Dumb math question

[illunious]

How do I get this range of hands to a final percentage or odds? The easier the solution the better since I want to be able to do this in my head.

88-99 (12 combinations) - 80%
JJ-AA (24) - 20%
AQ-AK (32) - 50%
TT (1) - 50%(?)

[Justin A]

I have no idea what you're asking.

[KJL]

12/69*.8=13.9%
24/69*.2=6.9%
32/69*.5=23.2%
1/69*.5=.7%
Add up all the numbers and you get 44.7%, which is about right for TT vs. 88-AA and AQ+.

[KJL]

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.

[illunious]

[ QUOTE ]
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.

[/ QUOTE ]

Yes, this is what I'm asking. I should have mentioned hero has TT and 100% puts villain on that range of hands.

[ QUOTE ]
12/69*.8=13.9%
24/69*.2=6.9%
32/69*.5=23.2%
1/69*.5=.7%
Add up all the numbers and you get 44.7%, which is about right for TT vs. 88-AA and AQ+.

[/ QUOTE ]

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%?

[KJL]

No, I cannot do this calculation in my head. I am not really sure how to come up with this during a game, besides maybe making it 12/72 24/72 and 36/72 or 1/6 1/3 and 1/2. This would make it easier to calculate.
My thought process? I am not exactly sure what you mean. I added up all the combinations to get the 69 and put the combinations over 69 and mutiplied by the approxiamte percantage of winning each group of hands has.

[SumZero]

[ QUOTE ]
[ QUOTE ]
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.

[/ QUOTE ]

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%?

[/ QUOTE ]

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%.

[illunious]

The 2nd solution would be the easiest for me to do live but I'm going to need to practice it. Thanks, that was exactly what I was looking for.