Winrate Theory

[BobboFitos]

NOTE: I could be WAY off base here, as I dont really know what I'm talking about. But it was an idea I had.

So, while in stats class tonight, my mind wandered over to the thoughts of statistics, and naturally, I reflected on poker. Anyway, this idea occurred to me, and well, someone stop me before I start believing this (below) if it's incorrect, and if correct, someone start saying "woohoo." Something like that. There's the preface.

The point of this post is to put some statements and definitives over "winrate," which is generally believed to be a somewhat intangible goal ("I was a good winrate") yet something everyone strives for. I am going to break down my idea into a full ring game (10 handed) and a 6max game.

10handed - For the examples lets say the Party NL2k, as alot of speculation and penis waving has been done. (Btw, my winrate @party NL2k is 14.47ptbb/100 hahaha ur all pwn3d!!!1!!11)

The forced action in such a structure is two blinds of 10 and 20 dollars. The 30$dead money is what alot of people often overlook, as people focus on the stack size of "2000" or "5000" or "600" etc. this isn't bad, but it ignores what people should be inherently fighting over. (Actually, <u>Theory of Poker</u> addresses this) The difference between a NL/PL game (Big bet) and limit is obviously the escalating pot size, as this should be obvious to us all.

(For a brief interlude, 1bbpot in limit, such as blind war, with a bet on each street turns into a 6bb pot, vs a 1bb each from nl turns into a 58bb pot, which is why 10/20 NL is similar size to 100/200. Why I mention this has to do with blind size, although I guess technically I should compare 20/40 with 10/20 due to similar dead money in the pot)

Anyway, if one is forced to donate 30$ in dead money every orbit, we can technically equate this to 3$/hand. Or, for 100 hands, 300$. (Everything so far, so good?) If we use for this demonstration a player who never plays a hand, labeling him The Worst Player Prototype, his winrate would be -300$/100 = -15bbs = -7.5ptbb/100.

A note here is if you're losing more then this for any extended time, you'd do better off never playing a hand, so perhaos moving down in stakes is best for you.

The converse of this is my idea. If that's technically the worst winrate sustainable, (as said, people who lose more then that are playing even worse then fundamentally possible!) then obviously this has to be made up somewhere.

If we take rake out of the picture, to the point where poker is a zero sum game, then if one player can lose -7.5ptbb/100 sustainably in a full ring setting another player can earn +7.5ptbb/100. *This is under the assumption that the othe r8 opponents are breaking even, basically; if they all never play a hand, hero will win every pot. Sometimes they divy up the negative ptbb players, as well. So, i'm projecting that since -7.5ptbb/100 is the worst sustainable rate, the positive of that should be the best sustainable rate.

What I think, then, is someone able to win more then that consistantly is both VERY good AND lucky. However, poker is a negative sum activity. Due to the rake, this projected optimum amount must fall a little lower, as sigma losing player (difference) sigma winning player must be &lt; 0, which is where the house edge occurs.

So, the optimum winrate falls more along the lines of ~6.8ptbb/100 in a full ring game.

The reason shorter games are more profitable are not because "people are put into more marginal situations where there is greater room for error," (which may be a factor) but the rational negative player type now allows greater earn for a smaller base of players. In other words, more dead money is being forced per "hand." (as in, 6max, 30$/round = 5$each, rather then 3$) So, players who would follow the most sustainable negative winrate are now losing more, as they must blind away more money/hand. In 6max, the numbers are more along the lines of -12.5ptbb/100, so for the winning player, as high as 11ptbb/100 or so is "possible" with rake and other considerations taken into effect.

So... hows this?

[Gregg777]

I think your contribution aspect would apply better if the blinds were a more substantial amount of the average pot.

6max still boils down to more marginal situations.

[BobboFitos]

[ QUOTE ]
I think your contribution aspect would apply better if the blinds were a more substantial amount of the average pot.

6max still boils down to more marginal situations.

[/ QUOTE ]

but imo alot of those marginal situations are fed off blind attack situations.

[okayplayer]

Interesting. I had thought about this the other day after the KKF WR thread, and wondered if there was a theoretical ceiling for WR, and if so, what it was. Like, where did the 5PTBB/100 come from, was it just empirical data from different posters or is there a more theoretical concept behind it. I haven't really thought about this mathematically, just philosophically, so maybe I will later...

[PickyTooth]

Always not sure when you guys talk about ptbb...

is that bb/100 hands in PT ?

[Prevaricator]

[ QUOTE ]
Always not sure when you guys talk about ptbb...

is that bb/100 hands in PT ?

[/ QUOTE ]

yes

[ilya]

Why are you assuming that the other players are breaking even? Shouldn't the max theoretical winrate be (7.5bb/100)*9, i.e 67.5bb/100, i.e. the max amount that all the other players at the table put together could be losing?

[BobboFitos]

[ QUOTE ]
Why are you assuming that the other players are breaking even?

[/ QUOTE ]

I'm not. I'm merely thinking/stating if the worst "sustainable" winrate is X, shouldnt the highest be the converse of that, like -X + X = 0.

I dont know, to me it seems easy to find the worst possible lossrate that could be sustained, which is just someone not ever playing a hand. As I assume someone playing a hand will somehow bungle themselves into pos EV situations; obviously, someone lets say moving 2k in blind every hand will have a lower loss rate, but then in effect they're blinding 2k/hand now, arent they?

[ QUOTE ]


Shouldn't the max theoretical winrate be (7.5bb/100)*9, i.e 67.5bb/100, i.e. the max amount that all the other players at the table put together could be losing?

[/ QUOTE ]
I think the numbers would fall if you won every pot would be .75ptbb/hand, or 75ptbb/100. Although your numbers look good as you need to take away the fact 1 out of 10 you're putting the blind money in there, too.

But thats not what Im saying, I think. I'm wondering (and really no clue about this!) that if it's possible to determine the worst winrate - which I have a hunch is not playing a hand - (over the long haul) then couldn't/shouldn't the positive be projected best. As in, because all things end up equal, (minus rake) you cant win more then the biggest loser.

The ONE problem with what I'm saying is this is dealing with just 2 people on a 10 person table, so maybe that alone disproves the worst loss rate isn't the same as a positive best win rate!

[amoeba]

hi Bobbo,

i'm not sure the worst lossrate is never playing a hand.

people frequently make the money in tourney just by not playing any hands in the early stages.

I gotta figure there are lots of guys losing more than 7.5/100.

[burningyen]

[ QUOTE ]
i'm not sure the worst lossrate is never playing a hand.

[/ QUOTE ]
I would have thought the worst possible lossrate not involving collusion would be your lossrate if you pushed every hand pre-flop, assuming a full table of opponents playing optimally against you and each other.