Re: Dumb math question
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I think he is asking the odds of TT vs the range of 88-AA and AQ+. He provided us with the odds of each hand occuring and the approximate heads up odds of TT vs that hand.
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Are you able to do these calculations in your head? It would take me like 15 minutes to come up with this during a game.
Can someone please explain exactly what their brain is processing step by step to come up with 44.7%?
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I'd simplify it and say there are 4*4 AK and 4*4 AQ which makes 32 TT vs overcard coinflips. I know from memory that we are a 55 or 56% favorite over those hands. That's 5/9 * 32 ~= 17.5/32 since 32 is about 3.5*9 and 17.5 is a 3.5*5. There is one TT and it is equal so that gives us .5/1 or 18/32.5. There are 12 88-99 and we are a 4/5 favoite over them (actually a little better than that ~82% iirc). There are 24 JJ-AA and we are a 1/5 against them (again a little worse than that, closer to 18% iirc). So (12*4+24)/5 of the 36 hands or [72/5]/36 ~ 14.5/36. Put that together and you get 32.5/68.5. 32.5*2 is 65 so we are under and we under by about 3.25 which is 10% of our numerator. This means in my mind we are (50-[.1*50])/100 which makes us about 45%. If I'm in an important all-in type decision I can totally do this math at the table, probably in about 25 seconds.
The other rough way to swag it that works in some cases (like this) is to say there are 32 (2 types * 16) overcards and 36 pairs (6 * 6 - I'm ignoring TT) so we should be slightly closer to the pairs than the overcards. The pairs are split 2-1 against you so you should be 2/3 of the way to 20% from 80%, that is 40%. Against the overcards you are 55%. The average of 40% and 55% is 47.5% and we said round closer to the pairs so that is about 47%. If you are lucky enough to have this narrow of a range, and not have to worry about more situations like 1 over card, 1 under card and 1 over card and one of your cards, etc. this method can be quite quick and can be done in 5-10 seconds at the table.
FWIW if I run TT against this range in a simulator I get you are ~47.5%.
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