity flops.

We want to know m/(n+m).

Some rough psuedo code:

<font class="small">Code:</font><hr /><pre>
Let m=0; // # of +EV flops
Let nFlops= 0; // number of flops simulated
Let nWins=0; // number of times hero's hand wins
Specify hero's hand and villain's hand
for(nFlops=0; nFlops &lt; large #; nFlops++)
{
Deal a random flop
for(nTurnRiv=0; nTurnRiv &lt; large #; nTurnRiv++)
{
Deal random turn and river cards
Determine winner
If hero wins, nWins++
}
Calculate equity= nWins/nTurnRiv
If equity &gt;.5, m++;
}
Calculate proportion of flops where hero is ahead= m/nFlops
</pre><hr />

Am I close?

Re: \"ahead on the flop\"-equity?
 

That pseudocode looks ok. You'd want to count ties. You might want to evaluate all 990 turn and river combinations given a random flop. You can speed things up if you can get away with using a sample (possibly representative instead of independent) of 31 combinations, which is enough to figure out who is ahead with over 95% accuracy if one side wins at most 35%. However, that would still introduce a bias, which would get larger for closer flops. Flush draws also often win more than 35% due to running two pair or trips. If you are worried about speed but want more accuracy, a hybrid method would be to choose a few random samples, and then evaluate all combinations if the sample is close.

Are you planning to add this to the tools you have on your web page? If you are planning to implement this, I suggest keeping track of the observed equity distribution (the frequencies of each number of wins out of 990 or 1980), as this would be interesting. That would say how often 96s flops a big draw against AA, and how far behind AA is when it gets outflopped.

Re: \"ahead on the flop\"-equity?
 

[ QUOTE ]
Are you planning to add this to the tools you have on your web page?

[/ QUOTE ]

Yes, but I'm big on planning and not so great at execution. Thanks for your suggestions. You've given me a number of things to consider that wouldn't have otherwise occurred to me.

I originally started writing those programs to assemble pieces of code I could later use to write my own calculator(s). Unfortunately, I lack both programming skill and knowledge of efficient techniques. Also, I'm lazy and only code when I'm in the mood. My only advantage is that I'm stubborn. [img]/images/graemlins/smile.gif[/img]

Tim Babb wrote PokerOdds and solicits suggestions on his webpage. Judging from his quick and very helpful reply to my email, he is a nice guy. He has seen this thread but I don't know if he is a 2+2 member. If he were interested in adding this capability to his program, that would probably be the best hope for a quick implementation in a free calculator as I don't know of anything else that comes close (though I haven't looked in a while).

Re: \"ahead on the flop\"-equity?
 

As I was finally getting my simulation to work, I remembered this site.

For the case of AhAd vs. 7h2d, the results from my simulation, PokerOdds, and Flopalyzer give the approximately the same result: ~96.4% (edit: this is also the result calculated by pzhon).