5's and 10's

[MSchmahl]

In case you're interested, I calclulated these from Heads-Up equity vs. random opponent's hand.

R(A) = 61.1%
R(K) = 57.8%
R(Q) = 55.4%
R(J) = 53.3%
R(T) = 51.6%
R(9) = 49.7%
R(8) = 48.2%
R(7) = 46.9%
R(6) = 45.9%
R(5) = 45.0%
R(4) = 43.8%
R(3) = 42.6%
R(2) = 41.4%

i.e.: If you dealt two hold'em hands face down and looked at exactly one card, R(x) would be the probability of that hand winning, where x is the rank of the card you looked at.

R(5)-R(4) = 1.2% > R(6)-R(5) = 0.9% is true
R(J)-R(T) = 1.7% < R(T)-R(9) = 1.8% is true

I don't know if these numbers are very meaningful, but it was an interesting way to waste half an hour.

[Bozeman]

Hmm, I wonder if the differences are meaningful:

R(A) = 61.1%
R(K) = 57.8% d12=3.3
R(Q) = 55.4% d11=2.4
R(J) = 53.3% d10=2.1
R(T) = 51.6% d9=1.9
R(9) = 49.7% d8=1.9
R(8) = 48.2% d7=1.5
R(7) = 46.9% d6=1.3
R(6) = 45.9% d5=1.0
R(5) = 45.0% d4=0.9
R(4) = 43.8% d3=1.2
R(3) = 42.6% d2=1.2
R(2) = 41.4% d1=1.2

Notice that d1=d2=d3, but for higher cards the differences increase, with the noted exceptions around 5 and T. (Note: in the absence of hig card value, d5 should be less than d1, since d1 involves an increase in the number of straights allowed.) Presumably high card value increases with the number of undercards, apparently non-linearly.

In a real game, I would guess that the weighting toward big cards is even more extreme.

Craig