Message Board : A couple questions derived from "Harrington on Hold'em Vol.1"

I’m currently engrossed in Harrington on Hold’em Vol.1 and I have a couple questions regarding part 4 (Pot odds and Hand analysis).

Passage 1 from p.134: [In an example hand where you hold a pair of aces and the flop comes 952 (rainbow flop) and your opponent puts you all in, Harrington goes on to say,] "There are only two hands your opponent can hold that scare you: a pair of nines and a pair of fives. (Very few players would make the mistake of calling a bet from an early raiser before the flop with a pair of deuces.) If he has one of those hands, he’s now got a set and you’re a huge underdog — about 10 percent winning chances with 2 cards to come."

Question: How do you determine your winning chances as exemplified by the author at the end of this passage? Is there a chart out there that depicts the winning chances of the various hand combinations? Or is there some algorithm that you can use to determine your winning chances?

Passage 2 from page 135: [Harrington just took his opponent's possible holdings and put himself into his opponent's shoes to see how good of a "fit" each possible holding was based on his opponent's behavior. Then he goes on to say,] "Before we divide our remaining 90 percent probability between these two cases [high pair vs. trips], let’s note one other fact. There are four times as many possible hands in the high pair case (kings, queens, jacks, and tens) as in the trips case (just nines
and fives) and four times the likelihood he has them because of card combinations."

Question: How does he know about this distribution of hands? Again, is it a chart I can memorize or is it an algorithm that I need to learn? If you know of some resource that would provide me with the facts about various hand matchups that would be very useful to me.

Thanks for your time.

If you’r a stox member, Ed did a really nice video on the math of hand reading covering a bunch of these combo scenarios.

I would say that you should ignore deuces at your own peril in that first hand.  I don’t know what the positions were, but any set is a real possibility.

Anyway, it is good to know your combos.  6 ways to make a paired hand, 16 ways to make a two card hand, etc.  You get beter with practice.