How is this calculated?

[jstill]

how did u decide to leave out the hearts as a means to compensate for the boat possibilities?

also we have AhQh villain has 88

fwiw I often use the 4x rule in quick calculations but this seems different than a time Id assume it would hold up, although your calculations seem to?

[jay_shark]

The approximate probability that pocket 8's wins with redraws is 6/41 + 35/41*9/40 ~ 33%

Again , let me emphasize that this is a very close approximation as the exact probability involves looking at different cases .

The approximate probability that A-Q H wins with a flush in hearts if we exclude 8's redraws is 6/41 + 35/41*6/40 ~ 0.2743 . This is very close to the actual answer since in some of these cases , 10-9h wins with a straight flush .

In other words , pocket 8's doesn't have much additional outs with his redraws . It is negated by the flush outs which does not increase his chances of winning much at all .

[R Gibert]

[ QUOTE ]
R.Gilbert , it looks like you're trying to be a nit here .

[/ QUOTE ]
Not at all.

You assert the hearts are offset by the redraws, but give no justification. How do you determine that they are offset? Are you psychic?

[ QUOTE ]
The runner queens and runner aces are not going to change the outcome very much . Why do you not see this ?

[/ QUOTE ]
I'm stupid.

Runner AA,QQ or AQ should amount to about 2.5%

[ QUOTE ]
I will repeat again , the flush cards will be somewhat offset by your redraws with 8's .

[/ QUOTE ]
Except that you are not repeating. You've inserted the word, "somewhat," which alters what you said quite a bit.

[R Gibert]

[ QUOTE ]
[ QUOTE ]
The runner queens and runner aces are not going to change the outcome very much . Why do you not see this ?

[/ QUOTE ]
I'm stupid.

Runner AA,QQ or AQ should amount to about 2.5%


[/ QUOTE ]Wow! I really am stupid! I'm getting < 1% now.

I gotta concede this one.

[jay_shark]

R Gilbert , do you not see any significance in using the 4x rule , even if you may be off by a percent or two ?

Are you that obsessed in knowing how to calculate the exact probabilities ?

I think you are since you decided to come up with your own version of the pocket pairs chart because Phil Gordon's was not accurate enough .

[jay_shark]

[ QUOTE ]

You assert the hearts are offset by the redraws, but give no justification. How do you determine that they are offset? Are you psychic?


[/ QUOTE ]

Read above . I gave a pretty good explanation already .
Did you not read it ?

[crashzzz]

[ QUOTE ]
[ QUOTE ]

You assert the hearts are offset by the redraws, but give no justification. How do you determine that they are offset? Are you psychic?


[/ QUOTE ]


Read above . I gave a pretty good explanation already .
Did you not read it ?

[/ QUOTE ]

[ QUOTE ]
In other words , pocket 8's doesn't have much additional outs with his redraws . It is negated by the flush outs which does not increase his chances of winning much at all.

[/ QUOTE ]

As in, any Q's (including Qh) or 7's or runner/runner pair on the board will give 88s a full house. Thus, 3outs+3outs+ (~1out) = 7outs
Now, the flush draw has 8 outs (remember, Qh gives a full house)

8-7=1outs.

Hence, like Jay_Shark mentioned, the reason why he didn't include the hearts as outs is because these outs are offset by your redraws .

[R Gibert]

There are 820 possible turn+river deals excluding order:
The AhQh win with a flush on 136 of these.
The 8s8c win with quads/fullhouse on 237 of these.

In other words, the 8s8c win about 10.4% more often with quads/fullhouse than AhQh do with a flush. They do not offset as you claim.

However, by adding in 6c5c's backdoor club flush which win 28/820 of the time and adding in Th9h's str8 flush which win 79/820 of the time, then I get:

233/820 = 237/820 [approx]

I may as well addin AhQh's quad/fullhouse possibilites, which win 16/820 of the time, but they do not change things much:

249/820 = 237/820 [approx]