How often are absolute nuts dealt?

[luckycharms]

What percent of the time would the absolute nuts be dealt in a 3 person game? I know that's very few people, but how often would the absolute nuts get dealt? How about if 4 of a kind wasn't available?

[ccwhoelse?]

i'm a little thick headed so maybe you should try to be a little bit more clear with your question. /images/graemlins/confused.gif

[luckycharms]

Out of all of the flopped, turned, and rivered cards, there is going to be one combination of cards (including your pocket cards) that will be the best possible hand. Most of the time, (in 3 person hold em, at least) the winner wins with a low flush or 99, even though a straight flush is possible. My question is, how often does someone get those two cards? I know there's a billion different instances, and must vary greatly (which might require a detailed answer,) but approximately how often does that nut flush or 4 of a kind get dealt? This may be too complex of a question to answer, but I'd appreciate some help.

[Ed Miller]

This may be too complex of a question to answer, but I'd appreciate some help.

This is not a complex question. All you have to do is a monte carlo sim.

I call "not it"!

[Bozeman]

One could calculate the exact probability (for various kinds of boards, and the probability of such a board) too.

Definitely not it,
Craig

[ccwhoelse?]

[Drunk Bob]

Appox 1 times out of 71 someome will be dealt AA.For more info you might want to ask BruceZ.

[DrSavage]

Depends on who's dealing

[Drunk Bob]

the absolute nuts when? AA is the asolute nuts preflop after that it changes with each card.

[Drunk Bob]

Idon't think your Question has any answer.


Except. IT Depends.

[Bozeman]

Slightly different, but Brian Alspach calculates the chance that AA,AKs-A9s make the nuts here: PokerDigest (http://www.math.sfu.ca/~alspach/pokerdigest.html) , under the caption Optimal Boards. A9s makes the most nuts (3.6%), so the probability that someone makes the nuts in a threehanded game is less than (much less than) 10.8%.

[Drunk Bob]

t00 ansewer you r Q uestion the aaabsolute nuts is dealt every hand. It just changes with each additional card so your original question has no meaning.

[Drunk Bob]

What values do you enter? AA @@ 77 27 43 THEY COULD ALL MAKE THE NUTS ON THE FLOP AND LOSE THEIR NUTTINESS BY THE RIRER. /images/graemlins/shocked.gif

[Ed Miller]

What values do you enter? AA @@ 77 27 43 THEY COULD ALL MAKE THE NUTS ON THE FLOP AND LOSE THEIR NUTTINESS BY THE RIRER.

I never lack nuttiness on the rirer with @@.

[Copernicus]

I believe what you are asking is that,since given any 5 card board there are between 1 and 23 card combinations that make or tie for the nuts (unless the board is already the nuts), what is the probability that one of 3 people has the nuts.

1-(1-1/1081)^3 to 1-(1-23/1081)^3 (.25%-6.2%) would bound it (disregarding when the board is the nuts). That "feels good" as a range since I might see the nuts myself once every couple of hours if I'm cold and 2-3 times if I'm running well.

Enumerating it and calculating shouldnt be that hard though.

<font class="small">Code:</font><hr /><pre>
Board texture Card combos for the nuts

4 to a SF (1 x 46)/2 = 23 make SF
3 to a SF 1 make SF
Trips or full house 1 or 23 make top quads
One pair 1 make quads
Two pair 1 make top quads
4 flush no pair (1x46)/2= 23 make nut flush
3 flush no pair (8x1)/2= 4 make nut flush
4 straight no pair no flush (1x46)/2= 23 make nut str8
3 straight no pair no flush (8x4)/32= 16 make nut str8
unconnected rags (3x2)/2 = 3 make top trips
</pre><hr />

Divide those by 1081 and weight by the probability of the board and youve got the answer (if I havent missed any) for any particular person to get the nuts.

I may be miscounting one or two of those, but I was up too late to think now!

[luckycharms]

For example:

board after river: 2 7 T K 7 rainbow. The nuts would be a pair of sevens in the hole (four of a kind 7). However, someone is gonna get the four sevens approximately one in 200 times (prob way off) that that hand is dealt.

K /images/graemlins/spade.gif 4 /images/graemlins/diamond.gif 10 /images/graemlins/spade.gif 6 /images/graemlins/heart.gif 2 /images/graemlins/spade.gif The nuts would be A /images/graemlins/spade.gif, X /images/graemlins/spade.gif But 90% of the time, nobody's gonna get that ace, X suited. There are a million combinations of boards, but how often is someone gonna get those hole cards that make it a 100% positive victory?


Not it for the sim. Someone send it to a math major /images/graemlins/grin.gif