Simple probability problem
 

On page 126, first paragraph of Harrington On Hold'em Vol1:

1. Higher pair versus lower pair. The higher pair is about 82% to win, or about a 4.5:1 favorite.

This is probably just my non-math brain kicking in and I've never commited any of this to memory since I've not been a no-limit player. But...can this be right? 100/4.5 =22.2 that's 77.8%. Yes?

---Leavenfish

Re: Simple probability problem
 

Your math is fine, but 4.5:1 means the higher pair wins 4.5 times and loses 1 time out of 5.5. 4.5/5.5 = 81.8%.

Re: Simple probability problem
 

[ QUOTE ]
On page 126, first paragraph of Harrington On Hold'em Vol1:

1. Higher pair versus lower pair. The higher pair is about 82% to win, or about a 4.5:1 favorite.

This is probably just my non-math brain kicking in and I've never commited any of this to memory since I've not been a no-limit player. But...can this be right? 100/4.5 =22.2 that's 77.8%. Yes?

---Leavenfish

[/ QUOTE ]

No.

100/5.5 = 18.2 -> ~82%.

4.5:1 favorite = 4.5/5.5 =~ 82%.

4.5:1 underdog = 1/5.5 =~ 18%.

Re: Simple probability problem
 

[ QUOTE ]
[ QUOTE ]
On page 126, first paragraph of Harrington On Hold'em Vol1:

1. Higher pair versus lower pair. The higher pair is about 82% to win, or about a 4.5:1 favorite.

This is probably just my non-math brain kicking in and I've never commited any of this to memory since I've not been a no-limit player. But...can this be right? 100/4.5 =22.2 that's 77.8%. Yes?

---Leavenfish

[/ QUOTE ]

No.

100/5.5 = 18.2 -> ~82%.

4.5:1 favorite = 4.5/5.5 =~ 82%.

4.5:1 underdog = 1/5.5 =~ 18%.

[/ QUOTE ]

So, I guess I was calculating this all wrong. Ex: KK vs JT is 5:1 and that is not 80%?

Re: Simple probability problem
 

[ QUOTE ]
So, I guess I was calculating this all wrong. Ex: KK vs JT is 5:1 and that is not 80%?

[/ QUOTE ]

5:1 means you win 5 and lose 1, so you win 5 out of 6, and 5/6 =~ 83.3%.

Re: Simple probability problem
 

[ QUOTE ]
[ QUOTE ]
So, I guess I was calculating this all wrong. Ex: KK vs JT is 5:1 and that is not 80%?

[/ QUOTE ]

5:1 means you win 5 and lose 1, so you win 5 out of 6, and 5/6 =~ 83.3%.

[/ QUOTE ]

I think I get it: A pair vs 1 higher and 1 lower card is a 2.5:1 favorite. Therefore the pair wins 2.5 out of 3.5 times = 71.4% Thanks BurceZ!

---Leavenfish