probability question for Mr. Sklansky please....

[flopmeister_1]

POsted this in the probability section but really want clarification please............

Allow me to quote from David's book called "hold 'em poker"

ON the very last page before the glossary I found some GOLD NUGGETS!

"If you hold a wired pair, you will flop trips or better 11.8% of the time. If you hold AK you flop an A or K 32.4 percent of the time. If you hold two suited cards you flop a flush 0.8% of the time and a four flush 10.9% of the time. If you hold two unmatched cards you'll flop the split two pair 2.02% of the time. If you flop trips, you make a full house or better 33% of the time.

Is this assuming a 10 handed game?

I am really hoping that Mr. Sklansky himself could respond to this question. I realize now that this reinvents my thinking on certain hands beating me during play when I am "seeing the boogie man" ie. "did he really flop the flush in a 4 handed situation?" NOT LIKLELY according to this piece of information from his book. [img]/images/graemlins/cool.gif[/img]

[tablecop]

the probalities quoted do not depend on the number of players dealt in. note that the quote is "when YOU hold..." it does not say "the chances SOMEONE will have..." however every time someone flops a flush it's on a 1 suited flop. once you see the flop is 1-suited the probability that someone has flopped a flush is considerably higher than 0.8% and does in fact depend on how many players have seen the flop and how likely they are to be suited. If you have three opponents and they each are about a 1/3rd (just a guess on my part) chance to be suited, they'd be a somewhat less than 1/18 chance to be suited in the flopped suit. Pretending it's exactly 1/18 then it's about a 16% chance one of your opponents has flopped the flush.

[DeeJ]

Assuming you don't hold any of a single-suited flop, each player has a 10/47 * 9/46 chance of holding two of the flopped suit. I think. This is only 3.8% per single player. The maths get more complex than I've got time to work out for multiple-players-with-both-suited-cards and chance-for-N-players.

If you hold one of the suit it would be 9/47 * 8/46 or 3.3% since there are fewer flush cards for everyone else to hold.

That's my basic maths [img]/images/graemlins/smile.gif[/img] so for practical purposes when there is a mono-suit flop I assume when there are only 3 other players in that nobody has flopped it (eg ~90% of the time) and someone is very likely to hold one of the suit. If there are 6 or 7 people limped in, the likelihood of someone holding the flopped flush must be somewhere around the 20+ percent and you gotta worry, especially as people are more likely to play suited cards.

Obviously betting will tell you more but if you're first to act it's some sort of clue.

A simulation would tell you the exact answers and humiliate my inaccurate maths [img]/images/graemlins/grin.gif[/img]

[tablecop]

you're ignoring some information, namely some of your opponents have paid to see the flop. suited hands are more likely to be played than offsuit hands.

[Officer Farva]

These probabilities are independent of the number of players playing. They would be the same if you are playing against one player or 20 players. Tablecop, your point is wrong. Even if you knew that all the players you were against were suited, they are just as likely to be holding your suit as an other suit, so the P(flopping flush) is unaffected.

[LinusKS]

The chance of being suited preflop is slightly worse than 1/4.

[The chance of being dealt a card of with a suit on it = 1. The chance that the second card is same suit is 12/52. 1(12/52) = 12/52, or slightly worse than 1/4.]

If the flop comes 3 suited the chance the flop matches your hand is also a little worse than 1/4. (Since you've already used 2, there are only 11 of your suit left to make the board-flush.)

The chances that a particular opponent will have both a suited hand and that his suit will match the board are something worse than 1/16.

Since people are more likely to play suited cards, you have to adjust that number upward, depending on how attached you think your opponents are to suited hands. (One mistake beginners often make is playing any two suited cards.)

With a few callers, it's not too likely anybody has the flush, even at an otherwise fishy table.

If seven people have called the flop, however, there's a real good chance somebody's got it - maybe even more than one of them.