Monday, November 22, 2010

On Rush LHE Tunamelts

So Bella, I'm inclined to agree with you and Patrick because your argument makes perfectly logical sense. You have an edge, more hands is more edge, etc, etc. The logic is pretty unassailable. I have several problems though:

1. No matter what, it seems like eventually in a LHE tournament after about level 4 if you ever lose 3 hands in a row you are basically out. Like no matter how hot you've run to that point, if you have been around for 5 hours in the WSOP limit hold 'em events and all of a sudden you lose 3 hands at showdown in a row, you're going to be crippled.

2. The Big Potato is a smart dude. I can't recall him being flat out wrong about anything, so I'm hesitant to declare him so on this point. He and I once had a discussion about tournaments where we sorta concluded the following from our limited observations. In NL tournaments as you look around later and later the players get more and more solid. In LHE tournaments as you look around later and later the field seems to get polarized. Super aggressive players who have run well are alive, and super conservative tight players are hanging on. The "solid" guys (the equivalent of like TAG or maybe LAGTAG winners online) seem to die out pretty quickly. It feels like this could happen because their games are built around having infinite (for all intents and purposes) bankrolls that seek out every ounce of value.

3. The limiting case argument is pretty strong here. I'm sure you're familiar with the idea, but for those who I have confused by making up a phrase and pretending it is common knowledge just now....I like to think of problems in terms of the limiting case. If you're not sure what will happen at a certain value N or as N increases or decreases, make N equal zero or infinity and see what happens there. Unless f(N) is complex (specifically with a complicated second derivative I think) this often gives you an idea if more N is a good or bad thing. Well in the case of this limit hold 'em tournament, there are two limiting cases:

A. You play infinite hands on a fixed bankroll.
B. You play zero hands on a fixed bankroll.

You can see what's going on here. In case (A) you can make a strong argument that you will go broke, since the stakes will be increasing rapidly, much faster than the expected rate at which you can accumulate chips. But that's not really that interesting and a little hard to wrap your head around. What's easy to see is that if you and your 8 opponents take 5 hours to play the first hand, you will finish in places 2 through 10 most of the time. Supposing there were 750 or so entries, like the FTOPS event we were discussing, even 10th place is obviously better than expectation for even the best player in the world (and especially for me lol). So if playing zero hands is better than playing the expected number of hands, we need a complicated derivative, and I don't really see how we're going to get one.

4. I like to argue with smart people and write interesting things and letting something like this go would be less fun than writing about it :)

6 comments:

bellatrix78 said...

quote:
"What's easy to see is that if you and your 8 opponents take 5 hours to play the first hand, you will finish in places 2 through 10 most of the time. Supposing there were 750 or so entries, like the FTOPS event we were discussing, even 10th place is obviously better than expectation for even the best player in the world (and especially for me lol). So if playing zero hands is better than playing the expected number of hands, we need a complicated derivative, and I don't really see how we're going to get one."
end quote

---

I don't understand this point. I finished 30th and by that point the Big Blind was 2x the starting stack. I don't see how to survive by folding?
Are you suggesting a SnG strategy by ramping up our aggression as we get shorter and shorter? Or something else? Maybe a reverse SnG, that is play fast in beginning where opponents are bad and almost time out in end when jumps matter and you have a polarized range of opponents. I have problems with this for a few reasons.

a) The critical zone in LHE (when large swaths of people suddenly have <10BB) happens about when 40-50% of the field is eliminated, much much much before the bubble. The eliminations during this time are fast and furious. It's critical during this time to amass your chips, imo. But I can see being conservative, too.

b) If those polarized times are much before the bubble, then chip value is much more important than survival. We are still very far from the money, 10% get paid in MTTs as opposed to 30-33% in SnGs.

c) I did not encounter any true fish when it was <100 opponents. It was funny the swath of purple (friends), red (good) orange (winning pro, but not LHE) and yellow (ok reg) notes I saw around. I can see stalling there, chip jumps become much more valuable. In fact this one guy that was short when I busted may have made >120$ by us dumbasses that busted before him (I busted 30th with some others quickly following, he managed to squeeze in on 27th and pay jump). Maybe I shouldn't have pushed with A5o in CO :P.

Anyway, I might have just as well misunderstood your comment, if that is the case, then sorry.

Patrick said...

You can't win a tourney by never playing a hand. You also can't cash in any non freeroll tourney by not playing a hand.

Lets say you have an expectation of 2 BB/100 against the field. Will you be more likely to cash in the tourney if you play:
40 hands per hour
200 hands per hour

Which is most likely to let the cream rise to the top?

The more hands you can play at a lower blind level, the higher chance you have built up a stack to survive a suckout or a cooler later in the tourney.

This is why LAGs win NL tourneys more often than TAGs. LAGs have built up a chip stack to survive a suck-out late in the tourney. TAGs usually get in as a favorite. Losing one 70/30 means gg to the TAG.

Tyler said...

bring this up next time i see any of you. i think some points are being missed.

mostly that not all situations where you exert an edge are created equal, both in terms of an edge they create and in how much variance/relative variance they create. the second part of that sentence is just as crucial as the first too. unlike a cash game, you are continually over betting your bankroll in a tournament and as a result managing variance should be a primary concern along with managing your 'chipEV'.

secondly, 200 hands/hr obv lets the cream rise to the top better than 40 hands/hr. if every hand of the tournament was played hand-for-hand, then you would want the additional hands/level. however that is a completely different question that having all tables playing 200 hands an hour save your table where you can choose 200 or 40 per hour...

jesse8888 said...

The most interesting thing to me is the following, hopefully simple, question, assuming it were possible to stall to the point of your table playing only 1 hand while everyone else in the tournament was eliminated:

If playing 1 hand is better than playing 1000 hands, what does the graph of EV vs Hands Dealt look like? Where does it increase as Hands Dealt decreases? It must somewhere, and I'd like to know what it looks like.

bellatrix78 said...

I thought about this some more. The situation of playing 1 hand the entire tourney is just not possible Jesse, not even in a theoretical venue. It's like saying, what if "deuces are wild"? It's a completely different game then.

However, you can find a floor of hands you play and by that lower your RoR. Ruin is everything in tournaments, you're out, you're out, that's it! And yes, ICM does play some consideration there.

I do believe that it is overblown and if the question is if you play 200,250 or 500 hands, then 200 might be optimal to playing 250 hands, but 500 is by far the best option because it is such a small effect.

And this is all assuming the skill of your opponents is static throughout the tourney, which it isn't of course.

Alan Bostick said...

Unless f(N) is complex (specifically with a complicated second derivative I think) this often gives you an idea if more N is a good or bad thing.

But f(N) at the late stages of a tournament *is* complicated, because of payout structure.

In the limit where you play 1 hand while everyone else in the tourney plays normally, you wind up at the final table with a microscopic stack. You win 10th-place money and have ~1/(# of entrants) likelihood of winning any more. Heaven help you if you finish your hand before the bubble, because then you will have a stack so small you'll be all-in when the blinds get you if not before, and ~ 1/(# of entrants) equity in the prize pool when everyone else -- even the small stacks shoving in desperation -- have many times more than that.

In reality, you can make your hand last at most seven extra seconds when you fold preflop, and seven extra seconds more for each betting round. This is far too short a time to make your hand last until the final table, and the edge x volume argument dominate. Delays mean less volume, so your expectation over time goes down.