When a tournament is down to heads up, or you're playing a HUSNG, and you're down to 10BB or less, most regs' default strategy is to go into push/fold mode. What is push/fold mode? It's where the players limit themselves to either shoving all in or folding. They'd use push/fold charts something like the ones found
here.
What are these charts? These charts are essentially the Nash Equilibrium solution to the game where the players strategic options are limited to either going all in or folding (and then calling or folding for the big blind). Now as stated on the website, this game only approximates full poker as the stacks get shorter and only recommends using this approximation for 10BB or less. But how far are these charts from equilibrium at these stack sizes?
Now we know for 2 player zero sum games we are at equilibrium when neither player can unilaterally increase their EV. So if we started by using the simple push/fold approximation, could we increase our EV by considering extra strategic options? Well for 8BB or less the answer is barely, but for 9-10BB the answer is yes. And by a decent amount as well. I'm will do all my explaining using the 10BB example and just provide the strategy for 9BB. A side note as well, this is just a better strategy to use. I am certainly not claiming the strategy is perfect equilibrium. The point of this post is to provide a strategy that is just as easy to use as push fold charts.
So what is the EV of the push/fold strategy for each player? A simple run on a solver will tell you that the EV of the SB is -0.05 per hand and +0.05 for the BB (as the game is zero sum). Now this might sound like it's close to break even for both players but remember -0.05BB per hand translates to -5BB/100 hands for a cash game, which is
huge disadvantage. Can the SB do much better by adding strategic options? The answer is yes.
Consider the game where the SB can shove, min raise or fold, and the BB can only shove over a min raise or fold (and then obviously call/fold to a shove). Now if you solve this game you'll find the SB never shoves (if you use a solver it'll converge to 0 as you run it for longer). So we can remove this as a strategic option for simplicity. So now the SB can only min raise or fold and the BB can only shove or fold to the min raise. What's the EV of the solution to this game? The EV for the BB is about +0.006 which is almost 10x smaller that the previous game. That's a
huge win for the SB. Now if you look at the solutions (I'll provide them down the bottom), this result makes sense. The SB is folding 10% less hands so they are losing 10% less of a SB (as they lose 0.5 blinds when they fold their hand) and 10% of 0.5 is 0.05 which is close the amount of EV they gained. I know that's not a rigorous explanation but I hope it made some intuitive sense. So by simply playing the charts I've given (and not considering adding more strategic options) when you are in the small blind you can improve your win rate by a significant amount. This is huge for tournaments as although you may not be at this stage of the tournament too often, when you are you are playing for huge sums of money and the increase in EV translates to huge sums of cash. HUSNG's are just as important as this stage of the match takes up a significant % of the total match. When I play HUSNG's I see too many regs just go into push/fold mode, without understanding they can increase their EV by adding strategic options.
Now there are a few questions to consider-
What about if we include calling for the BB?
What about if we allow the SB to limp?
What about if we consider exploitative strategies?
I'll talk about these 1 by 1. But before I do I'll briefly talk about solving post flop play as 2 of the questions consider this. Now when solving post flop play, sure, we could use a solver and it wouldn't be too hard to come up with practical strategies to use that closely approximate the Nash Equilibrium solution. But these solvers require you to put in a flop and there are 132600 different flops and we would need to put in heaps of different ranges 132600 times to determine which hands the BB should call with and which hands the SB should limp with. So this isn't a practical option.
What about if we include calling for the BB?
First thing to point out here is that many regs (not all) would just play an exclusive 3 bet shove strategy. They are already 3 bet shoving a bunch with 11BB-16BB stacks and for 9-10BB they are risking less chips and would be able to shove more often, so it'd be easier to never call. Some good regs though will adjust to the min raise strategy (rather than the push/fold strategy) by calling, but that isn't super worrying to consider as we are in position as the PFR, so we will realize more than 100% equity (for our whole range). Now consider how many hands the BB loses EV with by not 3 betting. I don't know the exact number but I'd say it'd be a something like 15% (could be anywhere between 10 and 20 percent). So if our opponent 3 bets these hands, we are also playing against a weak range when they call and will realize way more equity.
So to put this in simple terms. Let's say that our opponent will try to exploit our strategy. To do this, they shove with AA and call every other hand that's plus EV to do so. Now our 3 bet calling range is super -EV, but we make up for that in the post flop play. This is for 2 reasons: (1) our opponents let us realize more equity with hands that we shouldn't be seeing equity with. (2) Our opponent fails to force us to put money in the pot when they have strong holdings (such as KK). So if our opponent were to play a calling strategy it won't contain super strong holdings and will be easy to play against.
But if we were the BB there is still nothing wrong with playing a calling range, it'd just be difficult to construct a balanced one that'd prevent us from being exploited. And the alternate strategy I provided is supposed to be easy to use. If you were a HUSNG reg I'd recommend looking into playing a calling range here, for anyone else it's unnecessary.
What about if we allow the SB to limp?
Now this is a perfectly valid strategic option for the SB to use. There are a couple problems however. If we use a strategy of only limping or folding (no raising), we allow our opponent to realize a tonne of equity they shouldn't be, and we don't force them to put money in the pot when we have strong holdings. So this isn't a great option, and we'd need a strategy that consists of limping some hands and raising others. This would be a tough strategy to construct and employ but certainly possible. The point of this post though is to provide a simple strategy that is no harder to use than push fold charts, and by using this strategy you will not lose much EV by not including limping. However if you a HUSNG pro I'd recommend using a strategy that consist of limping.
What about if we consider exploitative strategies?
Now obviously the exact methods of exploiting our opponents is very much dependent on their leaks. So the thing to consider here is which strategy is our opponent more likely to make mistakes against? Then we'd use this as our default strategy until we determine their leaks. The answer is clearly the strategy I provided. Our opponent can easily look up push/fold charts online and play perfectly against us. However they can't look up how to play perfectly against the min raise strategy as it includes post flop play where they are very likely to make mistakes. Also only the serious regs would study how to play against this strategy, and they'd only do it if they played against people using it. So even the regs will make big mistakes when they first come across against people playing this strategy.
Another big thing to consider is fish will be more inelastic to bet sizing than what they should be, so they likely won't defend enough and this becomes a far more profitable steal. Shoving only becomes better when they defend too much vs min raises and shoving, but you can still use the min raise strategy as your default strategy until you find this leak, as fish that defend too much are less common than ones that don't defend enough. Also, the fish will call a lot more and including post flop play will allow a much larger edge vs the fish.
So when it comes to having an edge over our opponents the min raise strategy will allow us to have a much larger edge.
Note that these strategies round off the mixed strategies. Eg if you're meant to raise J2o 90% of the time and fold 10%, I'll say to raise it 100% of the time. This makes no difference in our EV (vs opponents playing an equilibrium strategy) and our opponent will never play enough against us to exploit us and even if they did it'd be so by so little.
10BB game. SB: Min raise/fold. BB: Shove/fold
SB raise (68.2%): 22+, Jx+, T5+, 95+, 87s, 76s
BB shove (48.6%): 22+, Kx+, Q2s+, Q8o+, J5s+, J9o+, T6s+, T9o, 96s+, 86s+, 75s+, 65s, 54s
SB call (45.5%): 22+, Kx+, Q3s+, Q8o+, J7s+, J9o+, T7s+, T9o, 97s+, 87s, 76s
9BB game. SB: Min raise/fold. BB: Shove/fold
SB raise (66.8%): 22+, Jx+, T6+, 96+, 86+, 76s, 65s
BB shove (48.5%): 22+, Kx+, Q2s+, Q7o+, J6s+, J9o+, T6s+, T9o, 96s+, 86s+, 76s, 65s
SB call (49.2%): 22+, Kx+, Q2s+, Q7o+, J6s+, J8o+, T6s+, T9o, 96s+, 86s+, 76s, 65s