how often can you win (general theory ?)

[Dave D]

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So, mostly this question is for middle or late stages in relation to stack sizes, but i suppose it could apply to early stages as well.

anyways, with N players left (say 5-25% of the starting field), later in the tourney, with blinds large, but not stupidly large such that the average stack is red zone, how often can a good (say 100% ROI) player win when they have an average stack? also, with N players, how big of a stack does a very good player need in order to win 1/N times?

i know of course it will depend a lot on how many players are left, as a very good HU player probably can't win much more than 60% when the stacks are equal and the blinds are fairly large. so thats only 120% of if he won only his share. but say there's 50 players left out of 500. a very good player with an average stack will certainly win more than 1/50 * 120% = 1/42. there must be some equation that takes into account players left that will give a solution to how often you win. does anybody know of such an equation that will at least approximate this?

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OP referanced this thread in another thread, so I'll bump/respond to it cuz I think it's interesting.

I'm pretty sure OP means "win" as in place first , assuming a standard payout structure right?

I don't think there's any real clear answer to this question. I think a lot has to do with the player's individual style, ie some people are better at playing a small stack, others' chances go up basically exponentially as their stack is bigger. I realize that everyone would do better with a bigger stack obviously, but what I mean is some players have *more* of a chance than others with a bigger stack. This is distinct from some players are better than others because I'm trying to make the subtle distinction that some players rely more on the post flop game which they need a bigger stack for.

This is where this question relates to the other one Ed Miller posted. I think there are two things that are crucial to trying to answer this question:

1. What's the rest of the field like. Your expectation changes a lot depending on the type of tourney. You can be a lot more confident in a party 10+1 than a 100+9. You know there will be a good number of weak players towards this stage of a 10+1 than a 100+9. As such, stack size becomes more important as you go up in buy in.

2. How fast are blinds going up? What is the payout structure? Basically I think we all know that a slower structure favors better players. We know therefore that these factors are crucial in determining your chances of winning. Payout structure is relativly minor, but also affects the way other people play. Namely, if it's really steep you know that you're playing for first, but others might be trying to stall so you can take advantage of that.


Overall though, I'd say that if you have the avg, you're going to win way less than 1/N times (I know you said greater than avg, but I'm stating this as a baseline). I think you're going to need at least 3x the avg to even come close to making any sort of expectation as to your chances of winning. Less than that, and for me it's a toss up.

Maybe I'm just jaded, but the bottom line is that in order to win, you're going to still need to win several more coinflips. So you need a lot of chips to simply survive luck. I would view this situation as having so many variables that it's basically useless to try to figure it out. You don't know the skill level at your table, your table compared to the rest of the tourney, and all kinds of other variables. I think all these unknown variables makes it impossible to ever come up with an equation, so I just wouldn't worry about it.

[pfkaok]

well. i know its going to depend on the opponents a lot. but i'm just saying in this example, hero is a 100% ROI player against that field. so on average his edge at the final table should be pretty consistant.

and 100% ROI is a very good player. so i don't see how he could possible win less than 1/N, with N players left and his stack is average. if there's 16 players left, and he has 1/16th of the chips, that just means he has to double up 4 times to win. unless the blinds are VERY big, and you're super shortstacked to where you have to take -EV gambles to avoid getting blinded out, there's no reason you shouldn't be more than 50/50 to double up (if you're a good player)

for example. in the 16 person field, if the blinds were reasonable, and hero has an edge, of say 53% to double up, then his chance to win would be 53% ^ 4 = 7.9% = 1 / 12.7

now i'm not sure that you can have that much of an edge in most online tourneys with the blinds as high as they are, but its just an example, and i'm sure that in bigger buyin live events the top players have at least that much of an edge.

so overall, the solution to this would almost certainly have to include a factor of, say, M of the avg player.

i think the 3 things i'd like to know most are:

1) % wins for good player with average stack

2) % of average stack needed for good player to win his share

3) % of average stack needed for good player to win twice his share.

it'd be very nice to be able to find this for a few different common structures. stars' normal tourney, party normal tourney, stars rebuy, party rebuy, and big buyin live event.

[Dave D]

Ok, well that clarfies things a little further than how I'd originally read your thread. Nevertheless I still disagree.

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that just means he has to double up 4 times to win

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Yeah, but this is no limit babby. He risks his whole stack those 4 times. Lets assume he's a 75/25 fav those 4 times, which means .75*.75*.75*.75=.316, which as we know means he's only going to survive those 4 all ins 32% of the time. That really has nothing to do with his skill level, he has to survive luck. Obviously it's not very often where we have to double up 4 times to win, each time risking our whole stack, but I think the point remains. Even if you only have to risk your whole stack 2 times, and you're getting it in as an 80/20, that's only ~2/3 of the time are you going to survive.

Think of that classic example (I think it's in the anthology of good posts or whatever) that says "I just saw player x go from tourney chip leader to busting in 10 minutes, why". I think that *because* of this variability, and the inherent variability of the game of NL, it's virtually impossible and ultimatly useless to make any sort of calculation here. Anything could happen at any time. I think you can *maybe* start making these kinds of calculations if you have a dominating huge lead (like top 10 in chips with 200 left or something). Even then it's hard though, because there are just too many unknowns.

What I'm saying is that I think you're way underestimating your chances of playing correctly, and still being knocked out. I think you're only looking at your chances of *winning*, rather than *losing*. Which are distinct here. Basically, a lot of unknowable things have to go right here in order for you to win.


Just for fun I'm gonna throw this in. I keep thinking of this analogy for this kind of situation: There's no way for someone to 100% prove there's a God to me, but that doesn't mean that I shouldn't live the right life, or at least what I judge to be the right way to live (and basically according to His rules). Play your game the best way you can, trying to figure out your expectation is just not worth your time because knowing it doesn't change anything anyway.

[pfkaok]

i don't understand how you're saying he'll only survive 32% of the time, yet he'll win less than 1/16 (6.25%) of the time.

he has 1/16ths of the chips in play. if he doubles up once he'll have 1/8th, twice he'll have 1/4th, 3 1/2, and 4 times he WILL WIN.

of course your 75% isn't possible, but it should certainly be over 50% for a good player.

it doesn't mean that he has to win 4 allins. i'm just saying, at any given time in a tourney, a good player is more than 50/50 to double up before he busts. this is obvious. if he were 50/50 to double up with 16 players left, then of course he would have a 1/16 chance of winning.

[Dave D]

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i don't understand how you're saying he'll only survive 32% of the time, yet he'll win less than 1/16 (6.25%) of the time.



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You were talking about modifying your chances of winning the tournament as your stack gets bigger right? So at the end of 4 double ups (I wasn't using your example in mine, I assumed more of a "he has a really good chance to win" not "every chip in the tourney win") he should be better than 1/16th (as in your example)? Are you really saying that if I have a 10k chipstack, and I work it to 80k, late in a 30+3 or something, that that really affects my chances of winning that that much? 80k is a lot, but my chances of winning the tournament are not as high as 32%. That's my point. I'd say you still are only 10% at best to win, or something like that. Anything could still happen.

And obviously using a 75% edge is a lot. Assuming 50% all the numbers become hideously bad.

All I'm saying is that trying to make in game calculations is pretty fruitless, until you're talking about extreme ends. To use my football analogy from the other thread, if going into a game USC is favored to beat ND 60/40, and USC is up 21-7 at halftime, nobody in the world is going to say that game is over, or even close to over, or would adjust the odds significantly. There's still a lot of game to be played, just like in the above example there's still a lot of tourney to be played, and only when you have a HUGE advantage can you start estimating your chances (ie if USC was winning 28-7 or something).

[pfkaok]

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To use my football analogy from the other thread, if going into a game USC is favored to beat ND 60/40, and USC is up 21-7 at halftime, nobody in the world is going to say that game is over, or even close to over, or would adjust the odds significantly. There's still a lot of game to be played, just like in the above example there's still a lot of tourney to be played, and only when you have a HUGE advantage can you start estimating your chances (ie if USC was winning 28-7 or something).

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well. if the better team (60% win from the start) is up 21-7 at half, they'll be quite a bit more than 60% to win. sure a lot can happen, THEY ARE THE BETTER TEAM. next time a 60/40 favorite is up by 2 touchdown at half, i'll give you 3:2 that they'll win. let me know.

[Dave D]

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To use my football analogy from the other thread, if going into a game USC is favored to beat ND 60/40, and USC is up 21-7 at halftime, nobody in the world is going to say that game is over, or even close to over, or would adjust the odds significantly. There's still a lot of game to be played, just like in the above example there's still a lot of tourney to be played, and only when you have a HUGE advantage can you start estimating your chances (ie if USC was winning 28-7 or something).

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well. if the better team (60% win from the start) is up 21-7 at half, they'll be quite a bit more than 60% to win. sure a lot can happen, THEY ARE THE BETTER TEAM. next time a 60/40 favorite is up by 2 touchdown at half, i'll give you 3:2 that they'll win. let me know.

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Well, I used college football for a reason, because of how unpredictable it is. If it's two good teams, anything can happen, even if one is up by 2 TDs. The example I gave in the other thread was Tennassee (who's had a dismal season) at LSU early this year. LSU was up 21-0 going into the half, at LSU, LSU was ranked #3 in the country, Tennassee was #10. Tennassee came back to win it 30-27 in OT.

Witness the red sox in the playoffs last year.

Do bookies ever take bets halfway through a game? I don't think so, but I don't know for sure because I don't bet on sports. It wouldn't make sense because you really have no idea unless it's pretty lopsided.

But lets talk about poker. Let me elaborate on my previous example. Say you're playing a 30+3 on party with 1000 players to start. You're down to 150 people. You have 10k in chips and the blinds are 300/600. I think this sounds about right for the kind of scenario you're talking about. The blinds are stupidly large, and you have 16.6 blinds. Not great, but not bad.

Now, lets assume you steal once an orbit or something (on avg), nobody challenges you, and the only way you increase chips is by going all in the 4 times we previously talked about (where you're a 75/25 fav). This results in you having an 80k stack when the blinds get to 2000/1000 (honestly I can't remember increments, it's been a while since I got this far [img]/images/graemlins/wink.gif[/img]) and 20 people left. Would you say you're anywhere NEAR a lock for first? Would you say your chances of making first are better than 32%? Personally I'd say no way. Chances are you'll make the final table, but at that point you're basically an avg stack. So I guess you could say your chances of winning are 1/10. But they're not because half the table has a bigger stack than you, and you can get knocked out at any time. Also, at least a few people are as good, or better than you. Realistically, I'd put my chances of actually winning at 10% or less.

My example assumes basically a best case scenario all around. Yet I'd put my chances of winning at 10% or (probably) less. So if we extrapolate backwards, there's no way increasing your stack right away by any less than a factor of 4 would be significant in figuring out your chance of winning. My point is that I believe there's a HUGE hurdle before you can start making judgements like you're trying to do, so much so that it's bascially useless.

Hope this makes sense.

[pfkaok]

sorry. i thought i made it clear in my last post, but you don't seem to understand. if you double up 4 times when there's 16 people left and you have an average stack YOU WILL WIN. its a pretty simple fact. if you have all the chips, you are the winner. if you start with 1/16th of the chips, 4 double ups will result in you winning.

[Dave D]

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sorry. i thought i made it clear in my last post, but you don't seem to understand. if you double up 4 times when there's 16 people left and you have an average stack YOU WILL WIN. its a pretty simple fact. if you have all the chips, you are the winner. if you start with 1/16th of the chips, 4 double ups will result in you winning.

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So at the end of 4 double ups (I wasn't using your example in mine, I assumed more of a "he has a really good chance to win" not "every chip in the tourney win")



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Yeah, I thought I made it clear that I wasn't using your example either.

My point is that even if you double up (once), even in the hypothetical HUGELY favorable example I gave, I wouldn't even give myself a 10% chance of winning if it resulted me making the final table, NEVERMIND the point in the tournament you're talking about.

[pfkaok]

how can you not have more than 1/10 chance of winning when you're at the final table with an average stack? are you sure there isn't something wrong with your FT play? a winning player should be able to win more than his share of FTs.