A small exercise

You are heads up with an effective stack size of 100bb. Villian is shoving preflop 100% of hands. Which hands can you profitably call with assuming a) no rake b) 1bb rake? Which is the minimum range you have to call with so as not to lose money from giving up your blind too often?

I don’t know the exact range, but you can obviously call very wide here. You can look on many sites to see what holdings are +EV against a random hand. It is a lot. If you were not concerned at all about the volatility, I’d be inclined to call with:

  • any pair
  • any ace
  • any suited king, and K8o+ (I think K2o actually has more then 50% equity against a random hand though)
  • Q3s+, and Q9o+
  • J6s+, and J9o+
  • T7s+, 98s, 87s

Some of these hands will be small losers, but I’m happy to encourage the continued shoves.

In terms of the minimum, you don’t need to call very often at all, but if you only call with AA, you will lose chips, as you’ll only get AA once per 200 hands, and you will have lost 200 chips before you can recover 100 (and you don’t have 100% equity when you call with aces, either, and so you’ll only be winning around 85 chips each time you have aces on average). I’m pretty sure only calling with AA-QQ and AK would be sufficient to show a profit, and suspect AA-QQ only wouldn’t quite be enough. A very conservative, but still very profitable calling range: AA-99, AK-AQ, AJs, KQs.

Ahhh… here is also a nice chart from Reddit.com, which shows the equity for each hand versus a random hand. It looks like I should have given a little more weight to high card value, and a little less weight to suited and connected hands. Oh, and it looks like AA-QQ alone would be enough to get you over the line.


If we consider the blinds as a sunk cost, then folding to the shove has ev=0. What about the ev of calling? We have to pay 99 bb in big blind or 99.5 in small blind to participate. The pot is for 200bb without rake and 199bb with rake.

EV big blind, no rake: 200 * equity - 99 which is > 0 if equity > 49.5%
EV small blind, no rake: 200 * equity - 99.5 > 0 which is > 0 if equity > 0.498%

EV big blind, no rake: 199 * equity - 99 which is > 0 if equity > 49.7%
EV small blind, no rake: 199 * equity - 99.5 > 0 which is > 0 if equity > 50 %

This chart showing equity with more precion show that for a few hands (J7o and T8o I think?) the rake and position matters, but most of the time it doesn’t. http://www.power-equilab.com/screenshots/