Optimum pushing and calling ranges
 

This evening while using SNGPT to review some situations from today's SNGs (PS 15 turbo), I came across this: 300/600 a50

UTG (t2755)
CO (t1785)
BTN (t905)
SB (t3360)
BB (t4695)

With SNGPT's "loose" calling range, it appears that UTG should push any two. This didn't seem right, so I entered a push range of 100% for UTG and computed a calling range for each position:

UTG pushes any 2
CO 48%
BTN 86%
SB 37%
BB 60%

Then I entered those calling ranges and computed UTG's pushing range: 43%. Now I started again and came up with these calling ranges:

UTG pushes 43%
CO 19%
BTN 44%
SB 14%
BB 26%

Then I entered those calling ranges and computed UTG's pushing range: 40%. Now I started again and came up with these calling ranges:

UTG pushes 40%
CO 17%
BTN 40%
SB 13%
BB 24%

We should be narrowing in, I thought. I entered those calling ranges and computed UTG's pushing range: 43%. Hmmm, that's the same pushing range from the ideal calling ranges associated with UTG pushing any 2. How about if I try a calling range in between the extremes:

UTG pushes ??%
CO 35%
BTN 65%
SB 25%
BB 45%

Turns out this produces a pushing range of 32%. Repeating:

UTG pushes 32%
CO 11%
BTN 34%
SB 9%
BB 18%

Using those calling ranges, UTG's pushing range: 87%. And, well, I'm going in circles, or so it seems.

There should be an equilibrium point of some sort, shouldn't there? A point where UTG's pushing range produces an ideal calling range that UTG cannot better exploit with a different pushing range.

Ahh, but we're just dealing with pushing and calling frequencies, not the net expected values associated with each pushing range and resulting calling ranges. Right?

What we'd like to know is which pushing range (when countered with optimum calling ranges) produces the biggest net expected value. Is there some way to come up with this value?

Re: Optimum pushing and calling ranges
 

This is interesting. Wish I could help, but the best I can do is... bumpity bump it....