Quote:
Originally Posted by TensRUs
I have an embarrassing question, but it's bothering me immensely...
pg 42 (or right before section 2.2.2 for eBook readers) we are given V's shoving range:
33+,A2s+,K2s+,Q5s+,J8s+,T8s+,A2o+,K4o+,Q8o+,J9o+
According to equilab, this range represents 40.42% of hands
We are given a shoving frequency of .4188 and a folding frequency of .5812
--------------
It seems intuitive to me that shoving frequency should equal the % of hands in V's shoving range, however we are given a .4042 shoving range and .4188 shoving frequency. Can someone explain to me the logic behind this?
Card removal effects. That range is 536 hands, and there are 1326 hands total, and 536/1326=0.40422.
But in this example, we hold 7h4c, so Villain can't have any hands with those cards in them, so his shoving range is actually
33,55,66,88+,A2s,A3s,A5s,A6s,A8s+,K2s,K3s,K5s,K6s, K8s+,Q5s,Q6s,Q8s+,J8s+,T8s+,A2o,A3o,A5o,A6o,A8o+,K 5o,K6o,K8o+,Q8o+,J9o+,Ac7c,Kc7c,Qc7c,Ac4d,Ac7d,Kc4 d,Kc7d,Ac4h,Kc4h,Ac4s,Ac7s,Kc4s,Kc7s,Ad7c,Kd7c,Ad4 d,Ad7d,Kd4d,Kd7d,Qd7d,Ad4h,Kd4h,Ad4s,Ad7s,Kd4s,Kd7 s,Ah7c,Kh7c,Ah4d,Ah7d,Kh4d,Kh7d,Ah4h,Kh4h,Ah4s,Ah7 s,Kh4s,Kh7s,As7c,Ks7c,As4d,As7d,Ks4d,Ks7d,As4h,Ks4 h,As4s,As7s,Ks4s,Ks7s,Qs7s,4d4s,4h4s,4h4d,7s7c,7d7 c,7d7s
which is 513 combos. And if we remove two cards, there are a total of nchoosek(50,2)=1225 total combos remaining. And 513/1225=0.41878.
Quote:
Originally Posted by TensRUs
This just becomes concerning for me because if I were to create example problems for myself to solve, I would have to ensure that the range I assign makes sense with the shoving and folding frequency I assign and vice versa. Ensuring something makes sense is not finite, and that potential margin of error has me thinking that the problems I create and solve for myself might be wasted time. Here is an exaggerated example:
V's shoving range - JJ+, AKs (2.11% of hands)
V's shoving frequency - .853
So clearly, shoving range cannot be less than shoving frequency. Does the same principle apply the other way around?
Also I tried to create and solve a problem myself. If anyone can check the math for me I would appreciate it:
H's stack (sb) - 13.2bb
V's stack (bb) - 9.7bb
H's hand - T7hh
V's shoving range -
A2o+, K4o+, K2s+, Q8o+, QTs+, JTs+, 22+
V shoving freq - .41
V folding freq - .59
Raise sizing - 2x
Raise/call off, raise/fold, or fold pre
EV h,a = max[ 12.7bb, 14.2bb * .59 + .41 * max(11.2bb, EQ * 19.4bb) ]
The bolded number looks incorrect. If you get it all-in and win, your stack will be 13.2+9.7 BB.