Simple Odds Question..

[stealyourface]

Ok so I was thinking of a theoretical hand, and ran it through the odds calculator on Card Player.

Hand 1: QhKh
Hand 2: Js5s

Flop: 10hJh2d

Now card player says that hand 1 is a 68.9% to 31.1% favorite.

I was always told that for an easy odds estimate on the flop, you take each out and add 4% for each one.

By that logic: 9 hearts, 3 Qs, 3 Ks, 3 As, and 3 9s...

(9+3+3+3+3) x 4 = 84%

what the hell am I doing wrong?

[LetYouDown]

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what the hell am I doing wrong?

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Well, for on thing...trying to apply generic formulas to more complicated scenarios like this. It's quite possible that your "formula" (4%) doesn't include knowledge of the other player's cards. It also seems at first glance like it's double counting some scenarios. For instance, you catch a heart on the turn and an offsuit K on the river.

[stealyourface]

Not to sound like a complete dumbass (which I am when it comes to math) but can you give an easy to understand answer with an example maybe.

Sorry I am just having a hard time following.

[uuDevil]

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I was always told that for an easy odds estimate on the flop, you take each out and add 4% for each one.

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That's a rough approximation that breaks down for large numbers of outs. A better approximation is:

1-P(missing on turn)*P(missing on river)

1-((47-21)/47)*((46-21)/46)=0.699

This is still just an approximation though. Somethimes you will hit one of your outs and still lose.

Edit: Since you know your opponents cards, that should be:

1-(45-21)/45*(44-21)/44=0.721

[pzhon]

[ QUOTE ]
Now card player says that hand 1 is a 68.9% to 31.1% favorite.

I was always told that for an easy odds estimate on the flop, you take each out and add 4% for each one.
...
(9+3+3+3+3) x 4 = 84%
...
what the hell am I doing wrong?

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The main problem is that you are using that estimate out of the context where it is reasonably accurate. It works much better in more common situations where you have 1-10 outs, not 21.

[stealyourface]

wait I take it back, the 4% thing is retarded.

But i do have another question for you...

Can you give me an easy formula to percentage to win based on outs?

[stealyourface]

Ok cool, thanks.

So if I have 1-10 outs I should use the 4% flop/ 2% turn calculation, and if I have more, I should do 1-P(not hitting on turn)*P(not hitting on river)?

[uuDevil]

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Ok cool, thanks.

So if I have 1-10 outs I should use the 4% flop/ 2% turn calculation, and if I have more, I should do 1-P(not hitting on turn)*P(not hitting on river)?

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It depends on how much accuracy you need. If you just want to know if you should call a bet, this rule of 4 should be fine most of the time. After all, if you have 8 or more outs, the pot will almost always be big enough to call (at least in most small stakes limit games), so it doesn't matter what method you use.

If you want accurate numbers for whatever reason, then you'll have to do more work or use a computer program like poker calculator or Pokerstove.

[Guernica4000]

Here's another way to get closer percentages than using the 4% method.

For example:
With a flush draw on the flop you have nine outs so 4x9= 36% but for every number of outs over 8 take that number and subtract it from the number of total outs (9-8=1) (36%-1=35%) and you get the exact number.

Say you have 15 outs: 15x4=60% then (15-8=7) (60%-7=53%)

Your 15 outs are 53% favorite.

For 21 outs. 21 x 4= 84% then (21-8=13) (84%-13=71%)

This is off by 2% from Card Player but it gets you closer to the real % than just multiplying the outs by 4 and it is easy to do in your head.