Facing a short stack shove in NL cash

This seems to come up a fair bit in the NL cash game, at least at $10 NL where I play. You open raise. Then a short stack with somewhere between 15-40 BB shoves over your raise. What do you do?

Some would say to call unless you are stealing with trash. They might say 30bb stack = fish stacking off so call. Or something like "AK vs a half stack = call". But lets look at it. After all without a read you typically wouldn't call a 100bb preflop shove with JJ. So is it correct to call say a 25bb shove?

In my experience and observation though although bad short players will stack off postflop fairly light [making set mining very profitable], they will only raise, or shove preflop with a strong range.

The tricky part is estimating that range. I would suggest that for a player buying in short then that range is JJ-AA, AKs, AK. I see them shoving those hands often and seldom TT or less, AQ or less.

Now with a range I can use PokerStove to calculate my equity against that range. Although you may be an underdog against the range, because the villian is short and the dead money in the pot it can be correct to call the all in depending on your pot odds.

First the pod odds against various shove sizes. In this example Hero has a 100 bb stack and opens for 4bb in early position, indicating strength. A short stack in middle position shoves on the preflop raise. Everyone else folds including the blinds. So when the action comes back to Hero there is 1.5bb from the blinds and Hero's 4 bb in the pot plus the short stack shove.

I've included a raked pot odds column to show the effect of an assumed 5% rake.

shove size (bb)  pot odds     raked pot odds
15               0.349206349  0.367585631
18               0.373333333  0.392982456
20               0.385542169  0.405833862
25               0.40776699   0.429228411
30               0.422764228  0.445014976
35               0.433566434  0.45638572
40               0.441717791  0.464966096
50               0.45320197   0.477054706

So as the shove size increases Hero is putting in more to call. So your hand needs more equity against his range for the call to be correct.

Now we calculate Hero's equity with some strong hands against the estimated range of JJ+, AKs, AK.

And with that the break even point can be determined. The break even point is when your hand equity is more than the percentage you have to put into the pot to call the all in. I used the raked pot odds to determine how much Hero must contribute to call the all in.

I'm using 15 as the minimum shove size to consider folding against. Below that villain is more likely to be really bad and just donking off the last of his stack and I don't think it would be bad to call with your entire preflop raising range.

hand  equity vs range  break even point
TT    33.7             none
JJ    36.6             15
QQ    47.4             35
KK    62.6             all
AK    39.8             18
AKs   42.8             25

So TT should fold to a 15 bb shove.
JJ can call a 15bb shove but no higher.
QQ can call up to a 35bb shove.
KK of course can call any shove against this range.

The suitedness of AKs helps a bit. AKs can call up to a 25bb shove but AK is only profitable up to an 18 bb shove.