Is pushbotting not always the optimal play? (Long)

[skegvegaspoker]

I would like to address a situation that has recently arisen on 2+2 and, in particular, it came to my attention in good2cu's excellent post earlier today. I would like to postulate my thinking by an example that I recently encountered.

Party Poker $22 Speed Tournament, Big Blind is t800 (4 handed) Converter on pregopoker.com

CO (t1730)
BTN (t7676)
SB (t5380)
BB (t5214)

The pretext for the hand is that BTN, SB and BB are 2+2ers and so you can be "pretty" sure that they will not be doing anything too crazy.

CO folds (probably a bad move with most card but, hey, he's a donkey and I'm not concerned about his play.)

If both blinds were completely sure BTN was pushing any two, and they only required a call to be +0.0$EV, their ranges would be 77+,AQs+. With this range, this makes the BTN push +EV with any two cards. In fact, for the button push not to be good with any two, the SB/BB calling ranges would have to be wider than 55+,AT+,A8s+. So, against two 2+2ers, I think we can safely say that it is +EV to push from the BTN.

However, I would like to argue that, although it is +$EV, and indeed inexploitable to push from the button, it is not actually optimal to push in this specific situation. So, if nothing else, please respect my bravery for postulating this theory in STTF on 2+2, where non pushbotters get hurt.

Say we are the BB. If we are 100% sure that the BTN has any two (which isn't that crazy for an assumption) our widest calling range should be 77+,AQs+. If we require a min. edge of 0.3% this becomes 88+,AKs. When asking several well respected STTFers, most responded with a much tighter range. So say, the typical 2+2ers calling range here, from what I have asked people, is 99+,AKs. I think that this is perhaps correct, as one tends to tighten up both due to the small stack hitting the BB next hand, combined with the fact its tough to be 100% sure that the BTN is pushing any two.

Now, in this hand, that I posted earlier in STTF, I pretended that the BTN has raised the pot to 2000 chips, and the SB had folded. I asked firstly if we would ever flat call. No, we would not. And rightly so. Secondly, I asked what hands you would come back OOT with. The average response seemed to put our repushing range at TT+,AKs. I believe this was the case for the following reasons. Firstly, a re-push would require the BTN to put only 3214 chips into a 7614 pot, getting almost 2.5-1. Therefore, it would seem we have very little fold equity as the BB. Secondly, the CO is reaching the BB next hand, and has only 2xBB for there is no need to put our tournament life on the edge.

So, what I am trying to get at is the fact that the BB's range for calling an all-in here, assuming he is a solid player, is very similar, if not identical, to the range that he would re-push with.

OK, so we now have two options:

Option 1: We push any two. Assume the SB/BB calling ranges as TT+,AKs (due to the fact they are 2+2 players). Let us now take a random hand from our any 2 range. T5o is sufficiently junk-like I would say. At a $109 STT, this is +1.6%EV or +$14.69 in monetary terms. Fine. I like that near $15 in my pocket. But, can we make more...?

Option 2: We raise to 2000 chips. Here, we will encounter the the following scenarios. I will explain after why these can be placed into these sections and these sections only:

1) SB folds, BB folds.
2) SB pushes, BB folds, we have AA.
3) SB pushes, BB folds, we have KK.
4) SB Pushes, BB folds, we have QQ.
5) SB pushes, BB folds, we have AKs.
6) SB pushes, BB folds, we don't have any of the above.
7) SB folds, BB pushes, we have AA
8) SB folds, BB pushes, we have KK
9) SB folds, BB pushes, we have QQ
10) SB folds, BB pushes, we have AKs
11) SB folds, BB pushes, we don't have any of the above.


1) doesn't need explaining
2-6) After the SB has pushed we have his range at TT+,AKs as is mentioned above, and so we can call only with QQ+,AKs for it to be profitable (see Appendix 1)
7-11) As above but with BB (See Appendix 2)

Also note that we are dismissing the times where SB pushes and BB calls, but as SNGPT ignores this, coupled with the infrequency of its occurrence, it will not have a significant effect on calculations.

So we have the following $EVs for each of the situations above. The maths is done through ICM model and Pokerstove.

1) $353.20
2) $386.85
3) $347.98
4) $311.55
5) $290.42
6) $288.97
7) $382.46
8) $345.28
9) $310.44
10) $290.09
11) $287.31

So, now, let's take just the situation where we have a junk hand. Let's go back to the T5o example.

This time, say we would raise to 2000 here. Some more calculations then:

- 94.09% of the time, it gets through and when it does, our EV is $353.20 (number 1 in the list).
- The rest of the time, 5.91%, we get re-raised all-in and we fold, our EV is approx $288.97 (taken on the SB pushing with TT+,AKs over us and us folding – number 11 on the list)

Therefore, this play has an $EV of $349.40. Remember, pushing only had an $EV of $311.98. Folding has a $EV of $297.28.

This is a huge difference. +$37.42 compared to pushing and a massive +$52.12 compared to simply folding pre-flop.

Where does this difference arise? Well, basically, we are avoiding all the times that we are dominated when we have a junk hand and one of the blinds has a very good hand. Losing ~5000 chips at this time really hurts us, but losing 2000 doesn't have even nearly the same effect. Remember, if we get all-in now and lose, we only have around 2000 chips left, only 300 more than the shortest stack.

Now, I admit this idea is only appropriate with fairly specific stack sizes and opponents. We basically need both SB and BB to be solid 2+2 multitablers. We need to know that there ranges are tight. However, after doing a little research, I believe that actually in game this is true. Moreover, we need to know that they won't be tricky and push over with marginal hands. This only has such a great effect if both SB/BB's over pushing ranges are the same as their calling ranges. However, again, from the (limited) research I have done on this, it seems that this is actually the case, or very nearly the case. This is for the apparent lack of fold equity that the SB/BB would have.

I think all these assumptions I have made, although not perfectly accurate, are sufficient so to ensure that they do not have a significant effect on calculation that may lead to such a difference in possible EV.

Try it with other junk hands, monsters and even marginal hands, it always produces at least as good a +$EV than pushing with these stacks. And although I foresee everyone's first response being that one cannot assume SB/BB re-pushing range is the same as their calling range, I honestly think that this is very nearly the case. I know for sure it if I am sat on the BB and from others' responses, it seems to be the same for much of STTF.

Please don't assume I'm advocating min-raising and even not pushbotting in general, I just think there are many scenarios in STTs where pushbotting is generally accepted to be the perfect way to play when it is, in fact, not. These situations do arise, and whilst I am of the belief that these are no way near as important as perfected early play and general later pushbotting, I do think there is a place for them in optimal STT strategy.

Also, before you berate me, I realise that if I presented this for my GCSE (from the UK) mathematics coursework, I would be failed, owing to random rounding errors, poor presentation, bad grammar and spelling etc. But, this isn't maths coursework. So there.

Finally, I would like to thank both Bluefeet and Gelford for their assistance with this post.

Disclaimer: I just read velocity's post in my other thread and it completely ruined everything. Well, not really, but it made it less accurate. You'll just have to remember if you want to make this move, not to do it against him. LOL. Oh well, would be interested in comments.

Thanks,

Graham.

APPENDIX 1 - Evaluating 2-5.

Here, SB has pushed with the range TT+,AKs and the BB has folded. Can we call with the following?

AA CALL: (78.66% WIN x $434.0205) + (4.00% SPLIT x $338.5528) + (17.33% x $184.0927) = $386.85
KK CALL: $347.98
QQ CALL: $311.55
JJ CALL: $279.18
AKs CALL: $290.42
FOLD: $288.97

So, we can call with QQ+,AKs here

APPENDIX 2 - Evaluating 6-10

AA CALL: $382.46
KK CALL: $345.28
QQ CALL: $310.44
JJ CALL: $279.47
AK CALL: $290.09
FOLD: $287.31

So, as in Appendix 1, we can call with QQ+, AKs here.

[aujoz]

this works the first time... until your opponents realise what you're doing, and then you get re-pushed a heap.

[blackize]

Very few are going to reraise light in this spot. However let's look at the converse of this.

2p2er in the BB knows you are raising any 2, and he knows that you think his push range here is very narrow and knows that therefore your calling range is QQ+, AKs or 2.5%

It then becomes profitable for him to push any two over your raise. Even if you call top 10%, it is profitable to push any two. In fact it is not until you call with the top 33% that it becomes BREAKEVEN for him to push any two over your raise.

Against a 2p2 multitabler who isn't capable of thinking on this level there are more profitable moves than pushing, but when you are up against someone who can think on this level and will abuse you as such, you are sacrificing a lot of $

[skegvegaspoker]

Aujoz: I can see that in the long-term this could be a problem, but these situations don't tend to come up in many games, and when they do, they are usually once per bubble, so it would be hard for an opponent to do. Possible, but I'm not sure I as an opponent would do it, for example.

However, blackize: I think this ruins the plan doesn't it? LOL. Would you then see this move as being profitable against any type of player? Maybe a tight non-pushbotter. There are some I believe.

[blackize]

Of course there are some who can be abused in such a manner, but in my experience "tight non-pushbotters" HATE when you steal their blinds and are much more likely to make plays at you or call loose than your average 2p2er or even average donkey.

[RexWoo]

This is thought-provoking and really interesting.

Thank you for this

[Gelford]

I found velocity's reply in your original post quite interesting, he saw right through the play and advocated pushing over you with a fairly wide range.

It all depends on the players involved but worth keeping in mind in big stack situations.

[Paul B.]

Summary?

[wiggs73]

Fantastic post.

I think the real key here is to not start doing this as a standard, but to mix it into your arsenal.

The reason why is that ok, say you ALWAYS push any 2 here. Your EV is basically set in stone if everyone is playing optimally. You'll go all-in, which is unexploitable (like you said) even if SB and BB only call with the hands that they should. And SB and BB will call with the hands that they should. It's a +EV move to push and that's that.

If you ALWAYS raise to 2k, your EV isn't set in stone because now, if they are observant players and aren't 16 tabling $20,000 SNGS readless, they will start to realize that they have additional equity - fold equity. You'll start to get re-pushed on and not just from hands that would call a push. BB might see you raise to 2k 3 times in a row on the button and look at KQ or A9 and decide to ship it. Hell, he might look down at 44 or TJs if he's confident enough in his read.

So I think the key is to mix this play in. Push 3 times and then raise to 2k. What does this random raise to 2k mean? Does it mean you have a monster that you don't WANT them to fold? Maybe, I mean this is the first time you've made this odd non-push raise. So at least in this instance, MOST people would have to treat this as a push. Only you're now getting additional equitiy because it isn't a push, you're actually losing less on average when the blinds wake up with a hand. So that's what's important I think - only doing this at a frequency where the other players have to treat it as a push. And that also means raising to 2k with AA-QQ quite a lot too, not just with your junk hands. Obviously if you ALWAYS folded to a push after raising to 2k, that would be very exploitable.

And of course, my entire premise is that if you mix this play in, other players will treat it as a push. You'll need reads to know whether or not this is true.

But I love that you're thinking outside the box some - it's something that I've been doing as well lately. I really don't think SNGs are as "solved" as a lot of people say they are - I think we've just found a way to play them that lets us grind out a steady profit without thinking. But maybe if we start thinking again, we'll find there is some extra profit to be had that we weren't taking advantage of before.

[Moose747]

I think the light raise increases the likelihood an opponent commits all his chips to the pot. This is a very bad thing in bubble situations. Bubble is all about fold equity; no need to get fancy.

I don't like the play, but I do like the thinking behind the play.