The pushbot chart tells you that you should push from the small blind with J4s with effective stacks of M=6. But does this apply on the bubble? The big blind has a tighter calling range, of course, so that means that we can push a wider range with +cEV. However, the bubble makes our range contract again - so what is the net effect?

I ran the numbers on a wide range of scenarios through SNGWiz to try and find the answer. The conclusions are as follows:

1. As expected, calling ranges ALWAYS contract (sometimes dramatically)
2. Against smaller stacks you push a wider range than in non-bubble equilibrium, except in a battle between the two smaller stacks.
3. Small stacks always push smaller ranges than away from the bubble

I ran all the scenarios on a 50/30/20 SNG with 4 players left. I compared the push/call ranges to the equilibrium ranges presented by Shaun Deeb in Kill Everyone. Here are the results:



A dramatic point to note is when the biggest stack is in SB and the second biggest in BB. Far from the bubble, SB would have pushed 53%. Now he should push 100%. Far from the bubble, BB would have called with top 30% of hands, whereas on the bubble he should only call 2% (AA and KK) despite the 100% push range.

Another dramatic point is with four equal stacks, all with M=3. SB's push range goes from 77% to 100%, whilst BB's call range goes from 67% to 26%.

BB

Notes:

• This is all based on ICM, and does not properly take into account who gets hit when by the blinds
• In the above, the assumtion is that the only available strategy is push or fold. This is for simplicity.
• The equilibria were found by comparing two graphical charts and reading the approximate values off those. Should be fairly accurate, but a margin of error of +/- 1% or so is reasonable to assume.

I think Nash Equilibrium give an optimal decision only if you have no any information about your opponent. If you put your opponent on a range intervall then Nash Equilibrium calculator do not give an optimal decision.

I totally agree. However, I prefer to make my decisions as adjustments from a starting point, rather than out of the blue. If I think his calling range is tighter than the Nash Equilibrium, I know I can at least push all the NE hands and then some. Otherwise, how am I going to decide my pushing range in a situation like:

I'm SB, he is BB, effective stack size M = 3, I am second stack and he is third on the bubble of a 50/30/20 SNG, His calling range is 22+, A2+, KTo+, KJs+, QJ, T9s+.

It is impossible to combine all this factors into a pushing range, unless you have some basis for that decision. On top of that, it is hard to work out villains calling range just like that. In the heat of the battle, you can have the NE play as default and then just adjust up or down based on a notion of "loose or tight caller".

Furthermore, knowing how incredibly tight our calling range should be against larger stacks on the bubble is very useful. I believe 90% of players call too lightly in this situation, and avoiding that is very +EV.

BB