Could you verify some math from SSHE? NPA Ed Miller's book?

[steamboatin]

I should have paid more attention in school and am incredibly weak in math. SSHE says, if I am quoting correctly, If you start with a suited ace preflop, you only make a flush 6% of the time.

Is that accurrate?

[Ed Miller]

You don't have the quote quite right.

SSH, p.58
[ QUOTE ]
If you hold two suited cards, exactly three more cards of your suit will appear by the river a little less than six percent of the time.

[/ QUOTE ]

It says nothing about how often you make a flush with four or five of your suit on board.

And yes, it's correct. To calculate it:

There are 11*10*9 / 6 = 165 combinations of three cards of your suit. There are 39*38 / 2 = 741 combinations of two cards not of your suit. Thus, there are 165 * 741 = 122,265 boards that contain exactly three of your suit.

There are 50*49*48*47*46 / 120 = 2,118,760 total boards.

Thus, exactly three of your suit appears 122,265 / 2,118,760 = 0.0577 or about 5.8% of the time.

[steamboatin]

Thanks, NPA Ed Miller. I like your book.

[Cyrus]

"If you start with a suited ace preflop, you only make a flush 6% of the time."

I presume you mean "make a flush" with any combination of outcomes.

The chance P of ending up with a flush when holding any 2 suited cards is

P = A+B+C

A = (The chance of flopping a flush) = 0.84%

B = (The chance of flopping a 4-flush)*(The chance of then hitting one or two suits) = 10.94% * 34.96% = 3.82%

C = (The chance of flopping one suit)*(The chance of then hitting two running suits) = 41.58%*4.16% = 1.73%

P = 0.84% + 3.82% + 1.73% = 6.39%

[steamboatin]

All that math makes my head hurt. Thanks

[steamboatin]

BTW, I figured NPA Ed Miller has eough self-esteem that my questioning his book, won't hurt his feelings at all. The book is very helpful but sometimes you need to hear things more than once. I am on my second read now.

[SuitedSixes]

I hold Kxs with three of the same suit on board, what is the probability that someone has Axs? What is the math so that I can figure it out for each descending rank? Thanks, in advance.

[Cerril]

I think at this point you need a heavy dose of game theory or other science than pure probability to figure out your answer. Basically the problem is once you've seen the flop you have fewer than a full load of people still in the game, and those people in most likely don't have unreasonable hands.

However, if you're talking literal NFE where every hand might be out there at a table of nine other people...

If you've got Kxs on a flop with three of your suit, that leaves 8 suited cards (with the ace still out there, one assumes) left. Seven ways to have the ace suited, 39 ways to have the ace unsuited, 2070 ways not to have the ace (1892 on the river). The odds are negligible you're up against the Axs (though on the flop the bare ace will be in one of the ghost hands fairly often - 40.43%). I'm not going to go through all the numbers because I think they'd be misleading, you're never in such a static situation at a table where you can calculate all your opponents' hands postflop with brute probability.

[steamboatin]

Quote from a poker book, can't remember which one,"If you have the King High Flush, the ace is only out against you 6% of the time."

I have no idea how to do the math or if this is accurrate but it has to be a relatively low percentage.