Couple questions and a problem

[novak79]

Ok, I need help with a few questions, I'll go ahead and get the easy ones out of the way first. I know that odds of winning preflop with a higher pair against a lower pair is 4.5 to 1 and like a pair v. 2 higher cards is 55-45 etc. etc. but

1) what if you have 2 middle cards to their 1 over card and 1 under card? Like A6 v. your QJ?

2) what is your preflop winning probablitlity in a domination problem? Same high card but different low cards?

My third one is a little longer and a little more complicated. Ok, say you had an opponent in the cut off seat that had been playing tightly but he had an M of around four. He folded the last several hands but then pushes all in. Action is folded around to you, the BB. There is 85,200 in the pot and it costs 62,000 to call so you're getting 1.4/1

You believe that he will push all in with only the following hands

All pairs 55 and up
Ax (x being a 6 or better)
Connectors 78 and up
KJ KT and QT

You assume there is a 40% chance he is holding a pair and 20% for each of the three remaining ones.

You have 44

Now I think I did the math right here but maybe someone can explain where I messed up or if I did

I take 1/4.5 to figure out your chance of winning with my smaller pair to his higher pair which is 22% chance of winning.

Then I take .4(.22) (the chance of him holding a higher pair times my chance of winning against one) plus .8(.55) (the chance of two over cards plus my chance of winning which comes out to

.4(.22)+.6(.55)=9%+33%=42%

So I would have a 42% chance of winning. Now given the pot odds this should be a clear fold. Right? Did I do the problem right? Does anyone have any hints for being able to do this at the table quickly?

[the_hawk]

For (1) and (2), have a play with the ITH Odds Calculator. It should tell you all you need to know.

For (3), I haven't worked through your numbers but if you're getting 1.4:1 about a 42% chance (your numbers), then that is pretty much a breakeven call in chip EV terms. You might choose to call or fold depending on the context (not least your own chip-count). Also, I would guess the chances of an M=4 player open-pushing from the cutoff having an overpair are considerably less than 40%.

As regards doing this at the table quickly, with this holding you are (at best, but most probably) slightly on the right side of a coinflip. Do you want to flip for this proportion of your stack getting somewhat better than even money?

[novak79]

Could someone work through the numbers for me? It is the first time I've tried a problem like this.

Also, I didnt punch that many hands into the ITH calculator but it appears to be about 55-45 in favor of the higher card with a weak kicker and about 60-40 with a stronger one that is more likely to play. (this is with a higher cand and a lower card v. two middle cards) do these numbers seem roughly correct to you guys? I'm not looking for perfect here, just something I can work with at the tables.