exact odds at the Gold/Binger/Wasicka hand...

[quirkasaurus]

What if it played out this way:

Binger TT -- ALL IN AFTER THE FLOP
Gold -- folds
Wasika -- 8s7s CALLS

FLOP: 6s 5s X

What are Wasika's odds to make his flush, or straight
to beat Binger's Tens ?

I calculate them to be:

15 outs:
45 chances, and then 44 chances if he misses... so...

( 15 + 15 ) / (( 45 + 44 ) / 2 ) == 66% about.

My buddy says Wasika's odds were much lower, maybe 54%.
What is correct ?

[Harv72b]

Check out a program called PokerStove--it'll do all this math stuff for you. [img]/images/graemlins/wink.gif[/img]

In particular, you need to remember that the turn card can have an effect on Wasicka's outs--if it's a T, for example, then it gives Binger a full house draw. If it's a 7 or 8, then it gives Wasicka additional two pair/trip outs. I also don't remember off-hand if Binger held the T[img]/images/graemlins/spade.gif[/img] in the hand, but that affects Wasicka's chances as well as it could give Binger a redraw to a higher flush when the turn is a spade.

Flopping an open-ended straight flush draw does make you a favorite in a heads up pot against an overpair, even when the overpair includes a card in your suit. I actually just ran that sim yesterday after finding myself in the same situation during a tournament, although it turned out my opponent just had two overcards that time. The example I checked out was Ts9s vs. AsAh after a 8s7s4h flop; my T9 was about a 52.5 to 47.5 favorite on the flop. I suspect that Wasicka's hand would have been about the same (or a bit higher if Binger did not have a spade).

[Lego05]

Well I happen to know that 15 outs twice is about 55%. I don't know the proper formula to figure this out. I should, but I don't....I just have this situation memorized. If ou want exact odds you need to fill in Binger's suits and the last card on the flop, but we can get a pretty good approximation. Let's see:


Text results appended to pokerstove.txt

990 games 0.265 secs 3,735 games/sec

Board: 6s 5s Ac
Dead:

equity win tie pots won pots tied
Hand 0: 56.263% 56.26% 00.00% 557 0.00 { 8s7s }
Hand 1: 43.737% 43.74% 00.00% 433 0.00 { TdTh }

[ocdscale]

[ QUOTE ]

I calculate them to be:

15 outs:
45 chances, and then 44 chances if he misses... so...

( 15 + 15 ) / (( 45 + 44 ) / 2 ) == 66% about.

[/ QUOTE ]

Your calculation is wrong.

A quick first approximation is:
2/3rd chance of missing on the turn
~2/3 chance of missing on the river
Total ~4/9 (2/3 x 2/3) chance of missing the turn and river
So ~5/9 chance of hitting, which is ~55%

[AngusThermopyle]

[quote
I calculate them to be:

15 outs:
45 chances, and then 44 chances if he misses... so...

( 15 + 15 ) / (( 45 + 44 ) / 2 ) == 66% about.



[/ QUOTE ]

See the above for the correct answers.
The flaw in your calculations is that you are counting some Turn+Rivers events as winners twice, ie
4 [img]/images/graemlins/heart.gif[/img] on Turn (straight winner) followed by A [img]/images/graemlins/spade.gif[/img] River (flush).
Since you hit the Turn roughly 1/3 of the time and on the river 1/3 of the time, roughly 1/9 of the time both cards will help. 1/9 = ~11%. So your approximation would be about 11% too high.
66 - 11 = 55.

[quirkasaurus]

Thanks for the replies. It took a few days to find my
thread again.

So how should one calculate odds ??

I saw a book once say that the shorthand method,
is just count up your draws, multiple by 2 and
subtract 2.

In this case, that would come out to be 58%.

Angus -- reread your answer while replying.

I think I got it: The 2nd card odds only come
into play when the first odds don't hit.

So... to rephrase:

(15/45) + ( 30 / 45 ) * ( 15 / 44 )

( outs/cards_left ) + ( 100 - (outs/cards_left) ) *
( outs / ( cards_left - 1 ))

Sound good ? Do you guys actually do these
calculations over the table ?? Or are there
only a few of these numbers that are really
important ?

Do you agree with these calculations:

Post-flop:
%-age needing 1 to make flush: 36%
%-age open-ended straight draw: 32%
%-age to improve after hitting trips: 34% ( 7 outs, 10 on river if you miss )

And finally, do you know what these odds are:

Pre-flop:
%-age hitting 2 pair w/ 2 different hold cards:
%-age hitting trips with a pocket pair:

[binions]

[ QUOTE ]

So how should one calculate odds ??


[/ QUOTE ]

With a draw with 2 cards to come, you figure out 1 minus the chance of missing the draw = chance of hitting the draw. For a 15 out draw:

1 - (30/45 * 29/44) = 1 - .439 = .561 or 56.1% to hit the draw.

Your original method overcounted the times you hit your draw on both the turn and the river.

[quirkasaurus]

Ok, thanks.

[PantsOnFire]

[ QUOTE ]
So how should one calculate odds ??

I saw a book once say that the shorthand method,
is just count up your draws, multiple by 2 and
subtract 2.

[/ QUOTE ]
In situations like this, it is too difficult to calculate the odds at the table. It is much better the memorize your possibilities.

Here, with a OESFD, you need to figure how you stack up against various hands. Oh and that X is important.

Against an overpair, you are about 55%. Against a set you are about 41%. Against AsKs you are about 44%. Against two pair, you are about 47%. Against other hands you are very good. Now you can start figuring out what is likely. AsKs is a very specific hand. If X=2, it's likely a brick. Two pair is probably not likely here either. Go from there. If there is a 2 as X, I'm going all-in figuring I'm ahead most of the time and even if not, it still looks pretty good.

You should generally remember those numbers or approximations. The most important number is the worst you can do which is a set. It would be pretty rare for the odds not to be there to go to war with an OESFD as you can see. That's the really important thing.

Of course, on the turn, things are completely different but that's another story. If it's a brick, all those odds are basically cut in half. If it's 9 or 8, now you can count outs.