Flopping Quads

[TITHEAD]

Last night i got dealt AA and managed to go all in against KK preflop.

The flop came KK2 and my aces got smashed.

Does anyone know what the odds are for flopping quads ?

If someone could run through the maths of it i would be much appreciated

Thanks

[SinPoker]

If you hold KK, the flops that will give you 4 of a kind are:

KK?, K?K, ?KK, where ? represents 48 possible cards. 48+48+48 = 144.

There are 19,600 possible flops (based on there being 50 unknown cards), so 144/19600 = 0.735%

I think that's right.

[bigpooch]

Disregarding other hands, there are C(50,3) = 19600 possible
combinations of flops of which quads are made on exactly
48 of them (you can only choose 48 "other cards" together
with the two remaining cards of the same rank), so the
probability is about 48/19600 = 3/1225 or about 0.0024490.

Of course, when you face an opponent and make quads, your
opponent has two "other cards", so in reality, your chances
are about 46/C(48,3) = 1/(8*47) = 1/376 or about 0.0026596
or 375 to 1 against.

[Silent A]

If you can't tell, bigpooch is correct and sini made the mistake.

[smartalecc5]

lol ya I was saying why don't I flop quads one in a hundred times lmao

[tarheeljks]

[ QUOTE ]
lol ya I was saying why don't I flop quads one in a hundred times lmao

[/ QUOTE ]

he accidentally did permutations instead of combinations. this is a pretty common mistake when using combinatorics.

[SinPoker]

LOL, yeah, oops, I'm a donkey.

I made 3 mistakes.

1. I was thinking permutations but plucked the wrong number from my memory. Should have been 117600, not 19600.

2. I missed out half the permutaions of flops which would yield quads. 288, not 144.

3. I thought "Wow, I didn't think quads was that probable" yet failed to consider that I might have worked it out wrong.

Doh!

[LastLife]

[ QUOTE ]
Disregarding other hands, there are C(50,3) = 19600 possible
combinations of flops of which quads are made on exactly
48 of them (you can only choose 48 "other cards" together
with the two remaining cards of the same rank), so the
probability is about 48/19600 = 3/1225 or about 0.0024490.

Of course, when you face an opponent and make quads, your
opponent has two "other cards", so in reality, your chances
are about 46/C(48,3) = 1/(8*47) = 1/376 or about 0.0026596
or 375 to 1 against.

[/ QUOTE ]



Can this be right? This would mean that every 6375 hand you get or every 375 pocket pairs you get you would flop quads? Through 5k+ PP I have never flopped quads.

[DarkMagus]

[ QUOTE ]
[ QUOTE ]
Disregarding other hands, there are C(50,3) = 19600 possible
combinations of flops of which quads are made on exactly
48 of them (you can only choose 48 "other cards" together
with the two remaining cards of the same rank), so the
probability is about 48/19600 = 3/1225 or about 0.0024490.

Of course, when you face an opponent and make quads, your
opponent has two "other cards", so in reality, your chances
are about 46/C(48,3) = 1/(8*47) = 1/376 or about 0.0026596
or 375 to 1 against.

[/ QUOTE ]



Can this be right? This would mean that every 6375 hand you get or every 375 pocket pairs you get you would flop quads? Through 5k+ PP I have never flopped quads.

[/ QUOTE ]

You've never flopped quads out of 5000 pocket pairs? Are you sure? Odds of that are about 1 in 200,000. You sure you checked correctly?