4 Player Hand from All Perspectives - Nash Example

[DrEppes]

I'm interested in people suggesting non-obvious scenarios to analyze. I think the following is pretty obvious, but it's common, and we can view it from the perspective of all of the players.

Blinds (300/600):
CO: 4466
BTN: 1780
SB: 9384
BB: 4370

The equilibrium if the CO pushes:

CO (push): 22+,A2+,K4s+,KTo+,Q8s+,QTo+,J8s+,JTo,T8s+ (31.22)
BTN (call): 66+,A9s+,AJo+,KJs+ (8.90)
SB (call): 77+,ATs+,AJo+,KJs+ (8.14)
BB (call): TT+,AKs,AKo (3.47)

- CO has a wider pushing range than I expected (short stack is not short enough to CO to coast), BTN is more slightly desperate than BTN, but SB is in a more comfortable position than BTN and has a wider calling range.


The equilibrium if the BTN pushes:

BTN (push): 22+,A2+,K4s+,K8o+,Q8s+,QTo+,J9s+,JTo,T9s (32.43)
SB (call): 22+,A2s+,A7o+,A5o,K9s+,KTo+,Q9s+,JTs,T9s (22.17)
BB (call): 22+,A2+,K2s+,K6o+,Q5s+,Q9o+,J7s+,J9o+,T7s+,T9o,96s +,86s+,75s+,65s,54s (42.38)

- Short stack can't push any two since SB and BB know he's got a wide range. Short's stack relative to the blinds gives BB more latitude in calling.


The equilibrium if the SB pushes:

SB (push): 22+,A2+,K2+,Q2+,J2+,T2+,92+,82+,72+,62+,52+,42+,32 s,32o (100.00)
BB (call): 88+,AKs (3.47)

- SB can push around BB, and BB can't do much about it because he is covered.


Again, this scenario seems pretty obvious, but without reads I think these ranges seem reasonable...