Is it possible to be a 50% ITM player?

[tadams]

Is it possible to be a 50% ITM player while playing SNG tournaments?

To answer this question one needs to consider how well you play versus how well the rest of the players at the table play. To start let's assume everyone at the table plays equally well. Now how often should you be ITM? In order to answer this question we need to know how often you are expected to win each of the ITM places, usually just 1st, 2nd and 3rd. We know you are expected to win 1st place exactly 1 in 10 times. You aren't going to win 1st place 9/10 times so if you don't win 1st place you will win 2nd place 1/9 times and by the same reasoning you will win 3rd place 1/8 times. Therefore if everyone at the table plays equally well each person is expected to be ITM exactly 1/10 + 1/9 + 1/8 = 33.6% of the time.

Now to answer the question as to whether you can be a 50% ITM player, let's work backwards to solve x + y + z = 50%.
Let's assume you will win 1st place 2/10 times = 1/5 and work from there. 2/10 + 2/8 + 2/6 = 1/5 + 1/4 + 1/3 = 78.3%. So theoretically, if you are twice as good as the average player at the table you will be ITM 78.3% of the time. The next question is how often will you be twice as good as the average player at the table? I don't think you will be very often, even if you happen to be the best player on the site, especially as the limits increase. Therefore, I would say the theoretical maximum sustainable ITM percentage is significatnly less than 78.3%. How much less?

I would say around 39%, giving you a 5.4% edge over the average player. Don't agree? Consider the situation when you are always the best player at the table. You will be ITM between 33.6% and 78.3% of the time. You have to be twice as good as the average player to be ITM 78.3% of the time which may happen once out of thousands of games. Most of the time, however, you will only be slightly better than the average player at the table and thus will only be ITM slightly more often than them.

I have seen many claims that players are over 50% ITM, however, based on my own experiences and calculations this feat is very difficult to sustain over a long period of time. As we all know, luck plays an important role in poker and can certainly account for a player being 50% or greater ITM over the short run, but over the long run I am not convinved it can be done.

If anyone has any theoretical/mathematical proof that it can be done, I would be very interested in seeing it.
In the meantime, I hope the calculations above will at least produce some discussion of the theoretical possibility of being a 50% ITM player.

May your skill overcome your opponent's luck,
Tom
tadams@mail.com

[Desdia72]

i believe i can be a 50%+ SNG player at the $5 and $10 levels over the long run but because of bankroll issues, it's not an endeavor that i'm steadfastly trying to prove. however, when i do play my SNGs...it's the #1 thing on my mind. profit is my main objective and since the majority of the money is in the 1st place finish,and we all know the chances of getting a lot of them is remote, i focus on getting as money places as i can in the ones i play to make up for the money difference. lately, i've been doing great. a lot of it, i give props to the purchase of Middle Limit Holdem by Bob Caifonne and Jim Brier. even though the book is geared toward limit ring games, i've been able to take a lot of what they wrote in the book and apply it to No Limit. i have'nt even been playing poker a year yet and i'm already a consistent, winning player (SNGs). playing online reduces the learning time if your a dedicated, serious player.

[Moozh]

We know you are expected to win 1st place exactly 1 in 10 times. You aren't going to win 1st place 9/10 times so if you don't win 1st place you will win 2nd place 1/9 times and by the same reasoning you will win 3rd place 1/8 times. Therefore if everyone at the table plays equally well each person is expected to be ITM exactly 1/10 + 1/9 + 1/8 = 33.6% of the time.

Think about it, the intuitive answer for 10 equal players playing for 3 spots in the money is 3/10ths, or 30%.

I just want to quickly point out why you got over 30% (which is the correct answer).

You will get 2nd 1/9th of the time you don't get first (which you said), but since you don't get first 9/10ths of the time, you actually get 2nd (9/10)*(1/9) of the time, which is 10% (1/10).

Third is similar. You don't get first or second 8/10ths of the time and you get third 1/8 times when you don't get first or second. This means you get third (8/10)*(1/8) times, or 1/10 again.

[mackthefork]

I started recording my results about 2 weeks ago, so I only have a small sample but over 30 SNGS at 5s and 10s on party and stars, I am 57% ITM 96% ROI, I beleive the previous 100 or so i played were more like 40% ITM, 45% ROI but i have no way of checking this. I'm well aware this can't last, as many 1st places as 2nd and 3rd together.

Regards ML

[ctv1116]

Of course its theoretically possible; you just play with a bunch of idiots, all of whom go all-in every hand until you're heads up. In reality, its impossible to mathematically prove/disprove that 50% ITM is possible. You would have to be able to play a perfect game, and see if that would yield you a 50% ITM. Of course, if we were perfect players, we wouldn't worry abot such silly academic discussions.

[Daliman]

Well, I think you may be a victim of paralysis by analysis here. You got alot of impressive #'s here, few of which I understand in their context, but they mean little. How you figure you can be 78.3% in the money by being twice as good as someone else is beyond my limited scooe, but here' what i do know;
50% IS possible and sustainable, but likely not at a higher level than $30 tourneys.
78.3% is NOT possible, under any circumstances, over any real period of time.

You may be falling victim to the assumption that if you are average, you cash 30% of the time, whereas if i am twice as good, I cash 60%. This is fallacious thinking. Other than the fact that differences in skill cannot be quantitatively measured, it's measured like this;
33% is baseline-break even in most cases.
35% is more than twice as good as 34%
40% is 15 times better than 34%

Now, without placement distribution, these #'s are mere estimates, but if broken down by placement, or even further, by ROI, you get exact results and comparisons.

If after 100 tourneys, I have a ROI of 16%, and you have 4%, i did 4x as well as you, though 100 tourneys is a barely more than a blip.
If same #'s after 1000 tourneys, nothing set in stone, but good chance i'm alot better than you, but not necessarily 4x the player.
After 10,000 tourneys, 3's are the same, well then, I'm 4x the player you are most likely, even though i may only cash 36% of the time vs your 33%. Believe it or not, this, with equal distribution, is all the difference needed in cashing %. to have 4x better results.
Hopefully, this has helped.

[Prickly Pete]

Dali, you're right on here. I don't know how anyone could quantity "being twice as good" a poker player. By the initial post's logic, what if I'm three times as good as the guy I'm playing heads up? Will I win 150% of the time? Not even Cris Brown can win that many.

[fnurt]

Just as in ring games, the question is not how much better you are than the second-best player, it is a question of how many bad players there are.

If every table has 4 people who are dead money and give away their chips in the first couple rounds by playing like maniacs, that leaves 6 people in contention for 3 prizes. In this simplified scenario you don't even need to be the best out of those 6 to finish ITM half the time, you only have to be average.

[tadams]

I wanted to start by thanking everyone for their responses and the general discussion as to whether it is possible to be a 50% ITM player. I will be the first to admit that I do not know whether or not it is possible. And in an attempt to find out, I posted my analysis of the possibility S&M style. My analysis is similar to the analysis from the chapter "Settling Up in Tournaments" in "Gambling Theory and Other Topics" by Mason Malmuth. In fact, I think it would be possible to expand on the ideas presented in that chapter to get a much closer approximation of the expected ITM %.

The difficulty with these problems is determining how well you play versus how well your opponents play. Even the worst player at the table will win sometimes, regardless of how well you play. So how often any particular player wins depends on a lot of factors including his skill, his cards, his opponents skill, his opponents cards, how well his opponents play against him, how well he plays against his opponents, etc. So my use of the term "twice as good as the average player at the table" was used in order to establish a base condition in order to analyze the problem. Similar to the way I used "all players at the table play equally well". If everyone plays the same then you can disregard the skill involved, so if you are twice as good as everyone, the way I mean it is that you will win 1st twice as often, 2nd twice as often and 3rd twice as often. Again, I am not saying it is even possible, but rather I am saying if it happens that you are twice as good as everyone else at the table then you should win twice as often as everyone else at the table.

Basically, the goal of my analysis was to determine the probability that you will win 1st, 2nd or 3rd place. To give a quick example, say P1 represents the probabilty that player 1 will take 1st place. If all players are equally skilled P1 = P2 = . . . = P10 = 1/10. In other words everyone is equally likely to take first place and the probability is 1/10. Now say player 1 is a more skilled player and the probability that player 1 wins first is 2/10. We also assume the rest of the players play as well as each other. So P1 = 2/10, which leaves P2 = P3 = . . . P10 = .89/10. So now player 1 will win twice as often as he would if all the players were equal and the other players at the table will win less often. I think this is pretty straight forward even though it assumes player 1 is the best player AND players 2-10 are as equally skilled as each other.

We can now generalize the formula by representing player 1's skill with S1. Therefore the probability that player 1 wins first place is represented by P1 = S1 * 1/10. So the probability that player 1 wins first place is equal to his skill relative to the other players at the table times the probability of him winning first place when all players are equally skilled. Setting S1 = 2 yields P1 = 2/10, while S2-S10 = .89. Therefore player 1 is exactly 2.25 times as good a player as the rest of the players at the table. There are two things left to do. The first is to determine the distribution of skill levels. In other words, what are practical values for S1-S10. The second is to compute the probabilities of winning 2nd and 3rd given the probability of winning 1st and the distribution of skill levels.

As I stated above, the difficulty with these problems is determining how well you play versus how well your opponents play (i.e. determing the values of S1-S10). One method of determining these values is by collecting enough data from online tournaments which would give you the probability of each player winning 1st, 2nd and 3rd place (i.e. the values for P1-P10) and working backwards to get S1-S10. The other method is to derive a formula to come up with the values of S1-S10 based on certain criteria, which would be similar to estimating the value based on core characteristics. Both methods are very difficult to do, which is way I made simplifying assumptions to get an idea of a sustainable ITM %. If anyone has another way to determine S1-S10 I am very interested in hearing from you. Also, if anyone has any ideas or thoughts on my analysis or how I can improve it, please feel free to post. No idea is a bad idea and I am open to hear all of them.

Profitably yours,
Tom
tadams@mail.com

[Bozeman]

Twice as good heads up means you win 2/3 of the time.

I think a good measure of twice as good (as average) is that you will do as well as an average player would do with twice as many chips. Thus, twie as good is like starting with 2x chips.

For equal players, if one starts with 2000 chips while 9 start with 1000, the player with the chip advantage will finish 1st p1= 2/11, 2nd p2~16.4%, and 3rd p3~14.6% for ITM=49.2%, 53.9% ROI (assuming 10% vig). Sacrificing some ROI you could increase ITM. At the low levels, I think it is quite possible to be twice as good (by this measure) as the average player, although party's fast structure is not as conducive to this as other places (but some compensation by really bad play occurs, though this may not be that helpful at low levels).

For the higher levels, I think being twice as good as the average is not possible, and there will be other players better than average. I imagine a best case being something like 1.6,1.5,1.4,1.2,1,.9,.8,.6,.5,.5. Here, the 1.6 stack does 16%,~15.1%,~14.0% for ITM=45.1% and ROI=39% (assuming 10% vig, 7.5% vig would yield 43% ROI if you could find fields this juicy). In addition, there should be some adjustment from this to account for the payout structure, so a good player in a decent field should have a few more 3rd's and probably a few less 2nd's.

There will certainly be players who do better than this at the $100+ levels, but from experience (mine and others I trust), those that do will have either small sample size (<500-1000 SNG's), or practice extreme game selection (such that it will be hard to play a lot of these).

Craig

[Bozeman]

1.6,1.5,1.4,1.2,1,.9,.8,.6,.5,.5

For this field, here are the approximate results

p# ROI ITM
#1 39% 45%
#2 35% 43%
#3 27% 41%
#4 10% 36%
#5 -9% 31%
#6 -18% 28%
#7 -27% 25%
#8 -47% 19%
#9 -57% 16%
#10 -57% 16%


(Approximate means using the independent chip (or malmuth) method, which slightly favors small stacks, outlined here (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=369811& Forum=,All_Forums,&Words=tournament%20finish&Searc hpage=1&Limit=25&Main=369811&Search=true&where=bod ysub&Name=134&daterange=1&newerval=1&newertype=y&o lderval=&oldertype=&bodyprev=#Post369811) )

Craig

[carpola]

[ QUOTE ]
You aren't going to win 1st place 9/10 times so if you don't win 1st place you will win 2nd place 1/9 times and by the same reasoning you will win 3rd place 1/8 times. Therefore if everyone at the table plays equally well each person is expected to be ITM exactly 1/10 + 1/9 + 1/8 = 33.6% of the time.


[/ QUOTE ]

Assuming 100 SNG's thats 300 ITM finishes. But your you say each person has a 33.6% chance which would mean 336 ITM finishes. This doesn't seem right. Can you tell me where I'm going wrong?

[Daliman]

yer not, he figured incorrectly.

[Lori]

I have seen many claims that players are over 50% ITM, however, based on my own experiences and calculations this feat is very difficult to sustain over a long period of time

See my post in the other thread, it shouldn't be difficult for anyone playing small stakes at UB or Paradise who has the ability to make a living at higher levels.

You (as a forum) are seriously overestimating how people play , but after the analysis in the JJ hand, that doesn't surprise me.

Lori

[tadams]

The reality is 50% ITM is difficult to sustain for anyone regardless of the game. The reason is you simply don't have enough of an edge over other players. I agree there are some bad players out there and very often these bad players are sitting at your table. However, the worse a player is the less your skills matter and the more it just comes to having the cards.

For instance, you can't read a bad player nor can you bluff a bad player out. The cards they play and the plays they make don't make sense. So you change your strategy against these players and make more value bets and never bluff because they call too often and never fold. You also go all in when you have the nuts and they will usually call. However, these players will often draw out on you, even though it was not correct for them to call in the first place, and cost you some of your stack. They also often have hands that you would never even consider playing and again cost you some of your stack. In ring games, their bad plays will eventually catch up with them, but in a sng tournament it's likely they won't.

Another type of bad player is the ultra-aggressive player that constantly goes all in. So you wait until you get dealt AA or KK and let him take you all in. Most of the time this play works great as you are likely a 75% or better favorite. But that 1/4 of the time he beats you, you are out of the tournament. You could also call him with lesser hands like AK, AKs, QQ, JJ, TT, etc but now you may be the underdog.

The point is I don't think it is easy and it may not even be sustainable over the long run, which is why I wanted to try and come up with some sort of reasonable proof.

Tom

[Lori]

If 2 years isn't the long run then I'll never prove it.

I'm telling you it's possible, and it's not even close.

If I can 52% for a two year period and then 47% three-tabling for a 9 month period, I _KNOW_ it's sustainable.

If the people here refuse to believe that to cover their own inadequacies, then that's fine, but I've read enough garbage here to know that people here are not as good as they think they are.

Lori

[Lori]

To be more constructive, I'll show the flaws in your aggressive player argument.

I think we will be able to agree that it's possible to double through once with better than 50-50 odds against these people.
Also you have to remember they are busy knocking each other out.
How often do you get to 2000 chips on UB or Paradise and NOT cash? If this answer is over 20% then you are doing something drastically wrong.
Also how often do you never reach 2000 and still cash.
Well that number is reasonably high.
Given that argument, no matter what a sensible value you put on 'reasonably' you will find your 50%.

Lori

[Harry]

OK..... What's your Party Poker sn?

You wrote:

If I can 52% for a two year period and then 47% three-tabling for a 9 month period, I _KNOW_ it's sustainable.

[Lori]

I don't play enough at Party to be able to judge.

40-50%, but my ROI is certainly lower than at the other two.

Lori

[Harry]

I'm not trying to pick on you alone Lori, but it seems to me that everyone in this forum claims that they are placing ITM 50% of the time and making a killing at online and/or BM poker. I just wanna see how well these people play. I'm not claiming to be some kind of a super judge of poker talent, and anyone can play great/poor depends on what kind of cards they are getting at one particular tournament but I and anyone who is half-ass ok can usually tell the ones who are really good which I would say 50% ITM belongs.

I mean it starts with these hand histories, with name changed to hero and UTG etc bs. And then moves to the real/unreal bad beat stories. So if any of 2+2er is doing as well as 50% ITM, well let us see it. Put up your partypoker or any site sn, so people can see how great you are playing. I suspect more than half of these people are losing money in the 0.5/1.00 tables.

You wrote:

I don't play enough at Party to be able to judge.

40-50%, but my ROI is certainly lower than at the other two.

Lori

[Desdia72]

[ QUOTE ]
I'm not trying to pick on you alone Lori, but it seems to me that everyone in this forum claims that they are placing ITM 50% of the time and making a killing at online and/or BM poker. I just wanna see how well these people play. I'm not claiming to be some kind of a super judge of poker talent, and anyone can play great/poor depends on what kind of cards they are getting at one particular tournament but I and anyone who is half-ass ok can usually tell the ones who are really good which I would say 50% ITM belongs.

I mean it starts with these hand histories, with name changed to hero and UTG etc bs. And then moves to the real/unreal bad beat stories. So if any of 2+2er is doing as well as 50% ITM, well let us see it. Put up your partypoker or any site sn, so people can see how great you are playing. I suspect more than half of these people are losing money in the 0.5/1.00 tables.

You wrote:

I don't play enough at Party to be able to judge.

40-50%, but my ROI is certainly lower than at the other two.

Lori

[/ QUOTE ]

i'm currently at 50% now but some folk consider my small sample of 150 to 200 SNGs not a real reflection of whether this is sustainable over a longer period of time. one thing that i've realized is that the 50% ITM statistics are not as important as ROI. early on in my SNG experiences, i logged more 3rd places on one tables and 4th places on two tables than i did 1sts and 2nds. on PS, if you take a sample of twenty $5 + $.50, the buy-in amount comes to $110. so 10 out of 20 cashes= 50% but if all those cashes are 3rds (1 table) and 4ths (2 tables) you're only making $3.50 profit per cash. 10 cashes X $3.50 per cash= $35.00. when you figure in the $55.00 in buy-ins (the other 50%) that you did'nt cash in, you're down -$20.00. so although i prided myself as a player with less than a year experience making it at least to the last paid spot, overrall i was losing money. now don't get me wrong, i was getting 1sts and 2nd place finishes too but more 3rds and 4ths. i knew the proper way to look at it was to be patient and commit more to studying the game. the aim/goal was to make the majority of my cashes 1sts and 2nd places which pay more and are the spots where you see the profit at the $5 level. over the past month i am around 55% ITM with more 1sts and 2nd places than 3rds. i did'nt include 4th places for two table SNGs because i have'nt really focused on them lately. i am by no means an elite or great player but i feel i'm above average at the $5 level.

[Harry]

so what's your party poker sn?

[Desdia72]

[ QUOTE ]
so what's your party poker sn?

[/ QUOTE ]

if you're talking about me, i don't play at Party. i play at Pokerstars and my sig is the same as my 2+2 name.

[Lori]

Here are last years King of the Zoo rankings versus posters on the internet forum.

some proof? (http://www.kotz.co.uk/2003/kotzrankings.html)

Edit prize money list 2003 (http://www.simongreig.com/kotzmoney.html)

Final tables made (http://www.simongreig.com/kotzfinals.html)

Lori

[tadams]

I use pokerstat to track all my poker statistics. Here are my statistics on Paradise for the $10+1 sng.

Total of 135 tourneys processed

Statistics for player tadams:

Total invested: $1485.00
Total won/lost: +$375.00
Return On Investment (ROI): +25.25%

Average percent rank finished: 54.24%
Percent times in the money: 39.26%

Average buy-in: $10.00
Average fee: $1.00
Total fees: $135.00
Total prize pools: $13500.00

Average tourney time: 0.98 hours
Total tourney time: 132.90 hours

-tom

[tadams]

Ok here is more mathematical proof of the difficulty in sustaining 50% ITM.

Again, I am not arguing that it is impossible, but merely difficult to sustain over a long period of time.

If you are not familiar with odds and probabilities I recommend you read the chapter on it in David Sklansky's "Getting the Best of It".

To start off, I assume you are the best player at the table. What follows are the probabilities that you, as the best player, will go out first, second, third, fourth, fifth, sixth or seventh. If you don't go out at one of these times then you will place either first, second or third and therefore be ITM. I also include the average
probability that one of the other players goes out, which is simply (1 - the probability that you go out) divided by the remaining players.

Probability of going out first.

P1 = 0.01 = 1/100
Prest = 0.11 = 11/100

Notice you will rarely go out first. I came up with this number because I assume the only way you will go out first is if you suffer a bad beat. For example, if you are
dealt AA or KK, go all in and lose.

Probability of going out second.

P2 = 0.05 = 5/100
Prest = 0.12 = 12/100

Again, you will probabily only go out second if you suffer a bad beat. Blinds are still small, so your chances of
blinding out are very small. You should get your fair share of good cards and so your stack should be going up moderately. Other players stacks may go up more because they get lucky, they play too many hands, they go too far with their hands, etc.

Probability of going out third.

P3 = 0.09 = 9/100
Prest = 0.13 = 13/100

You are still significantly favored over the other players, but stack sizes are starting to play a factor as well as skill. You, as the best player, only increase your stack
size moderately so I assume you have an average size stack.

Probability of going out fourth.

P4 = 0.13 = 13/100
Prest = 0.145 = 14.5/100

Probability of going out fifth.

P5 = 0.13 = 13/100
Prest = 0.174 = 17.4/100

Probability of going out sixth.

P6 = 0.17 = 17/100
Prest = 0.2075 = 20.75/100

Probability of going out seventh.

P7 = 0.22 = 22/100
Prest = 0.26 = 26/100

At this point you are guaranteed to place either 1st, 2nd or 3rd. We can figure out the probability that you made it this far by multiplying the probabilities you made it past each level together. The probability that you made it past each level is 1 - the probability that you would go out. So multiply each of these together to get the chance you make it into the money.

(1 - 0.01)(1 - 0.05)(1 - 0.09)(1 - 0.13)(1 - 0.13)(1 - 0.17)(1 - 0.22) =

0.99 * 0.95 * 0.91 * 0.87 * 0.87 * 0.83 * 0.78 = 0.42

Again, notice these are the probabilities that you don't go out first, second, third, fourth, fifth, sixth and eventh. They are quite high and may or may not represent attainable figures. For example, with four players left I use a figure that gives you a 22% chance of going out next, compared to the 26% chance that the other players have. This figure takes into consideration many factors. First of all the other players are probably better than the players that have been eliminated. Other things to consider are your average stack size when you make it this far, the other players' stack sizes compared to yours, the size of the blinds, etc. I tried to show some justification for how I choose the numbers, but it is difficult to determine precisely what your chances of going out at each level are. I suggest you play with the numbers and try to find a reasonable probability for yourself at each level to determine what might be sustainable for you.

Good luck,
Tom

[Bozeman]

Your mathematics are ridiculous. For more meaningful math, check out my post above.

[tadams]

The mathematics can not be refuted. However, you could argue that the probabilities I use are not valid.

I did read your posts that "accurately calculate probability of finishing in a given place as a function of the stack sizes". However, as Malmuth states in his book "Gambling Theory and Other Topics", "The analysis in this series is based on two assumptions. First, we will assume that all of the remaining players are of equal strength. Second, we also will assume that all of the remaining players have a substantial number of chips in relation to the antes and/or blinds and the amount they expect to invest in any one pot."

Furthermore, Malmuth goes on to say "unfortunately, this [the second] assumption will prevent us from applying these techniques to pot-limit or table-stakes tournaments."

In other words, your calculations only apply to limit tournaments when all the players are of equal strength.