Heads up odds

I know that a pair vs. 2 overcards is a 11:10 dog (although I can't figure that out myself). And I know, obviously, that a lower pocket pair to a higher one is a big dog. Now let's say you raise with pocket 2s preflop and get one caller- you're obviously an underdog (excluding how well or poorly the hands are played) but how much so? Can you show your work also please. Gracias.

"Now let's say you raise with pocket 2s preflop and get one caller- you're obviously an underdog (excluding how well or poorly the hands are played) but how much so? "


I havent much time right now to do the calculation and it might be better if you do it yourself with a few hints.


First calculate the chance that you´re against an over pocket pair. Then calculate the chance that your underpair wins (i.e. hit a set when the other dont hit a set, or hit quads when the other dont hit quads) with 5 cards on the come.


For overcards: that 1 minus the chance that he has an overpocket pair or also 22. Now figure the chance that the overcard make a pair or more when you DONT hit your set. You should make a different calculation for hands from your opponent containing a deuce. Furthermore calculate the chance that you make your set but still loose (examine in which situations this is possible and calculate the likelyhood of them).


Then you should combine this all in a statistical way (which is pretty straighforward if you know basic statistics) and you know you chance of your pocket 22 holding up against a random hand. I´m sorry if I forgot a scenario.


But far more easy is to run a simulation. Just give a player fixed 22 and the other player a random hand and run let´s say a 1000000 hand cold sim.


Hope that helped.

22 vs. random hand 1,000,000 times:


22 wins 50.31% of the time.


Once a jek, always a jek.

I am kind of a newbie here, so can someone please explain... How do you come up with a pair being an 11:10 dog vs. overcards?


I just ran a sim and got the following:


1) pocket pair preflop vs. two higher cards (I ran 88 vs. KQ): 88 wins 54.32%


2) top pair on flop vs. two overcards (59 vs. AK, with a flop of 369): 59 wins 77.86%


3) middle pair on flop vs. two overcards (59 vs AK, flop 258): 59 wins 76.24%


4) bottom pair on flop vs. two overcards (59 vs AK, flop 57T): 59 wins 75.36%


In what situation is a pair not the favorite?


I do have another question regarding win ratio versus win percentage. For example, I read recently that a lower pocket pair is a 5:1 dog vs. a higher pocket pair (this was in a Poker Digest recently where Phil Hellmuth said he was seeking out a 5:1 situation in a tournament). When I run the simulation (AA vs. 22) higher pocket pair will win 82.83%. Doesn't this mean the higher pocket pair is a 4:1 favorite?


My logic: play 5 hands. AA will win about 80% of them (4 games). 22 will win about 20 % of them (1 game). So, doesn't AA win 4-to-1 (4:1) vs 22?


Thanks,

Rich