Resteal Redux

I think a bunch of people missed the point of my last post. I don't really mind sticking my neck out once and a while and being a bit controversial, because it tends to get people thinking deeply about important concepts. That was what I was trying to do. There have been tons of posts about making moves with ATC in MTTs (not just Hoy). I often cringe inside when I read these, as there is typically no justification given other than the results of a single hand (which is never a valid justification). A bunch of times, I wanted to really rip apart the poster in the comments, but I have always held back. If someone has the balls to put their opinion out for all to see, I am not going to rain on their parade by nitpicking the math, like I tend to do. So I read Hoy's resteal post, and did not like the conclusion from the very beginning of the post. This was a very specific example of a steal and a resteal from the end stages of an MTT. I liked the resteal example because it was a resteal push, which simplified the math and made it possible to at least put together the form of the equation to calculate expectation value. Since this was a post about making moves, and no hand value was given for either example, I am assuming we are talking about ATC here. Hoy goes on in the post to show how you don't really do this with ATC, but in the beginning this statement caught my eye.

And the thing about restealing is, it is worth way more in terms of chips won than any kind of a regular blinds-and-antes steal, so that makes it all the more important to a long-term survival strategy in the low-M late stages of mostly all online mtts.

The problem I have with this statement is that the number of chips won on a given hand, does not say anything to the importance of a strategy to winning a tournament. You could autopush 32s whenever you get it, and if you are called and it wins a big pot, that does not make it an important or good strategy. The fact that a resteal will win you more chips proves nothing.

I was trying to communicate two things in my post.

1) The very specific resteal example given in the beginning, may be -EV.

2) If you compared the steal vs. resteal with ATC of the two examples, the steal would have a higher EV.

That was it.

I was not saying the following in my post.

1) Restealing is never +EV.

2) Restealing is bad in general.

3) Restealing in general never happens in cash games.

So now that I have opened up this can of worms, I guess to dig myself out, I will need to calculate the expectation value of the steal with ATC from Hoy's example. This is not trivial at all, and why I did not try to do it before. If you guys did not like my resteal calculation, I am sure you will not like this one either. But I will give it an honest shot, and we will see what falls out.

Assumptions

1) For the steal, like I did with the resteal it will be done with ATC. ATC does not include any of the top 20% hands. If you raise the button with a top 20% hand, that is not a "steal" though it may appear so to the blinds.

2) To simplify things the button, BB and SB will all have a 100k stack to start the hand.

3) To further simplify things the SB and button may call the steal or may push all-in. They can't make a smallish reraise that would pot commit them any way.

4) The stealer will fold to a single push for all 0-70% hands, and call 70-80% hands.

5) The stealer will always fold if both blinds push.

Blinds 4000/8000, Ante 1000 7-handed. It folds to the button who raises to 24k with ATC.

SBs strategy preflop.
SB is out of position to both the button and BB and will need a strong hand to play on. SB will push a top 10% hand, call a 10-20% hand, and fold all other hands.

BBs Strategy preflop
BB has more money invested and is more priced in. BB will push a top 15% hand, and call a 15-30% hand.

Chances that the steal wins preflop.

(.8)(.7) = .56 or 56%

EV when won preflop = .56 (19,000) = 10,640

Chances that both blinds push preflop.

(.1)(.15) = 1.5%

EV when both blinds push .015 (-24000) = -360

Chances that the SB only pushes and stealer folds.

(.1)(7/8)= 8.75%

EV for this is .0875 (-24000) = -2100

Chances that the BB only pushes and stealer folds

(.15)(7/8) = 13.1%

EV for this is .131 (-24000) = -3144

Total EV for this ending preflop is +5036

All-in preflop situations

All-in vs. BB

BB has a top 15% hand, and stealer has a 70-80% hand. I will assume that with these ranges the BB is a 60/40% favorite.

EV for this situation.

Stealer wins (.15)(1/8)(.4)(109,000) = 817.50
Stealer loses (.15)(1/8)(.6)(-100,000) = -1125

All-in vs SB

SB has a top 10% hand, stealer has a 70-80% hand. I will assume with these ranges that the SB is a 65/35% favorite.

EV for this situation.

Stealer wins (.1)(1/8)(.35)(113,000) = 494
Stealer loses (.1)(1/8)(.65)(-100,000) = -812

Total EV for all-in preflop situations = -626

Post flop assumptions

I need to make some further assumptions postflop if I want to give myself a shot at doing the calculation. All betting on the flop will be push or fold, and will end right there. I am not going to take the calculation all the way to the river (could not even if I tried). SB and BB will push all flops with top pair, middle pair, an over pair or a draw, and check all other flops. Stealer needs top pair or better to call a push post flop. Stealer will c-bet push 100% of the time a blind checks the flop. (I must make this assumption, or we will go to additional streets.). I will also eliminate the both blinds call case preflop (both push and its over already for the stealer). If either blind pushes and is called by the stealer (or check raises), I will give them a 65% chance of winning the pot.

I wish I could nail this part, but this is very, very difficult.

The stealer does not have a pair as he does not have a top 20% hand. You can't assume both cards the stealer has could make top pair, since he has ATC, so just one of them has a shot. I give him 3 outs x 3 cards or about a 20% shot of catching something he can call a push with.

I will put the chances of a blind picking up the required hand at at least twice that, so I will say 45% chance. I will also say that the blinds will go for a check raise 1/3 of the time they catch like this (probably higher, but since the stealer will autopush I will leave it like this.)

Vs. BB post flop.

BB check folds

(.44)(.55)(2/3)(34000) = 5430

BB pushes, stealer folds

(.44)(.45)(2/3)(.8)(-25000) = -2610

BB pushes, stealer calls and wins

(.44)(.45)(2/3)(.2)(.35)(109000) = 977

BB pushes, stealer calls and loses

(.44)(.45)(2/3)(.2)(.65)(100000) = -1699

BB Check raises the Stealer, stealer wins

(.44)(.45)(1/3)(.35)(109000) = 2492

BB Check raises the stealer, stealer loses

(.44)(.45)(1/3)(.65)(100000) = -4247

Total EV of post flop action with BB

+253

Since the action against the SB heads-up will be pretty much the same, I will double this value to include both blinds expectation values. Adding everything together now will give you the expectation value of the steal with ATC from the button.

Expectation Value of a Steal from the button with ATC.

5036 -626 + 253 + 253 = +4916

This is a positive number and is much better than the -12,300 I got for the resteal with ATC. I rest my case. Let the hating begin!