Reading this article at the table today....

[slavic]

The chart at the bottom looks off to me.

http://www.cardplayer.com/?sec=afeature&art_id=13913

[Nottom]

At first glance everything looks ok to me, what looks off to you?

[slavic]

It's that he listed % and not odds. The look correct.

In the case of flopping a set.

(100 - 11.8)/11.8 gives 7.47 so the number is right.

For some reason I had a larger percentage memorized for AK flopping an ace or a king. Looks like I should sit down and rework my numbers again.

[rayrns]

I must be doing something wrong. But here is what I came up with.

19,600 possible 3 card flops
1 of 6 cards will give us an A or K on the flop.
44 cards that are not an A or K

Math:
44*43/2*1 = 946 combinations that won't contain an A or K
946*6 = 5676 combinations that will contain an A or K

5676/19600 = .28959 = .29 or 29%

So you should get an A or K on the flop 29% of the time.

I think Warrens Book has the answer at about 40%. What am I doing wrong?

[Ed Miller]

Flopping ace or king:

Flops without an ace or king (given you have AK): 44 * 43 * 42 / 6 = 13244

% to flop ace or king = 1 - 13244/19600 = 32.4%

[nepenthe]

The correct calculation, I think is the following:

6/50+(44/50 x 6/49)+(44/50 x 43/49 x 6/48)

Assuming you have AK, there are 3 A's and 3 K's in the deck, or 6 out of 50. The equation translates to:

(A or K as 1st card) or (Not (A or K as 1st card) AND (A or K as 2nd card)) or (Not (A or K as 1st or 2nd cards) AND (A or K as 3rd card))

I get 32.43%.

[sthief09]

another way:

[C(6,1)*C(44,2)+C(6,2)*C(44,1)+C(6,3)]/C(50,3)
= 6356/19600
= .324

or

1-C(44,3)/C(50,3)

[rayrns]

Thank you for the way you added in the meaning of each of the numbers. That helps a lot.