Question:Why 4.5 to 1

#1 30th November 2011, 3:38 AM

Here is what I read from Harrington's book:
There are six possible ways to hold
any pair, and there are eight pairs higher than yours (66), so there
are 48 possible card holdings that leave you about a 4.5-to-1
underdog.
I dont know how to calculate this conclusion.Why?How?

#2 1st December 2011, 2:49 AM

Any pair higher than your 66 is about a 4 to 1 favorite - some are a little higher like 10,10 because they necessary for all high straights. Also if your suits match then that eliminates your flush draws.

Side point your hand is only a 6 to 5 favorite against two over cards - probably also somewhere in Harrington's book. One of his books has a list in the back that breaks down all the important hand over hand odds.

#3 3rd December 2011, 8:59 AM

Quote:

Originally Posted by luckytvguy

There are six possible ways to hold
any pair

Sorry, I know I'm a little tired, but what does that phrase mean exactly?

#4 3rd December 2011, 9:25 AM

Quote:

Originally Posted by PurgatoryD

Sorry, I know I'm a little tired, but what does that phrase mean exactly?

There are 6 possible combinations of the 4 suits
2h2d, 2h2s, 2h2c, 2d2s, 2d2c, 2s2c,

#5 5th December 2011, 4:03 AM

Quote:

Originally Posted by Samango

There are 6 possible combinations of the 4 suits
2h2d, 2h2s, 2h2c, 2d2s, 2d2c, 2s2c,

But of course! Thanks a lot for breaking it down.

Quote:

Originally Posted by luckytvguy

I dont know how to calculate this conclusion.Why?How?

I think the confusing thing is that the 4.5 to 1 underdog conclusion doesn't actually directly follow from the number of ways to hold pairs. To the best of my knowledge, to actually calculate this conclusion, you'd have to compute the odds of winning, losing, and tying each combination of hands. That would be quite involved.

I just used Poker Stove and it showed that 66 has 18.358% equity against 77, for instance. That's about a 4.5 to 1 underdog. Poker Stove is free and it's a great utility for figuring these kinds of things out since the math is just too involved.

#6 7th December 2011, 4:03 AM

thanks a lot to all of you.

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