I was reading Barry Greenstein's "Ace on the River" book and in it i read something i need some help understanding.

The book is just a general guide in winning in poker so it does not contain a lot of detail. But one thing struck me as weird because i had never heard it before.
I'll quote from the book:

"When players get beat with the best hand, they sometimes spout mathematical nonsense about how big a favorite they were. For example, when they lose with Ace-King against King-Jack in hold'em, you may hear them complain that they got beat by a three-outer and were a 45 to 3 favoirtie. In reality, they were between a 2.3 to 1 favorite and a 3.1 to 1 favorite, depending on the suits" (Greenstein, 2005, p. 152).

Can anyone explain to me how that works, because often i have heard this complaint and have voiced this complaint myself.

How did he reach those odds? (2.3 to & 3.1 to 1)

Not sure if youll get an answer here, I haven't seen any crazy math types around these parts.

Its probobly the chance of a jack hitting over 5 cards without an ace hitting the board also, but I have no idea how to figure that out.

Might try posting on the twoplustwo.com probobliliy forum.

If your curious about playing with these kind of things in general, cardplayer.com has a hand calculator where you can put in hands and see what percent each one is to win.

Well, if you ignore straights and flushes, then basically, they guy with K-J has to catch a Jack somewhere on the board to win. Once you remove his and his opponent's cards, there are 48 cards left in the deck. So, the odds that he *won't* get a Jack are

(45/48) * (44/47) * (43/46) * (42/45) * (41/44) = 0.7135

So, the odds that he won't get his Jack are 0.7135 : 0.2865 or 2.49 : 1

The various flush and straight possibilities cause those odds to vary based on the specific situation.

Another good shortcut is (2% * # of outs * cards to come) = % chance to win. In this case there are 3 outs (the 3 Jacks) with 5 cards to come, which gives us 2% * 3 * 5 = 30%, which would give us odds of 2.33 : 1. While that shortcut doesn't give you the exact value, it's close enough for most quick analyses, particularly when applied on the flop and turn.

I think what he's saying is that once the flop doesn't produce a jack, people are saying they are 45 to 3 to win on that flop. In other words, before the jack spiked they were a "15 to 1" favorite, which is not accurate. Once the money is all-in the odds of winning are locked at the odds being laid at the time, they do not change because of the flop. The odds of the card coming along for the underdog to win do change, but the overall odds do not.

Since you already have the nice complete answers, the short answer is that the 45:3 number is wrong because the board will contain more than one card.

?????

This is a pretty basic poker probability question that most people here should be able to answer, and have in many other threads.

Mark

As Kd-74.59%
Ks Jd-24.16%

KJ has no flush possible, 3-1 dog

As Kd-69.04%
Kc Jc-29.85%

KJ has best possible flush situation, suited and cant be conterfieted(sp), and is a 2.3-1 dog
thats how