Showdown Equity For 10% Mid-Ranges
Using Equilab's hand ranking, I determined the showdown equity vs a random hand for ranges, 0-10%, 10-20%, etc. It was nearly linear. The regression equation is
Eq = 0.6727 - 0.0032 * R
where R-=10, 20, 30 etc.
The R^2 was 97%. The largest deviation was in the 0-10% range, 68% vs estimated 64%. For all other ranges,the deviation was no greater than Abs(2%).
I realize I may be the only person on the planet who finds this useful.
2 Replies
Because of the great interest in my showdown equity formula for hero range vs a random hand, I did the same for hero range vs a top 50% hand. The regression equation is more complicated but the fit is very good at R^2 = 98.6%.
Hero showdown equity = 0.6563 *X^(-0.305),
where X = 1 for 0-10% range, X=2 for 10-20% range, etc.
The very large number of responses to this thread (0)😊 has motivated me to do a third analysis, namely, one of hero facing an opponent playing a top 20% hand.
So, to summarize:
Hero showdown equity playing mid 10% ranges denoted by R.
(1= 0-10%, 2= 10-20%, ..., 10= 90-100%)
Playing against a very loose opponent(random hand)
Eq = 0.6727 -0.032 * R (slightly revised)
Play against a loose/moderate opponent (top 50% hand)
Eq = 0.6563 * R^(-0.305)
Playing against moderate/tight opponent (top 20% hand)
Eq = 0.5457 * R^(-0.277)
If you have need for a different opponent range, it takes maybe 15-20 minutes with Equilab to generate the data and then you can Excel's charting trendline function to obtain the regression equation.
