Odds of hitting set with all 5 cards, not just flop.

[Isles]

I have done a search but can't find the odds of hitting your set by the river.

I am not looking for the odds from the flop to the river, instead, I am looking for the odds preflop, knowing there are five cards to come.

For example, it is 7.5 to 1 to hit on the flop, so I assume the odds of hitting by the time all five cards are out is close to 6 to 1?

[Luzion]

[ QUOTE ]
I have done a search but can't find the odds of hitting your set by the river.

I am not looking for the odds from the flop to the river, instead, I am looking for the odds preflop, knowing there are five cards to come.

For example, it is 7.5 to 1 to hit on the flop, so I assume the odds of hitting by the time all five cards are out is close to 6 to 1?

[/ QUOTE ]

(50/52)(49/51)(48/50)(47/49)(46/48) = 0.815

1 - 0.815 = 0.185

Probability is 18.5% you will get a set or better by the river.

[LetYouDown]

You hold a specific pair, say 3-3. The odds that a 3 will appear on the board:

1 - C(48,5)/C(50,5) = 19.18%

[LetYouDown]

[ QUOTE ]
(50/52)(49/51)(48/50)(47/49)(46/48) = 0.815

[/ QUOTE ]
There aren't 52 cards left, there are 50.

[ QUOTE ]
Probability is 18.5% you will get a set or better by the river.

[/ QUOTE ]
No. This is wrong for what you're getting at, and still doesn't factor in straights/flushes, etc.

[Gregg777]

LetYouDown,

Can you please explain the formula?

1 - C(48,5)/C(50,5) = 19.18%

By "explain", I just mean how do I enter that into a caluclator to get the same figure?

[Luzion]

[ QUOTE ]
[ QUOTE ]
(50/52)(49/51)(48/50)(47/49)(46/48) = 0.815

[/ QUOTE ]
There aren't 52 cards left, there are 50.

[ QUOTE ]
Probability is 18.5% you will get a set or better by the river.

[/ QUOTE ]
No. This is wrong for what you're getting at, and still doesn't factor in straights/flushes, etc.

[/ QUOTE ]

Yeah damn. Just woke after 2 hours of sleep and now I couldnt even figure out this simple problem. [img]/images/graemlins/frown.gif[/img] I was sitting at my screen trying to figure out why our answers werent identifical because our technique is basically the same thing. Good job.

It shouldve been (48/50)(47/49)(46/48)(45/47)(44/46) = 0.808

1 - 0.808 = 0.192 = 19.2%

P.S. When I said set or better, I meant you make a set/quads with your pocket pair and or fill up to a boat. It was implied, but I guess it wasnt obvious.

[LetYouDown]

[ QUOTE ]
P.S. When I said set or better, I meant you make a set/quads with your pocket pair and or fill up to a boat. It was implied, but I guess it wasnt obvious.

[/ QUOTE ]
No worries. It took me about 30 seconds of staring to figure it out myself. And yes, it was implied...but if he's asking this question, odds are he can't necessarily derive that. That's the only reason I even mentioned it...it was obvious what you meant.

[Luzion]

[ QUOTE ]
LetYouDown,

Thanks for the percentage.

Can you please explain the formula?

1 - C(48,5)/C(50,5) = 19.18%

By "explain", I just mean how do I enter that into a caluclator to get the same figure?

[/ QUOTE ]

If your calculator has a PRB or a nCr key then just use that and enter in the two variables. Otherwise...

C(N,r) = N!/r!(N-r)!

Im assuming you got at least a factorial button.. otherwise you are gonna be really doing this the loooooong way.

[img]/images/graemlins/grin.gif[/img]

[Isles]

Thanks guys, better than I expected [img]/images/graemlins/cool.gif[/img]

[LetYouDown]

It would probably be easier with excel or google if you have those tools available. I've illustrated combinations below, sorry if it's vague. If you have trouble following any of it, let me know. Luzion's math is fine, he just had the wrong numbers the first time. You can use that approach if all you have is a calculator. Most scientific calculators have Combinations and Permutations.

C(N,R) = N!/(N-R)! * R!

...so:

C(48,5) = 48!/(48-5)! * 5!

X! = X * (X - 1) * (X - 2) * ... * 1

5! = 5 * 4 * 3 * 2 * 1

48!/43! has a lot of repeating numbers, so it's just (48 * 47 * 46 * 45 * 44)/(5 * 4 * 3 * 2 * 1).

Hope this helps