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]

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

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There aren't 52 cards left, there are 50.

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

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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

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There aren't 52 cards left, there are 50.

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

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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. /images/graemlins/frown.gif 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]

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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.

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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.

/images/graemlins/grin.gif

[Isles]

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

[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

[Gregg777]

I just have the calculator on my computer, it doesn't have Combinations and Permutations.

I have been wondering the same thing about sets by the river and other variables, and wanted to know how to go about it on my own.

[LetYouDown]

Is google an option?

1 - 48 choose 5/50 choose 5 in google will give you the answer.

[Gregg777]

Just tried it. That's cool!

Didn't know Google did that /images/graemlins/tongue.gif

[LetYouDown]

Google does everything. I'm still shocked that they're behind Yahoo. Granted, Yahoo has a ton of name recognition, but c'mon...who hasn't heard of Google and how vastly superior it is?

[Siegmund]

[ 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.



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1 - (45*44) / (49*50) is quite within reach of calculators without factorial buttons. In fact,
45x44 = 1980; 50x49 = 2450; 1 - 1980/2450 = 1 - 198/245 = 47/245 is quite doable with no calculator at all.

As the other posters have mentioned, lots of things cancel. 48C5 = 48*47*46*45*44/(5*4*3*2*1) and 50C5 = 50*49*48*47*46/(5*4*3*2*1), and when you divide 48C5 by 50C5, the 5*4*3*2*1, the 48, the 47, and 46 all go away.

Always pays to think before you start pushing buttons on a calculator.

[Luzion]

[ QUOTE ]
[ 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.



[/ QUOTE ]

1 - (45*44) / (49*50) is quite within reach of calculators without factorial buttons. In fact,
45x44 = 1980; 50x49 = 2450; 1 - 1980/2450 = 1 - 198/245 = 47/245 is quite doable with no calculator at all.

As the other posters have mentioned, lots of things cancel. 48C5 = 48*47*46*45*44/(5*4*3*2*1) and 50C5 = 50*49*48*47*46/(5*4*3*2*1), and when you divide 48C5 by 50C5, the 5*4*3*2*1, the 48, the 47, and 46 all go away.

Always pays to think before you start pushing buttons on a calculator.

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What you just said is the "long method." Luckily lots of the bigger numbers cancel out in something like C(48,5) but you wouldnt be so lucky if it was like C(52,24) and you had to do it by hand.

In the end, imo its a lot easier to do my method instead of doing a combination divided by a combination. Just dont be dumb and make simple mistakes like I did. /images/graemlins/frown.gif

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

1 - 0.808 = 0.192 = 19.2%

Hello, I am a newbie, and I was wondering what the variables in the equation below represent. I assume that r = the number of cards to come, and C(N,r) is the probablitiy of catching your set. What does N represent?

[Luzion]

[ QUOTE ]
Hello, I am a newbie, and I was wondering what the variables in the equation below represent. I assume that r = the number of cards to come, and C(N,r) is the probablitiy of catching your set. What does N represent?

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C(N,r)

The C is just to tell you that this is a "combination" problem; this solves problems where order is NOT important and you want to find how many different ways "r" can come out from a sampling of "N."

If you go back to LetYouDown's answer, he finds out what C(50,5) is. This means he is calculating how many different ways 5cards can uniquely come out from a sampling of 50cards. (Because OP already is holding two pocket cards)

Btw, C(50,5) = 50!/45!5! = 2,118,760