From last's month's magazine

[PhatMango]

Hi, I just got here and was reading the previous issue of the magazine. I noticed in the article by Mr. Jim Brier that there is what appears to me to be an error in the probabilities.

In the article Discussing Small Stakes Hold 'em: Part I Mr. Jim Brier writes:

"T [img]/images/graemlins/heart.gif[/img] 7 [img]/images/graemlins/club.gif[/img] 5 [img]/images/graemlins/club.gif[/img]

It is checked around to the button who bets. Assume you just call. Assume the other players call except the limper with the unknown hand who folds. According to the Card Player "Hold 'em Odds Calculator," here are the winning probabilities of the various remaining hands:


Your Hand 8 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img]18.2%
First Limper 9 [img]/images/graemlins/spade.gif[/img]9 [img]/images/graemlins/heart.gif[/img]10.0%
Middle Limper A [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/spade.gif[/img]9.1%
Last Limper 6 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/heart.gif[/img] 23.3%
Button (Preflop Raiser) J [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/heart.gif[/img] 39.4%

I then assumed that you raised and eliminated both the first limper with pocket nines and the middle limper. I assumed that the last limper cold-called your raise because he has a pair, a backdoor flush-draw, and a runner-runner straight draw. Keep in mind that we are dealing with loose, low limit players. Of course the button at least calls. Now the Calculator showed the following winning probabilities:


Your Hand 8 [img]/images/graemlins/diamond.gif[/img]7 [img]/images/graemlins/diamond.gif[/img] 18.9%
Last Limper 6 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/heart.gif[/img] 22.1%
Button (Preflop Raiser) J [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/heart.gif[/img] 59.0% "

Intuitively, at a glance something seemed wrong. How could the 6 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/heart.gif[/img] hand actually have a worse probability after two hands were eliminated? I confess that I was astonished when I ran the numbers to get the same amazing result. However, I made the same mistake as Mr. Brier, I didn't take the four now dead cards out of the possible cards to be dealt. The actual odds (minus the 9 [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/heart.gif[/img] A [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/spade.gif[/img]) are, I believe:

8 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img] 20.0%
6 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/heart.gif[/img] 23.9%
J [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/heart.gif[/img] 56.1%


Sorry in advance if this has already been covered, but I figured Mr. Brier might want to know in case he is going to publish this elsewhere and I couldn't find any posts concerning the article.