Hypothetical HU situation with even stacks

[Robert]

Imagine this hypothetical situation: You are HU in the end of the sng, and you both have 10xBB. (Sng at Party, blinds 200/400, both players have 4000 chips).

1) Is it +EV to push every hand from the SB ? If not, what hands are +EV to push?

2) If your opponent pushes every hand from his SB, what calling range is +EV?
What if he pushes 75% of his hands?
What if he only pushes only 50% of his hands?

[Stripclubjunkie]

Imagine this hypothetical situation: You are HU in the end of the sng, and you both have 10xBB. (Sng at Party, blinds 200/400, both players have 4000 chips).

Is it +EV to push every hand from the SB ? If not, what hands are +EV to push?

22+,A2+,K6o+,K2s+,Q8o+,Q2s+,J7o+,J3s+,T7o+,T4s+,97 o+,95s+,86o+,84s+,76o,74s+,65o,64s+,53s+ (57%) is +EV.

If your opponent pushes every hand from his SB, what calling range is +EV?
What if he pushes 75% of his hands?
What if he only pushes only 50% of his hands?

If he pushes every hand from SB, it is +EV to call with
22+,A2+,K2+,Q3o+,Q2s+,J6o+,J3s+,T7o+,T6s+,98o,97s+ ,87s (57%)

If he pushes 75% of his hands, it is +EV to call with
22+,A2+,K3o+,K2s+,Q8o+,Q5s+,J9o+,J8s+,T9s (41%)

If he pushes 50% of his hands, it is +EV to call with
22+,A2+,K9o+,K6s+,QJo,QTs+ (28%)

Strip

[MAX]

1. I don't know.

2. K high or better and I'm calling if he is pushing 75%-100%. If he is pushing 50% I might lay down K7 but pretty much same as above.

How he responds to your limps, non-push raises, and pushes is also very relevant info.

edit: TY for the post strip.

[Rondavu]

Each time you push his calling requirements get lower and lower.

[krimson]

Imagine this hypothetical situation: You are HU in the end of the sng, and you both have 10xBB. (Sng at Party, blinds 200/400, both players have 4000 chips).

1) Is it +EV to push every hand from the SB ? If not, what hands are +EV to push?

I've written a program that finds the minmax (roughly equivalent to optimal) pushing/calling ranges for a preflop push/fold game (depending on stack depth). So far it works in terms of chip EV, which may be different from $EV in a tournament.
The output for 10BB stacks is about the same as what Strip posted above (the most striking difference is that my program suggests that you should push any K).
If anyone wants the program I can send you the (horribly messed-up and undocumented) source code (in C).
Strip: how did you compute the range you give?

[TLR]

please do send it if you dont mind, or even better post it

[krimson]

I've put in on the web: http://cstein.kings.cam.ac.uk/~johan...h/humatch.html.
It's not the least bit user-friendly, but then it wasn't expected to be used by anyone but me.

[TLR]

Thanks

[a500lbgorilla]

If either person has a 3:1 chiplead, I push every sb reguardless of which one I am when stacks are 10bets. +EV?

-'rilla

[Fortune 500]

If either person has a 3:1 chiplead, I push every sb reguardless of which one I am when stacks are 10bets. +EV?

-'rilla

Without running math on this.... I'm inclined to say yes particularly as the short stack. Big stack, I don't know.

Blinds are high. This pursuit works against both tight and loose players, given the fold equity.

Tight players will lay down more (and often better hands). Loose players have such a wide calling range, that even with a call you're not as likely to end up far behind. Coupled with the possibility of picking up the BB uncontested + chance of having the best hand + chance of winning even without the best hand... definitely EV.

Particularly with only 20 BB in play... every BB you pick up Is 5 percent of the total... 75/25 can turn around real quick with a couple steals and a legit hand.

I play on AP where there's about 13500 chips in play... once blinds reach 400/800 and up... I'm pushing any two right down my opponents throat... and don't really care if I get called.

[krimson]

If either person has a 3:1 chiplead, I push every sb reguardless of which one I am when stacks are 10bets. +EV?

Not unless your opponent is way too tight.*
Restricting the possible actions to pushing or folding preflop makes the game simple enough that you can actually solve it by direct computation. There is a "minmax strategy", a range of hands you play that guarantees that no matter what your opponent does you have at least 50% chance of winning (starting with equal stacks and button is allocated randomly). If both players play the minmax strategy the outcome just depends on who gets the best cards. If you play the minmax strategy and your opponent does not you get an edge.
What you give up if you play the minmax strategy is the ability to exploit weaknesses in your opponents play.
Paper, scissors, rock is an example of a game with a very simple solution. The minmax strategy is to pick one of the three with equal probabilites each time. No matter what your opponent does he can't get an edge over you. But if you get a "read" on your opponent's strategy you could be better off picking a strategy that exploits that (like in The Simpsons where Bart and Lisa play, Bart thinks "Good ole rock, nothing beats rock!" and Lisa picks paper).
In summary it is possible to make a bot that is essentially unbeatable HU (in the sense that you can't get an edge over it) as long as you stick to push-folding PF. And such a bot would push about 58% of hands when stacks are 10BB.*

* minor caveat: so far I've only done the computations for chip EV, not match equity EV. My hunch is that under optimal (minmax) play there is not much difference heads up.

[Robert]

Have anyone done some ICM calcutions on this HU situation?

[krimson]

Have anyone done some ICM calcutions on this HU situation?

I don't think ICM is very meaningful in this case. For HU matches ICM just amounts to the assumption that chip EV = $EV. (Or have I missed anything?) For maximising chip EV see above.

[zenbitz]

If you play the minmax strategy and your opponent does not you get an edge.

But your edge is not necessarily bigger than the edge you would get by exploiting tendencies (opp too tight or too loose).

As blinds go up, being too loose becomes less and less of a leak, finally approaching optimal when your M=1 (maybe 2?)

[krimson]

If you play the minmax strategy and your opponent does not you get an edge.

But your edge is not necessarily bigger than the edge you would get by exploiting tendencies (opp too tight or too loose).

Indeed the very next sentence in my post read "What you give up if you play the minmax strategy is the ability to exploit weaknesses in your opponents play." It cuts both ways though: if you play the minmax strategy your opponent can't get an edge by reading you either. If you can outplay your opponent (despite stacks being shallow) then do so, but if you think that your opponent is as good at reading you as you are at reading him then minmaxing seems like a good idea.

Before moving slightly side-ways to other things that have come up in the thread I'd like to mention that to date I have played about 150 SNGs. It is my understanding that some people here play that much in a few days. I therefore have to admit that I cannot speak with any sort of authority from experience, but I hope that my thoughts make some sense anyway.
Maybe I'm not giving people enough credit, but my feeling is that a lot of players simply accept that aggression and stealing is good without thinking carefully about why it works and to what extent this is applicable to a HU game. At the most basic level blind stealing is just a matter of equities: add folding equity to hand equity and you find that it's +EV to raise some less-than-premium hands.
I think there are two factors beyond that that make blind steals work:
1) Position. If there is money left behind calling a raise out of position with a potentially dominated hand is yucky, so the stealer gets extra fold equity, not to mention the opportunity to buy the pot on later streets.
2) Mutually assured destruction (kind of). If two even stacks go AI at a point where differences in pay-outs are large for each place then the winner gains less $ equity than the loser loses, and the difference is gained by the other players, who reach a higher pay-out at no risk. If stacks are shallow and the stealer is already committed to the hand it can therefore be correct for the victim to fold even if he has an edge.
The point is that in a HU situation with shallow stacks neither of these factors are in effect. Stealing therefore has no particular merit beyond the mere equity calculations.
Equity calculation is of course what the minmax strategy is all about: it tells you for which non-premium hands the fold equity is large enough to justify pushing, under the assumption that your opponent plays well.
OK, so there is one third factor that does apply in the HU case:
3) Psychology. Putting your tourney life on the line by calling AI with K5o doesn't feel nice, even if the maths shows that the EV is about +$0.05.
This is not as tangible as the other two factors though. It should not work at all against a good disciplined player (or for that matter one that mechanically plays the minmax strategy HU). I don't think that this factor is large enough to justify pushing any two when HU, but it's hard to measure.

This pursuit [pushing any two] works against both tight and loose players, given the fold equity... Loose players have such a wide calling range, that even with a call you're not as likely to end up far behind.

Incorrect I think. If your opponent is too loose with his calls the correct response is to push less. If your opponent starts calling 10BB pushes with mediocre hands like Q4s or T9o the pushing hands that go up in value are Ax and Kx - but you would push those anyway. Hands like J4s and 53s, which play adequately against most hands but are rarely favourites, are no longer pushable when the fold equity decreases.

[bigg_nate]

Krimson,

I believe it can be proven (under certain assumptions) that chip EV is proportional to $EV when a tournament is heads up. So that solves that problem.

Do you happen to know what type of edge your Nash equilibrium strategy has against a player who always calls, and against a player who always folds? The Nash equilibrium strategy is often far from optimal against poor players (your rock-paper-scissors example is a perfect illustration of this). I'm curious if that's the case here.

- Nate

[krimson]

Do you happen to know what type of edge your Nash equilibrium strategy has against a player who always calls, and against a player who always folds?

*clickety click*
Take as an example BB = 2 and stacks = 20. Then the chip equity for SB is
-0.09 if both play minmax
+1.01 if SB plays minmax and BB calls with any two
+1.14 if BB calls with any two and SB plays optimal exploiting strategy
+0.74 if SB plays minmax and BB always folds
+2.00 if SB pushes any two and BB always folds
So if the BB always folds the minmax strategy is some way behind - but autofolding is an extremely daft strategy. The edge from pushing any two decreases quickly when BB starts playing premium hands.
If BB always calls minmax is not very far behind the exploiting strategy, and I think this is probably true in most cases.

[bigg_nate]

Thanks, that's interesting information. Also, the fact that being SB is -EV even though you're forced to put fewer chips in the pot is a nice illustration of the benefits of being in position.
- Nate

[krimson]

Also, the fact that being SB is -EV even though you're forced to put fewer chips in the pot is a nice illustration of the benefits of being in position.

The break-even point for the push/fold game is when stacks are about 8BB. Below that SB has an edge because the BB's forced bet is larger, above that BB has an edge because of the positional advantage.
The push/fold model probably breaks down about there. When stacks are >8BB making a small raise (with some hands at least) from SB and playing position post-flop may be better than just pushing. Or?

[a500lbgorilla]

Krimon, I need you to explain your minmax theory again. It's just not sinking in.

Running ICM calculations for this scenario

BB 4k, SB 2k, blinds 100/200. If BB calling range is 44+,A7s+,A9o+,KJs+, I can push 96% of all hands profitably.

What does minmax say about a similar scenario?

[krimson]

BB 4k, SB 2k, blinds 100/200. If BB calling range is 44+,A7s+,A9o+,KJs+, I can push 96% of all hands profitably.

What does minmax say about a similar scenario?

It says that BB's calling range is too tight. With 10BB stacks (only the shortest stack matters) the (chip EV) minmax calling range for BB is: Any PP, Ax, Kxs, K5o+, Q7s+, Q9o+, J8s+, JTo, T9s (37% of hands).
Some of these are only marginal calls though, in the sense that while they have >45% equity against the minmax pushing range (and hence pot odds to call) they have less than 50% equity. The ones that have >50% equity against the minmax pushing range are: 44+, Ax, K7s+, K9o+, QTs+, QJo, JTs (26% of hands). With these hands it would be correct to call even if you would get your BB refunded if you folded (assuming that your opponent is not tighter than minmax in his pushing).