Flop Stats

[Robert Marsella]

Where can I find out the approximate frequency of an ace coming out on the flop in NLH?
Thank you

[slcseas]

Odds of any single card hitting the flop(assuming you don't hold one in your hand) is: 4/50 + 4/49 + 4/48. All that equals about 1 time in 4.

If you are looking to pair an ace in your hand, then it would be 3/50 + 3/49 + 3/48, you do the math on that one.

[MKR]

If you hold no aces, the probability that at least one of the cards on the flop will be an ace is .1176 or about 7.5 to 1 against.

The math goes like this:

P(at least 1 ace) = 1 - P(no aces) = 1 - C(48,3)/C(50,3).

[slcseas]

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If you hold no aces, the probability that at least one of the cards on the flop will be an ace is .1176 or about 7.5 to 1 against.

[/ QUOTE ]

If I held AA then my odds of flopping a set would be 11.8% or 7.5 to 1 against. This is with only two Aces left in the deck.... I think you need to check your calcs.

[MKR]

[ QUOTE ]
[ QUOTE ]
If you hold no aces, the probability that at least one of the cards on the flop will be an ace is .1176 or about 7.5 to 1 against.

[/ QUOTE ]

If I held AA then my odds of flopping a set would be 11.8% or 7.5 to 1 against. This is with only two Aces left in the deck.... I think you need to check your calcs.

[/ QUOTE ]

Whoops!

[ QUOTE ]
The math goes like this:

P(at least 1 ace) = 1 - P(no aces) = 1 - C(48,3)/C(50,3).


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The required probability is given by 1 -C(46,3)/C(50,3) (there are 46 not 48 cards in the deck which are neither aces nor your hole cards) and the probability is .2255 or about 3.4 to 1 against. Good catch.

[slcseas]

Sounds a lot better.

[mttsemipro]

Thats bad math. Thats how u calculate the expected number of aces on the flop, but not the odds of at least one ace. Listen to MKR.

[Robert Marsella]

Thanks everyone for the helpful info

[slcseas]

My math is rough calculation of fractions that I can do in my head, and was only 2% off of MKR's done with algebra. I'll ignore the fact that this is your 2nd post and simply state that there are plenty of methods to perform math functions that will get you the same results. Since I don't take my TI-96 Graphing calculator to the tables with me, I'll stick to my very correct methods.

[Cobra]

Just like the 4/2 rule for estimating your chance of improvement after the flop you can use 5.5 to estimate your chance of one or more cards coming out on the flop. See the examples below:

1. You hold KK probab of 1 or more Aces on flop 5.5*4=22%

2. You hold AK probab of 1 or more Aces on flop 5.5*3=16.5%

3. You hold AK prob of 1 or more A or K is 5.5*6=33%

This is just an estimate but is relatively accurate.

Cobra