NLHE Tournament Hand Ranking for All-In

[PairTheBoard]

I believe Aisthesis is using the simple criteria that your All-In bet is called by the Best of the hands that are a heads up showdown favorite against yours. You assume at most one player calls you. The trouble is it's very time consuming for Aisthesis to do this by hand. Just Coding an automated program for these criteria would be extremely useful as it would give us a complete table of results.

A small improvement on the criteria would be to assume that the Best hand that has Pot Odds to call does so. With this criteria the results would flow completely seemlessly into the K-S results for the SB.

I think it would be better getting a complete table of results for one of the above criteria before worrying about the possibilty of getting called by more than one player. Better to get the results for the simplified criteria than get no results worrying about complications.

PairTheBoard

[Jerrod Ankenman]

[ QUOTE ]
By the way, while I definitely prefer the all-in in this situation, I can't provide any objective reason why limping or a raise less than all-in is a bad play (hence, the "survey" aspect in the subject line).

[/ QUOTE ]

Well, this is no means a proof, but if we make the following assumptions:

There are 5 people behind you left to act.
If one of them calls, then that's the ballgame, everyone else folds, and you showdown with that person.
Each person will call with AK-AQ, AA-88.

So given that you hold 77, that's 76/1225, or .062.
The odds that noone will call is (1-.062)^5, or .726.

.726 * 825 = 599 chips

The rest of the time, you'll get called by one of these hands.

Your equity against this range is 34.142, so you get that percentage of a pot which contains about 5200 (depending on whether the blinds call or someone behind you), less your 2400.

((.34142 * 5200) - 2400) = -624
That's chips per time you get called, so
-624 * .274 = -171

So your net profit from this play is 428 chips.

In order for any other play to be better than jamming, it has to have an expectation greater than 428 chips. I leave it as an exercise to the reader to figure out whether limping with 5 blinds left in your stack can make a profit of a full blind.

Jerrod

[Jerrod Ankenman]

[ QUOTE ]
Hey Jerrod, great to have you join the forums. Can I hereafter refer to you as Noted Game Theory Authority JA?

[/ QUOTE ]

If you wish, although "Jerrod" is the usual way. [img]/images/graemlins/smile.gif[/img]

Jerrod

[Aisthesis]

Hey, that's pretty good! In light of the brevity of your first response, I wasn't completely sure whether it was just a "snappy answer to a stupid question," although Karlson's "respected game theorist" had me suspecting you might have some serious stuff to back it up!

I'll hit you with a more difficult one (in terms of my "chart" in this thread) soon. Your calculation is actually coming from a somewhat different angle, so I will be extremely interested to see whether or not the results agree.

[Aisthesis]

Here are some of the more important EP hands I’ve been working on with regard to the shortstack all-in question--including the 10-player addition to the chart.

I won’t go into the math behind it but should make a few comments on interpretation. First, the columns refer to number of players at the table and possibly in the hand. So, if you’re at a 10-player table UTG, the “10” column is the one to look at. The “9” column applies to a 9-player table OR a 10-player one at UTG+1 IF UTG has folded. Basically, if you apply it as a positional criterion at a larger table, the assumption is always that it’s been folded to you. If not, I’m not making any kind of claims.

The value entered is a maximum stack-size relative to total pot (NOT to the blinds). That way, it should apply whether or not antes are involved.

But I should emphasize that it’s a MAXIMUM stack-size. At the stack-size indicated, going all-in should have an EV of exactly 0!! Hence, you want to go all-in (on the basis of cards alone) only if your stack is actually SMALLER than the one indicated on the chart. There are also some indications that these figures may be a little aggressive by a small amount, so knocking off around 10% of the given stack-size is definitely safer.

Anyhow, here are the hands I’ve run that I consider relevant for the EP scenario:

----------------10-------------9---------------8
AKo-----------10.21--------11.85---------13.97
TT-------------8.87----------10.07---------11.62
AQs-----------8.64----------10.02---------11.80
99-------------6.95-----------7.91-----------9.15
88-------------5.70-----------6.50-----------7.54
AQo-----------5.65-----------6.60-----------7.82
AJs -----------5.52-----------6.43-----------7.62
77-------------4.70-----------5.39-----------6.27
66-------------3.88-----------4.48-----------5.24
AJo------------3.84-----------4.51-----------5.38
A9s------------2.64-----------3.14-----------3.80

So, just as an example, at a 10 player table UTG with blinds at 100/200 and a stack of 1,500, moving in with 88, AJs, AQo or any better hands than that is a +EV play. Moving in with 77 or AJo, on the other hand, will on the average cost you tournament dollars. You still may want to wait for something better than 88 (or, if the table is too tight, move in with 77), but this hand will on the average make tournament dollars if you move in with it even from UTG in this situation.

I’m not claiming at all that this is the “best play” or anything like that. The claim is simply that against good opponents who will call your all-in with good hands and fold bad ones, you will make money moving in with 88 but lose money moving in with 77. So, I am claiming that it would be a mistake moving in UTG at a 10-player table against good players when you have 77 and the given stacks and blinds.

The best way to view it, then, is probably as the minimum hand you need if you’re thinking about moving in in the given situation.

Any comments, questions, or critique always welcome!

[Aisthesis]

Same basic scenario with a few differences: NLHE tournament in the early middle phase. Blinds are at 100/200 with no antes. There are 9 players at your table, and you are again short-stacked, this time with 1,200 in tournament chips (sorry, but we're only going to be playing shortstacks in all of these...). Almost half of the players have been eliminated. Again no reads except the assumption of pretty decent players at this point.

This time you are dealt A8o in early MP (UTG+3), and it is folded to you. What is your best play this time? Would you play differently if you were holding A9s?

[Aisthesis]

Well, in editing a post on the "unusual hypothetical situation" thread, I noticed you could attach a file. So, I'm going to try giving you folks my complete Excel spreadsheet, so that anyone can check my formulae, math and whatever. For anyone who has Excel, the format is also WAY better.

Anyhow, if no attachment appears, please just ignore this post. If it does, I enourage anyone interested in the thread who has Excel to take a look at the spreadsheet. It's really much better for viewing the results, so even to those who are not interested in the math, I would highly recommend it. (And of course to those interested in the math: please let me know of any errors!!!)

P.S.: "complete" means here the hands I've run. I'm still working on filling in a number of blanks.

Blast! Can't get this to work... How do you get a file to attach here?

[PairTheBoard]

I think Jerrod's analysis is nearly identical to yours Aisthesis. The only difference is that he has AK-AQ calling while you have them fold since they are a heads up showdown underdog to 77. You guys are definitely on the same page though.

PairTheBoard

[Aisthesis]

Very close, anyway. I'm hoping he'll still go for my quiz #2, where I put in very borderline cases on my analysis.

As I recall, I also have JTs calling 77, as I'm pretty sure it actually is a favorite (QJs may have been in there as well, I can't remember for sure on that).

What will interest me particularly here (if I can get him to respond--hint hint!!) is how a game theorist is going to deal with the whole "open cards" issue (or find a way to get around it). And secondly, whether it really matters much whether the cards are open or not.

Anyhow, in scenario number 2 the player potentially making the all-in is going to have reduced standards for making the all-in. Hence, potential callers are also going to want to reduce their calling standards.

[PairTheBoard]

These are great quiz questions Aisthesis. Each one might even deserve it's own thread.

A8o, 6 playrs left, 1200 stack, 100-200 blinds, Zero Table Image? Normally I would be totally guessing here. I think I would probably pass but I'll bet there's been times I've made the All-In move here. Now looking at your chart I see that under your assumptions the move is good for stack sizes less than 800. How much should we adjust that to take into account the fact that people will not play perfectly behind you? It looks like this situation might be very close to the bubble. From your chart I'd have to say that A9s is definitely worth moving in with as far as expected value goes. With only half the players gone from the tourny I'd think you were far enough away from the money to dismiss surviving to the money as a factor. imo, you've got to build your stack. Make the move with A9s.

PairTheBoard