Chance of winning

[Gene2x]

How do you calculate your hand's chance of winning on the flop? For instance, you hold QJ, have six opponents (random cards), and the board is 6-8-5. Software tells me my equity (chance of winning) is about 7%.

Is there a quick way to ballpark the answer using some simple math? Or, do you have to know basic Hold'em statistics and then do math using those numbers? Is it even possible to do within 30 seconds before your PartyPoker timer expires?

Thanks,
Gene

[Gene2x]

Here's another problem and how I analyzed it. Please tell me if I'm going about it wrong:

3 opponents (random cards), you have K4, board is T-A-K.

Analysis: Chance of anyone having an A on the flop (one on the board) is about 13%. With three opponents, there's a 40% someone has an A. There's a 17% chance anyone has any one card of a particular rank (not on board). With three to a straight on the board here, there's a 51% chance someone has a J and an 18% chance they'll get the Q for a straight by the river. Multiplying the odds of both happening gives about 9%. Same calculation for someone having a Q and hoping to hit a J.

Odds of being beat by river: 40% + 9% + 9% = about 60%. Equity is about 40%.

Now, in actuallity, there were two of the same suit on the board. So, it seems like the situation is a lot more complicated and I must be missing stuff. Software tells me my equity is 41%. So, I came close- but was it coincidence?

[AaronBrown]

You can only do this quickly in simple cases. For example, if you hold A/images/graemlins/heart.gif 2/images/graemlins/club.gif and the flop is K/images/graemlins/diamond.gif Q/images/graemlins/heart.gif J/images/graemlins/heart.gif, you're likely to win if a heart shows up, win or tie if a T shows up, possibly win if an A shows up, and probably lose for most of the other turn and river card combinations.

In the example you gave, there are too many unknowns. Someone could have a straight or straight draw; someone could have a pair, two pair or a set; someone could have a pocke pair; someone could have A or K or both. You didn't give suits, but flushes are another thing you have to analyze. For each of combination of cards for the six other players, you have to figure what could happen on the turn and river.

This is staightforward to analyze by computer, although it can take a long time to run. For practical poker, you analyze the important situations, like top pair, top kicker against someone who called your preflop raise from the big blind. You do this beforehand, either by yourself or relying on someone's book. You don't worry about what to do with QJ when you miss the flop; and you don't worry about random other hands.

Allegedly, the following is MEANT to work to tell you the odds of hitting on the next card (figures in percentages).

On the turn - multiply the number of outs by 4.
On the river - multiply the number of outs by 2.

In this particular case, you've got pretty decent odds of hitting your outs - 4x12, assuming the flush isn't on and your opponents don't have any 9, 10, J or Q, = 48% of hitting one of your outs. Hitting an out on the river is 2x11 = 22%.

However, with 6 opponents, your equity is reduced considerably (48/6 = 8%) (22/8 = 2.75%).

Which works for me if I've got time to work it out...

[Jesus H]

[ QUOTE ]
Allegedly, the following is MEANT to work to tell you the odds of hitting on the next card (figures in percentages).

On the turn - multiply the number of outs by 4.
On the river - multiply the number of outs by 2.

In this particular case, you've got pretty decent odds of hitting your outs - 4x12, assuming the flush isn't on and your opponents don't have any 9, 10, J or Q, = 48% of hitting one of your outs. Hitting an out on the river is 2x11 = 22%.

However, with 6 opponents, your equity is reduced considerably (48/6 = 8%) (22/8 = 2.75%).

Which works for me if I've got time to work it out...

[/ QUOTE ]

Problem with the above calculation is that you only have 6 outs on the flop, not 12. (3 Queens and 3 Jacks). I don't know how zyg is coming up with 12 outs.

So you have a 24% chance of hitting on the turn, and a 12% chance of hitting on the river, but as noted by zyg, this doesn't mean you have the nuts (of course).

Generally, fold your overcards when you don't hit on the flop. Not an absolute... depends on who you're up against, what you've read them for, etc., etc. It's amazing how many players chase with overcards at the casinos. I LOVE those players! /images/graemlins/wink.gif

[Gene2x]

Ok. So, basically, unless it's a simple case of outs, don't worry about trying to figure out equity since without a computer it just isn't practical in a live game.

12 outs because I'm counting hitting the straight draw (9s and 10s)...

And then you've got to count the flush possibilities...

It's a rough calculation...

/images/graemlins/grin.gif

[ QUOTE ]
12 outs because I'm counting hitting the straight draw (9s and 10s)...

And then you've got to count the flush possibilities...

It's a rough calculation...

/images/graemlins/grin.gif

[/ QUOTE ]

9s and 10s as outs. Come on be real.

Technically, he could hit a 9 and 10 for the gutshot straight draw. It is possible (and Lord knows I've seen it happen to me online far too often).

As I said, it's a rough calculation.

Gut shot is 1.5 outs, back door straight draw is another 1.5 outs.

[Gene2x]

You must be talking about the QJ problem. The software puts it at 7%. That's about 1.5 outs total.