[Buzz]

Hi Mack - [ QUOTE ]
Let's look at the 36/44 number. The 36 represents the missed clubs.

[/ QUOTE ]Hmm. Not exactly. Usually after the flop there are 45 cards whose whereabouts are unknown. (And that is actually the case here). Some of those 45 cards are favorable while others are unfavorable. As you know, we call the favorable ones “outs.” I didn’t want to count the ten of clubs (which makes the flush but also pairs the board) one way or the other. I wanted to just consider the other 44 cards and use 44 for the denominator rather than the normal 45. Any respectable mathematician or math teacher might cringe at the idea of taking such liberties with the math - but I was trying to make a fast approximation while playing a hand of poker, and that’s how I was thinking.

I know we can’t just discount the ten of clubs and not count it one way or the other. I know we really need to figure the percentage of time Hero will win with the ten of clubs and add that to the “outs” column, while adding the percentage of time the ten of clubs will lose to the “non-outs” column. These two columns are going to add up to 45 if done properly (because 45 is how many cards Hero cannot see after the flop).

But I have been through the rigorous math for other similar situations and realize that I can take this small libery with the math to get an approximation that is good enough for my purposes. To be more precise, I could have fractionated the ten of clubs, counting part of it as good and part of it as bad. Instead I ignored the ten of clubs and changed the denominator from 45 to 44. Can I do this and still be rigorous about the math? Of course not. Can I do this and get close enough? I think so.

At any rate, rightly or wrongly, I ignored the ten of clubs and changed the denominator from 45 to 44.

Then I had 11 outs. 1, the ace of clubs, for the nut flush, the other 7 clubs for the 2nd nut flush and 3 non-club queens for the Broadway.
44-11 = 33, so that I also had 33 non-outs.

But the 11 outs won’t win 100% of the time. I estimated that collectively they would win about 70% of the time (and would lose 30% of the time)
11*.70 = 8 (close enough)

So I mentally changed the 11 outs to 8 outs. And he added 3 to the 32 non-outs (to make 35 bricks).

So that is where the 8 came from. I didn’t do it exacly that way, but that is about what it amounts to and maybe is more understandable.

[ QUOTE ]
But what if the missed clubs pair the board?

[/ QUOTE ]Only one club pairs the board on the turn (the ten). However, now that you mention it, Hero could make the club flush or Broadway on the turn, then the board could subsequently pair on the river, and Hero could possibly lose to a full house or quads.

At the time, I estimated Hero needed two opponents to call the flop bet to justify initiating fresh money into the pot from an odds standpoint. In making this estimation, I neither directly considered implied pot odds nor reverse implied pot odds. In other words, if I made the flush on the turn, I would presumably be able to collect from somebody on the third and fourth betting rounds - but if I made the flush on the turn, the board could pair on the river, possibly making an opponent a full house or quads. Those two effects probably sort of, although not exactly, cancel each other.

You think Hero should have four opponents to call the bet. I certainly like four better than two, but four is not what I was thinking at the time. In retrospect and to be on the safe side, from the viewpoint of getting proper odds to initiate fresh money into the pot, maybe Hero needed three opponents instead of just two.

There were actually five opponents in the hand when Hero bet the flop. Hero thought he needed just two to call, but as I think more about it now, perhaps should have been thinking he needed three. (I still think four is more than needed). Actually three of the five opponents called the bet, which was fine.

There were also some other excellent reasons to bet the flop, including knocking out the very probable A2XY hand(s) behind me - and just the general good that comes from playing aggressively (but not over-aggressively).

When I wrote the article, I was merely trying to describe what (rightly or wrongly) I was thinking and how I was approximating the odds while playing the hand.

I hope this response makes the matter clearer for you. Keep after me if it doesn’t and maybe I can think of a better explanation.

Take care.

Buzz