November 22, 2010
Dog with a Bone (part2)
With the same preconditions for Dog with a Bone Part 1 of 2.5x btn vs two regulars who 3bet vs steal of 6% and Flat call 5% with depolarised range - with no accounting of range overlap or MW pots.
This time we are opening top 40% of hands
22+,A2s+,K2s+,Q2s+,J7s+,T7s+,97s+,87s,76s,65s,A2o+,K8o+,Q9o+,J9o+,T9o
 40*0.12 = 4.8
40*0.10 = Â 4
8.8% of the time
31.2% - we win 1.5bb =Â 0.47bb
4.8% of the time I will face a 3bet  10.5% I will continue 89.5% of the time I will fold
89.5% of 4.8 = 4.296
4.3% of all time I will surrender 2.5bb = 0.043*2.5 = (0.107)
4% of the time I will be called with a range ~
22+,A2s+,K2s+,Q2s+,J7s+,T7s+,97s+,87s,76s,65s,A2o+,K8o+,Q9o+,J9o+,T9o
Vs 99-22,AJs-ATs,KJs,QJs
45% vs 54%
Thus we have 45% of 2.5bb of 4% total incidents = (0.45*2.5) *0.04 = 0.045 bb = (0.05)bb
31.2 = +0.47
4.3% = (0.107)
4% = (0.05)
0.5% =?
0.47 - 0.107 - 0.05 = 0.31bb
40% steal range nets 0.31bb
If you recall 100% of hands returned us = 0.56bb
Given we invest 2.5bb - our rate of return on total investmentÂ
0.56/2.5 = 22% or 0.31/2.5 = 12.5%
This appears to be a 80% slashing of returns on our steal if we choose to tighten up.
So with those fixed variables it would appear that - it is more profitable to continue opening rather than tighten up because the compensation in having a stronger continuing range when called does not offset the foregone profit of not opening.

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