limit vs. no limit

[HoosierAlum 0]

people confuse the answer to this question because they don't know what they are asking in the first placeif i said "which has more variance, no limit or limit?" you might say the $30/$60 limit game has more variance than the $0.5/$1 no limit game, but that is a silly comparison.alternatively, you might compare the variance in limit and no limit games that have the same blinds, e.g. the $100NL game and the $0.5/$1 limit game.  But this isn't a great comparison either.  By some accounts you need a bankroll of $2000 to play the no limit game and a bankroll of $300 to play the limit game.A better comparison would be a no limit game and a limit game with the same bankroll requirements.  I think this yields, in order of decreasing variance:SH limitring limitSH no limitring no limit

Op, ignore everything else in the thread but this. The above answers your question accurately.

[Abbaddabba 0]

There's no such thing as short run and long run variance.A given data set has a sample standard deviation (and variance).It doesnt naturally decrease in the 'long run' for no limit. I assume that the variance for both are normally distributed - that might touch on what is being discussed. I dont know though; im not mathematician.

[justblaze 0]

people confuse the answer to this question because they don't know what they are asking in the first placeif i said "which has more variance, no limit or limit?" you might say the $30/$60 limit game has more variance than the $0.5/$1 no limit game, but that is a silly comparison.alternatively, you might compare the variance in limit and no limit games that have the same blinds, e.g. the $100NL game and the $0.5/$1 limit game.  But this isn't a great comparison either.  By some accounts you need a bankroll of $2000 to play the no limit game and a bankroll of $300 to play the limit game.A better comparison would be a no limit game and a limit game with the same bankroll requirements.  I think this yields, in order of decreasing variance:SH limitring limitSH no limitring no limit

Op, ignore everything else in the thread but this. The above answers your question accurately.

actually, it doesnt, and its not even close. tim, despite his good intentions, has erred. the comparision between a 30-60 LHE game and a 50c $1 NL game is not silly, and can easily be done. variance is a very specifically defined mathematical term. variance can be calculated exactly. no limit hold em is a higher variance game than limit hold em. this is because of the nature of the game: more money is risked at once (given stakes with similar bankrolls). most of the posters in this thread do not understand the concept of variance. say we were flipping coins. in example A, we are flipping 1 coin for 10 betting units, 10 times. in example B, we are flipping 10 coins for 1 betting unit, 10 times. which example would be higher variance? the answer is obvious, and the comparisions are identical when discussing NL and LHE.

[justblaze 0]

i should also add that any theoretical comparision between LHE and NLHE must assume identical risk adversity for both games. this means that the hypothetical player in this type of comparision must be willing to gamble with the same edge in both games. if he accepts 50-50 situations in LHE, he must accept 50-50 situations in NLHE, or else any theoretical comparision is invalid. of course, this is unlikely to occur in the real world. in a practical examination, players will have different thresholds of risk adversity in different betting structures, i.e. they will have different playing styles. therefore the difference in variance between the two games will vary for each individual player. the maxim that LHE is lower variance only holds universally true on a theoretical level. in reality, there are many ways to play both games. some styles are higher variance than others. it is possible to choose a style specifically designed to lower variance in both types of games. additionally, with a significant sample size in both games, it is possible to calculate YOUR variance, and make a comparision based on your play specifically. we should note that variance is not necessarily a bad thing. in fact, the optimal strategy in both games (in terms of EV) is necessarily one of high variance.

[HoosierAlum 0]

i should also add that any theoretical comparision between LHE and NLHE must assume identical risk adversity for both games. this means that the hypothetical player in this type of comparision must be willing to gamble with the same edge in both games. if he accepts 50-50 situations in LHE, he must accept 50-50 situations in NLHE, or else any theoretical comparision is invalid.  of course, this is unlikely to occur in the real world. in a practical examination, players will have different thresholds of risk adversity in different betting structures, i.e. they will have different playing styles. therefore the difference in variance between the two games will vary for each individual player.  the maxim that LHE is lower variance only holds universally true on a theoretical level. in reality, there are many ways to play both games. some styles are higher variance than others. it is possible to choose a style specifically designed to lower variance in both types of games.  additionally, with a significant sample size in both games, it is possible to calculate YOUR variance, and make a comparision based on your play specifically.  we should note that variance is not necessarily a bad thing. in fact, the optimal strategy in both games (in terms of EV) is necessarily one of high variance.

good post blaze.

[justblaze 0]

i should also add that any theoretical comparision between LHE and NLHE must assume identical risk adversity for both games. this means that the hypothetical player in this type of comparision must be willing to gamble with the same edge in both games. if he accepts 50-50 situations in LHE, he must accept 50-50 situations in NLHE, or else any theoretical comparision is invalid.  of course, this is unlikely to occur in the real world. in a practical examination, players will have different thresholds of risk adversity in different betting structures, i.e. they will have different playing styles. therefore the difference in variance between the two games will vary for each individual player.  the maxim that LHE is lower variance only holds universally true on a theoretical level. in reality, there are many ways to play both games. some styles are higher variance than others. it is possible to choose a style specifically designed to lower variance in both types of games.  additionally, with a significant sample size in both games, it is possible to calculate YOUR variance, and make a comparision based on your play specifically.  we should note that variance is not necessarily a bad thing. in fact, the optimal strategy in both games (in terms of EV) is necessarily one of high variance.

good post blaze.

ty. now if only i could hand that in as my poly-sci paper due tommorow morning :cry:

[Abbaddabba 0]

For justblaze (and others ive seen in the past), i think i have to put an end to this once and for all...It's risk aversion, not risk adversity.You cannot be "adverse" to risk. You can, and most rational human beings are, _averse_ to risk.To econ_tim...What's interesting is that, when deciding which has a higher standard deviation/variance, you used LHE and NLHE stakes that required comparable bankrolls.Think about what that means. The way in which one would go about deciding an adequate bankroll would be the variance, and now you're comparing the variances relative to bankroll requirements.When you say that LHE has a higher variance than NLHE for limits that require identical bankrolls, you're essentially saying that the conventionally cited bankroll requirement for LHE offers relatively less certainty than does the conventionally cited bankroll requirement for NLHE.

[justblaze 0]

For justblaze (and others ive seen in the past), i think i have to put an end to this once and for all...It's risk aversion, not risk adversity.You cannot be "adverse" to risk. You can, and most rational human beings are, _averse_ to risk.oops, you are right. To econ_tim...What's interesting is that, when deciding which has a higher standard deviation/variance, you used LHE and NLHE stakes that required comparable bankrolls.Think about what that means. The way in which one would go about deciding an adequate bankroll would be the variance, and now you're comparing the variances relative to bankroll requirements.When you say that LHE has a higher variance than NLHE for limits that require identical bankrolls, you're essentially saying that the conventionally cited bankroll requirement for LHE offers relatively less certainty than does the conventionally cited bankroll requirement for NLHE.interesting point. fortunately for us limit players, tim is wrong.

[Abbaddabba 0]

Im not sure that he is. I dont think it matters much thoughThe fact that you're equating stakes from LHE and NLHE that require identical bankrolls means that there should be no difference in the variance.If there is, it's simply a case of having bankroll requirements that offer different levels of ROR.

[justblaze 0]

Im not sure that he is. I dont think it matters much thoughThe fact that you're equating stakes from LHE and NLHE that require identical bankrolls means that there should be no difference in the variance.

the suggested bankroll requirements are only a starting point. they are calculated based on risk of ruin given assumed variance, which obviously will usually not be the actual variance of a player who adopts such bankroll requirements. Each players actual bankroll requirements in order to achieve a <1% risk of ruin will be dependent on their individual play and, accordingly, their variance. however, this argument needs to be divided into 2 components in order to have any meaning: theoretical and practical.theoretically, NL is a higher variance game. we need not consider the stakes. they are irrelevant for the purposes of this comparision. practically, the question is impossible to anwer on a generalized level, as it depends on too many factors specific to an individual, some of which are hard to quantify without significant data (such as propensity to tilt).

[Abbaddabba 0]

Suggested bankroll requirements are based on typical variances.Obviously not all players will conform to those standards. It's just an 'on average' kind of thing.On average, tim is saying that 2/4LHE will be higher variance than .50/1 NL. I dont know whether or not that's true, but for reasons mentioned in earlier posts, it doesnt mean much of anything.

theoretically, NL is a higher variance game.

It is for identical level blinds.I dont think that anyone has questioned that.

[AlanBostick 0]

i should also add that any theoretical comparision between LHE and NLHE must assume identical risk adversity for both games. this means that the hypothetical player in this type of comparision must be willing to gamble with the same edge in both games. if he accepts 50-50 situations in LHE, he must accept 50-50 situations in NLHE, or else any theoretical comparision is invalid.

Two words: "Kelly criterion."

of course, this is unlikely to occur in the real world. in a practical examination, players will have different thresholds of risk adversity in different betting structures, i.e. they will have different playing styles. therefore the difference in variance between the two games will vary for each individual player. the maxim that LHE is lower variance only holds universally true on a theoretical level. in reality, there are many ways to play both games. some styles are higher variance than others. it is possible to choose a style specifically designed to lower variance in both types of games. additionally, with a significant sample size in both games, it is possible to calculate YOUR variance, and make a comparision based on your play specifically.

You can calculate the variance of the data in your hand histories. In a game with changing players, changing skill levels, changing emotional states, changing game conditions, and so on, it takes quite a leap of faith to believe that there is One True Probability Distribution whose statistics can be efficiently estimated by analyzing your hand history data.

we should note that variance is not necessarily a bad thing. in fact, the optimal strategy in both games (in terms of EV) is necessarily one of high variance.

Sometimes, variance can be your friend. Just about half the time, actually.

[Abbaddabba 0]

we should note that variance is not necessarily a bad thing. in fact, the optimal strategy in both games (in terms of EV) is necessarily one of high variance.

it is necessarily a bad thing for all except those with gamboooling problems (or at least risk loving individuals, which is really the same thing).when it comes in a package deal with a higher winrate, we tolerate it.

[econ_tim 0]

all rightto respond to some of my critics:One's risk aversion doesn't affect the variance of a game. It is true that, given a choice between two games with the same expected winrate but different variances, a risk-averse person would choose the low-variance game and a risk-loving person would choose the high-variance game.But the variace of both games would be the same for the risk-loving and risk-averse players.The definition of variance has already been addressed, but to reiterate, we are talking about a well-defined statistical concept. That is the average of squared deviations of a random variable from its mean; in this case the variable is a player's winrate over a given number of hands. For a game to have zero variance, a player would have to win (or lose) the same amount on every single hand he ever played. This is clearly not the case in poker (not even in O8b).As justblaze said, it is possible to calculate and compare the variances of $30/$60 limit and a $25 NL game. So maybe it is not a "silly" comparison, but it is not a very useful comparison. To play $30/$60, you should have a bankroll of at least $20,000 and you should have mastered basic and intermediate poker concepts. Someone could play $25NL with $500 or less and virtually no knowledge of poker.Some have said it isn't right to compare games with the same bankroll requirement because bankroll requirement is a function of variance. But bankroll requirement is also a function of winrate and the player's risk tolerance. If we a talking about one player, than his risk tolerance will be constant, but his winrate could vary across games. If we keep the bankroll requirement constant, then the winrate will vary inversely with the variance of the game. So my list assumes the winrate is highest for bankroll X at short handed limit and lowest for the same bankroll at full ring no limit.Of course different players may be relatively more skilled in limit or no limit, so their rankings of games could differ. As justblaze said each player can simply calculate their own variance using pokertracker. This will depend on the player's playing style.To address another post, using words like short-term and long-term variance are misleading. It is best to talk about variance over a given number of hands. Someone also asked whether variance is distributed normally. A player's true variance has no distribution -- it is simply a number. We cannot know a player's true variance though. Instead, we measure the sample variance by looking at a finite number of hands. The central limit theorem states that repeated observations of sample variances will be distributed normally with the true variance as the mean.

[AlanBostick 0]

One's risk aversion doesn't affect the variance of a game. It is true that, given a choice between two games with the same expected winrate but different variances, a risk-averse person would choose the low-variance game and a risk-loving person would choose the high-variance game.But the variace of both games would be the same for the risk-loving and risk-averse players.

Playing style affects one's results. A risk-averse player will be making different decisions than a risk-loving player, even supposing that both of them have sufficient discipline to wager only when they believe they are getting the best of it. In identical game conditions, with identical basic skill levels, the risk-averse player will tend to play a lower-variance game than the risk-loving player, and the risk-loving player will have at least a marginally better win rate than the risk-averse player.

The definition of variance has already been addressed, but to reiterate, we are talking about a well-defined statistical concept. That is the average of squared deviations of a random variable from its mean; in this case the variable is a player's winrate over a given number of hands. For a game to have zero variance, a player would have to win (or lose) the same amount on every single hand he ever played. This is clearly not the case in poker (not even in O8b).As justblaze said, it is possible to calculate and compare the variances of $30/$60 limit and a $25 NL game. So maybe it is not a "silly" comparison, but it is not a very useful comparison. To play $30/$60, you should have a bankroll of at least $20,000 and you should have mastered basic and intermediate poker concepts. Someone could play $25NL with $500 or less and virtually no knowledge of poker.

And not go broke?

Some have said it isn't right to compare games with the same bankroll requirement because bankroll requirement is a function of variance. But bankroll requirement is also a function of winrate and the player's risk tolerance. If we a talking about one player, than his risk tolerance will be constant, but his winrate could vary across games. If we keep the bankroll requirement constant, then the winrate will vary inversely with the variance of the game. So my list assumes the winrate is highest for bankroll X at short handed limit and lowest for the same bankroll at full ring no limit.Of course different players may be relatively more skilled in limit or no limit, so their rankings of games could differ. As justblaze said each player can simply calculate their own variance using pokertracker. This will depend on the player's playing style.To address another post, using words like short-term and long-term variance are misleading. It is best to talk about variance over a given number of hands. Someone also asked whether variance is distributed normally. A player's true variance has no distribution -- it is simply a number. We cannot know a player's true variance though. Instead, we measure the sample variance by looking at a finite number of hands. The central limit theorem states that repeated observations of sample variances will be distributed normally with the true variance as the mean.

The Central Limit Theorem assumes the a priori existence of a well-behaved probability distribution governing the behavior of the random variable of which we have taken samples. Given that game conditions and player mental state are arbitrary and can change arbitrarily, I have serious doubts that any one probability distribution can be said to govern a player's results, and therefore I have serious doubts that the CLT is cleanly applicable.

[econ_tim 0]

Playing style affects one's results.

A risk-averse and a risk-loving person could play the same way and just have different bankrolls.

And not go broke?

Yes, there is a well-known 20 word NL strategy posted on this site that will beat $25NL

The Central Limit Theorem assumes the a priori existence of a well-behaved probability distribution governing the behavior of the random variable of which we have taken samples. Given that game conditions and player mental state are arbitrary and can change arbitrarily, I have serious doubts that any one probability distribution can be said to govern a player's results, and therefore I have serious doubts that the CLT is cleanly applicable.

It's true that a player's true varaince will change as they grow as a player or as they move to different limits. However the CLT applies to a very broad class of distributions and we can imagine for the purposes of this thread that we are trying to find the variance for a player at his current skill level in a given game (or given population of players).

[Jordan 1]

nlhe tournaments take all skill.ask phil hellmuth. he has all the mobney.

[CoolHandLaw 0]

POT LIMIT!

[Wingmaster05 0]

I play tic tac toe and win about 60 percent of the time. That should explain how much of this conversation i understand.

[AlphaOmega 0]

I play tic tac toe and win about 60 percent of the time. That should explain how much of this conversation i understand.

I did not think this thread would get the heat that it did. I was expecting a "yeah x has less variance, duh" or something like that.What prompted this question was what I saw over at 2+2 when a guy posted his stats on six max limit and he had a 50k hand period where he was playing losing or break-even poker. If I had a stretch like that I don't think I'd be able continue to play poker because I could never replenish my bankroll to compensate for all of my withdrawals.I'll probably end up doing my own rersearch on this subject, and I think a lot of it has to do with what game I am best or most comfortable with, and when I finally get pokertracker I'll probably try and compare the statistics between all four games over 10k hands or something like that.

[Abbaddabba 0]

Do you have a link to that thread of the guy with 50k hands of break even poker? (presumably who is otherwise a strong, winning player, otherwise who cares?)That's insane.

[AlphaOmega 0]

Do you have a link to that thread of the guy with 50k hands of break even poker? (presumably who is otherwise a strong, winning player, otherwise who cares?)That's insane.

http://forumserver.twoplustwo.com/showflat...550&page=0&vc=1He's a winning player, and I believe I exagerrated a bit (looks more like a 10k downswing followed by a 15-20k of break-even poker, about 40k til he gets back even)

[Canada 0]

Do you have a link to that thread of the guy with 50k hands of break even poker? (presumably who is otherwise a strong, winning player, otherwise who cares?)That's insane.

http://forumserver.twoplustwo.com/showflat...550&page=0&vc=1He's a winning player, and I believe I exagerrated a bit (looks more like a 10k downswing followed by a 15-20k of break-even poker, about 40k til he gets back even)

Depending on a lot of conditions this will happen on 1% (very roughly) of 40k sample sets for winning playersWhat this means is that if you play enough it is highly likely to happen to you at some stage.To make things a bit easier for the OP a few points to explain why I said your original question was redundant with good BR managementA bankroll is a function of

• chosen risk of ruinyour varianceyour win rate
  • Its pointless to debate NL vs LH vs SH vs Ring without knowing your values for the last 2 of those.You could be a 4BB/100 player at SH LHE and a break even player at NL ring. Apples to orangesYou got the idea a few posts up.Play 10k (preferably a lot more) of each to give yourself sample sets.From there you can work out your bankroll requirement for each and more importantly the number that you are probably seeking.Return on investment

[Demiparadigm 0]

This thread is ridiculous.A bunch of people pretending to look smart.Variance can ONLY be considered in relation to WIN RATE.Not to the size of the blinds, not to bankroll requirements... not in terms of straight $$$Any other way to consider variance is idiotic.Yes. Variance has a specific mathematical definition.It is the average of the squares of the differences in your results from the mean, for a given amount of time/hands. Therefore Variance does not decrease over time, but remains relatively constant. There is NO short term/long term variance.Standard Deviation is the square root of variance.Therefore, by definition, No Limit has more variance for a given blind structure.However for a given WIN RATE Limt has a good deal more variance. This is because a skilled player's edge is greater in NL.Look at your winrate for LHE and NLHE.divide your Standard deviation by your winrate.The one with the higher number has more variance.Standard deviation can be found in Pokertracker under "session notes""more detail"The thing that makes me the most sad about this post is I am sure this debate will continue despite people reading this.Good Luck.

[Abbaddabba 0]

I dont think that you've addressed the issue much at all in terms of the discussion. Most have agreed on a lot of the issues...What we can know is that:No limit for identical blinds has a higher variance (sum of squared errors relative to winrate).No limit requires a larger bankroll because of this, in terms of blinds (or big bets).Variance, in as much as it effects you, is proportionate to how high the stakes are. A high variance game that is for stakes 1/4th of a similar game with high variance (SSE relative to WR) is going to be 25% as volatile. The variance is the same, since it's a function of the SSE and winrates, but it isn't in as much as it presents you with risk.In that respect, despite the fact that NL is a higher variance game, LHE played for blinds twice as large (and big bets 4 times as large as the bb) will be close in terms of how volatile the outcomes are in dollar terms.For bankrolls that offer comparable certainty, variance will be identical precisely because bankroll requirements are formulated based on variance (in relation to winrates).Supposing that a 1200bb NL bankroll and a 300BB LHE bankroll offer comparable certainty in ROR avoidance, which would you say is more profitable?That is the important question that needs to be asked.There is no answer that is true for all players, or all situations.Is 3BB/100 for limit more or less reasonable than 12bb/100 at NL for the corresponding stakes? I think that it's close.I think what makes limit more profitable is the fact that one can multi table much more efficiently.