## 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

Â 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 Â 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 ofÂ  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 thatÂ  - 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.