Calculating all-in race probabilities (simplifed)

[RoyalSampler]

If I have A2d vs 78h since each has a 50% chance of a pair, this should be ~ 1:1.

If I have A7d vs 82h each has 50% chance of pair, but both hands might pair. The chance of two specific cards, one from each hand pairing should be the chance of two pair 3%. Since in 3 in these scenarios (A paired vs 8 paired, A paired vs 2 paired, 7 paired vs 2 paired) the lesser hand loses, I take 9% from 50% and come up with ~ 3:2 in favour of A7.

Using the same logic for A8d vs 72h we now take 4 * 3% from 50% and come up with 38:62 a little better than 3:2, not quite 2:1.

I specified the suits to rule out the flush, also I ignored the 87 having 3 times the straight chance in the first hand, but other than that are these fair approximations of common allin race scenarios? Taking account for each getting two pair seems to be getting down into the ~ 1% error range, which I don't care for.

Are these numbers close to the mark and the logic sound? Thanks

[theKGBwins]

I think that your calculations, although seeming logical at first, may be slightly off. You see, with A2 vs 78, or even A7 v 82, it would not be 1:1. Whoever has the ACE would be ahead in the hand, but it would be very close. More like 55%-45%. Itd still be a race nontheless.

[RoyalSampler]

Yes I checked and the numbers are quite a bit out, but can someone spot my logic flaw?

[SossMan]

[ QUOTE ]
Yes I checked and the numbers are quite a bit out, but can someone spot my logic flaw?

[/ QUOTE ]

The ace high wins unimproved about 3-4% of the time. Also, everyone knows that diamonds are luckier than hearts...sheesh, what are you, a beginner??

go here for some good stats.

Interestingly, A2o is 50/50 with 67suited.