Heads Up NL Holdem: Best strategy against all in every hand

Question

Assume you are playing a NL Holdem tournament heads up where the starting stack is 200 times the big blind. What is the best strategy against these all-in scenarios, and what is the expected win percentage when implementing the best strategy against these scenarios?

1. Opponent goes all in every hand.
2. Opponent plays Sklansky's System.

I'm guessing there is some software out there that has already calculated the answers?

Update: Bogdan mentions in his answer below that in the case of Sklansky's system, if the opponent moves all in on your raise, you should fold since you know he has AA, KK, or AKs. (I assume he meant fold unless you have AA.) He all but said the perfect strategy would then be to make a small raise every hand you are first to act, and therefore you will either win, or end up folding to AA, KK, or AKs. In light of this, I think we would have to revise the system a bit, or else you could simply make a small raise every hand you act first (yielding nearly 99%ish win rate of those hands), and just letting the opponent fold when he doesn't have a push hand when he's first to act, so you can blind out the opponent with this strategy. Since we're talking about heads up, I think it would be better to omit the part of the system that says what to do if the opponent raises. So for #2 above maybe we should just assume the system will use the same all-in hands regardless of first to act or not.

Note, what I'm actually after is the expected win percentage in this scenario. I'm expecting the answer to #1 to be something like: call the all in with the sklansky system hands and you'll win this tourney 5X% of the time. Or call with pocket pairs and you'll win 6X% of the time. Or call with Ax, 88+ and you'll win 7X% of the time, etc. I have no idea how to figure out how to calculate what those percentages are for this though, since you get blinded off every time you don't play a hand.

Answer 1

Of course that you can beat both systems by calling with KK+, but we are here to win and exploit our opponents, so we won't play only the nuts. You can build your own calling ranges to get the preflop equity that you want, but remember that here there is a trade-off between equity and how many times you actually win the HU battle. If you play only AA, against a random hand you're an 85% favorite... but how often do we get AA?

Against shoving every hand, my best bet is to call with 22+ and AJ+. This might seem a little nitty, but you will win, in the long run, in about 68% of the time, with the added bonus that your opponent will never know if you'll call or not and, until he figures out your strategy, he'll get stacked off 7 times out of 10. You can add some more hands in the mix, if you like to gamble, but I'm more of a pragmatic type and I want to win also. So, I'll stick with the range stated earlier.

Against Sklansky's method, it's even easier. You know his ranges, you know his play, so it won't be a big deal building a counter-exploitive strategy.

If there is a raise in front of you, then you go all-in if you have any of the following hands: A pair of aces A pair of kings Ace king suited

Counter-strategy: fold every time.

If no one has raised in front of you, then you play a little bit looser. You're going to go all in with any pair, any suited connector bigger than 34 suited, and ace - little card suited, and any ace king.

Here, we can talk a little bit. The range recommended by Sklansky, 22+, 45s+, A2s+, AKo is 13.12% of the total number of combinations. To be at least flip against this range, you need... well... the same range. To win more than 50% of the time, we go back to range building, by trial and error. My rule of thumb here, when building ranges against a defined range, is to begin with a range that is half the given one. So, we'll take 13.12/2 = 6.56% of the entire range, which is:

88+, A-10s+, KJs+, AQo+

Against his range, you have 58.61% equity.

But I am not satisfied. 58% is too low to take against a mechanical, known strategy. So, we'll refine the initial range a little more. Let's get rid of the Kx hands, because we can get into a domination situation, with us on the wrong side. Our refined range #1 will be:

88+, A-10s+, AQo+

Which is 6.18% and which gives us exactly 60% equity.

How much you want to refine this range is up to you. In the end, it will be an optimum between the pre-flop equity and the actual number of times that you get your cards and he shoves.

I hope it helped.

Good luck!

Answer 2

Check out these two great links. These people have already done the math for you.

http://www.pushfoldcharts.com/headsup/

http://www.holdemresources.net/h/poker-theory/hune.html

Generally people call way too tights in short stacked heads up, so you can even shove wider than these charts (I promise), depending on your opponent.

You haven't mentioned how deep you are playing, but for under 20 BB these sites have solved the game for you. As stacks get deeper I would advice to call off tighter, since if he really is shoving every hand, you can wait and get it in as a big favorite.

Answer 3

Villain goes all in every hand

Say blinds are 1, 2 and you start with 200 (100 bb)
You need all 400 to win

It would seem safe to just wait for AA but the problem there is getting blinded off as you only get that 1/221. If you wait 110 orbits you have paid 330. Most likely you will hit AA in 2/3 but you still go broke as are behind where you started.

You are going to need to win two hands as you are getting blinded off. So the problem is reduced to what is the maximum blinds you can lose. That magic number is 66.67 chips = 22.22 orbits.

start       200.00
lose blinds -66.67
net         133.33
double up   266.67
lose blinds -66.67
net         200.00
double up   400.00

You can play a little tighter as if you cripple them they would have to win back to back. If you allow yourself to lose 80 chips and win back to back villain is left with only 80 chips after you win 2 pots. And the number are cleaner.

start       200.00
lose blinds -80.00
net         120.00
double up   240.00
lose blinds -80.00
net         160.00
double up   320.00
lose blinds -80.00
net         240.00
double up   480.00  

So now you are playing 26.67 orbits = 53.33 hands. You can be very selective - the top 1.88% of the hands. That is JJ+. But on average you hit in 2/3 the number. If your chance is 1 in 100 then you will typically hit in the first 67. So you can tighten up to QQ+. After you win the first you can afford to get blinded off some more so you can tighten up to KK+. If you crush them to 80 chips of less after winning the second pot then tighten up to AA only - you only need to get it in before they get to 200 chips. If it goes 3 and you lose the 3rd then loosen up to JJ+ as you risk getting blinded off - you want to get it in before you get to less than 120 chips. You may even take them down in 2 pots as there will be variance in how many hand you need to play. About 1/2 the time you will take then down in pots. With this strategy you win 2/3 of the time.