New calculations
Argh... I just lost a huge post. I'll try to sum up:
SeaEagle gives some estimates for AK's pot equity in various flops. Jake the Snake points out that I messed up the odds of improvement. I calculated the following new numbers:
AK unimproved, check pf:
I guess that weaker aces capture .15 SB of the pot with their 30% chance at having nailed their 2nd pair
flush draws capture 3.5 SB (surprise) because they do so well with the implied odds from the AK.
There isn't not often a flush draw out though, I estimate AK captures about 3.7 SB of the 4.5 SB pot.
AK unimproved, raise pf:
weaker aces are more profitable, capturing 8% of the pot instead of 3%, despite winning at exactly the same rate. Flush draws are somewhat less profitable as a percentage of the pot, because their implied odds are smaller relative to the pot. All told, I figured AK captures 6 SB of the 8.5 SB pot. That's 71% of the big pot, compared to 83% of the small pot. A tighter range than before, as suggested by chief.
AK improved, check pf:
AK folds often, so his 24% equity is cut down a lot. I estimated 9%
AK improved, raise pf:
AK is not forced to fold as often, capturing maybe 12% of the pot.
Adding it together:
EV (check): (1/3 * .09 + 2/3 * .83) * 4.5 - 1 = 1.75 SB
EV (raise): (1/3 * .12 + 2/3 * .71) * 8.5 - 2 = 2.33 SB
Still favoring raising, but still within the margin of error. I find that estimating the EV of the draws against us when we hit will still have a significant impact on the numbers. Next round of refinement anyone?
Good luck.
Eric
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