Winrate vs Variance?

Hi guys. For all the Live 1/2 crushers on here. I was wondering if you found that having a higher winrate lowers your variance and the length/size of your downswing? Online you have to play something like 30k hands to reach a reasonable level of certainty that your winrate is real (because the edges can be so small) Is this reduced in live low stakes games vs. softer competition? Example graphs are welcome

Thanks.

ventrolloquist said:

Hi guys. For all the Live 1/2 crushers on here. I was wondering if you found that having a higher winrate lowers your variance and the length/size of your downswing? Online you have to play something like 30k hands to reach a reasonable level of certainty that your winrate is real (because the edges can be so small) Is this reduced in live low stakes games vs. softer competition? Example graphs are welcome

Thanks.

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I never really kept track about my real statistics so I can't give you a definitive answer about comparing exact hand number and winrate so no graphs from my part.

Regardless, I would say that a smaller sample size in live games (smaller then 30K hands) would be sufficient to give you a good enough answer whether you are and whether you will be, profitable in the long run.

Also, I am not sure that having a higher winrate reduces variance?! I don't think it works in that direction.

I'd personally say, based on my experience which is not anywhere near exp a pro would have, that variance is still very high in low stakes cash games! Just thinking about my last several sessions, I saw hands like 63o going all in pre, also a lot of pre flop action with medium AXs etc. Whenever I am playing, the biggest stacks are behind the biggest nits so that should count for something.

Variance is also a lot about your playing style. If you play an aggressive style and 3-bet bluff a lot the variance is bigger when you could hit the flops or your oppenent and you are playing bigger pots. If you play basic ABC well and don't do anything stupid you know when it's more about luck in the important hands and when it's skill. Play your game and think after session was it more luck or skill today.

Yes I agree Tunkki variance has a lot about the playing style. The effective stack depth in the game also plays a role as well.

I think in live game the game is soft enough you can take significant +EV spot consists of high equity hands * high certainty game play (i.e equity distribution is more robust throughout all streets or realization rate is high) and give up small +EV spots that you may have >50% equity but lower certainty realization path (more change of equity distribution throughout all streets or preflop flipping event like QQ vs AK).

By taking more higher certainty plays, the variance of win rate is reduced and less sample would be required to converge towards your true long term win rate.

In comparison, one can choose to fold EVERY hand preflop and the "win" rate would be converged very quickly.

Thanks guys. Solid answers. My logic was if you're playing against bad recs then they will take a lot of -EV lines, meanwhile if you play your standard game, with +EV lines, then the difference between the EV of your plays and the rec's plays will be higher than the EV edge you have vs. a good player. And if there is anything I learned from PLO (as an example), it's that when hero and villain's EV's are closer the variance becomes much higher (and the opposite is also true, when EV edge is big there is a lower chance of the opponent's lower EV line coming out on top). This is why it makes sense that ABC poker has lower variance than LAG, even though LAG will have the higher winrate; because you're only selecting very high EV lines.

But what my question boils down to is the statistical certainty of being a winning player; let's imagine you are playing a super soft home game with people that play any suited hand, and let's say they give off blatantly obvious live tells. By how much does the number of hands needed to show you are a winning player decrease? Is 2000 now enough vs. the most fish of players? Or maybe even 500? Or is it still quite high like 10k?

Bozovicdj said:

I'd personally say, based on my experience which is not anywhere near exp a pro would have, that variance is still very high in low stakes cash games! Just thinking about my last several sessions, I saw hands like 63o going all in pre, also a lot of pre flop action with medium AXs etc. Whenever I am playing, the biggest stacks are behind the biggest nits so that should count for something.

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Lmao. 63o all in pre sounds like playchip games. Sound very lucrative . For the sake of my question, let's assume you play ABC poker with the multiway maniac pots, and only bet on safe board textures with 2 pair or better to increase EV edges. Multiway pots are a variance nightmare.

Where do you play out of curiosity?

quant1986 said:

give up small +EV spots that you may have >50% equity but lower certainty realization path (more change of equity distribution throughout all streets or preflop flipping event like QQ vs AK).

By taking more higher certainty plays, the variance of win rate is reduced and less sample would be required to converge towards your true long term win rate.

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Thanks. Great explanation this is what I was thinking is the case.

ventrolloquist said:

Hi guys. For all the Live 1/2 crushers on here. I was wondering if you found that having a higher winrate lowers your variance and the length/size of your downswing? Online you have to play something like 30k hands to reach a reasonable level of certainty that your winrate is real (because the edges can be so small) Is this reduced in live low stakes games vs. softer competition? Example graphs are welcome

Thanks.

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Good discussion. There are many such discussions written about this and I think the answer is complex. First I'll give my opinion that a higher winrate does not guarantee lower variance or length / size of downswing in at live 1/2 in the time frames we are accustomed to thinking in. I think there is definitely a correlation there, for example a losing player will have a lower win rate and larger and longer downswings than a crusher. But from a variance point of view, as you eluded to, covering on an accurate measure of win rate or variance is a statistical measure requiring 10s of thousands of hands. I've also heard that about 30k hands is a good indicator. Which at about 30 hands per hour live would be 1,000 hours. Most players don't log this many hours in a year unless they are pro. And most pros don't play 1/2. And there are so many moving parts and changing variables that by the time you have 1,000 hours your play style has likely evolved. Your opponents may have also evolved. Your game / rake structure could change, etc. So in the end we will probably never know our true win rate or variance playing live.

Now to add some thoughts about other responses. I found a thread that actually made a compelling case for the opposite assumption that LAGs had higher variance than TAGs. And it kind of made sense to me. It's several pages with tons of equations and graphs and online database analysis but the idea was that both players being equal the LAG will play more hands and make more decisions and win many smaller pots than the TAG. The LAG is then statistically less effected by a bad suck out since they are in tons of pots and not all of them are huge. This makes the distribution smoother with less variance. The TAG however plays many less hands per hour and wins more tiny pots pre and flop and likely loads up on more big hands where they need an overpair or set to hold vs a draw. This player has a much higher chance of having one suck out ruin their session since the number of hands are lower and the number of those hands that are big pots is more significant. If they "run bad" it is harder to recover. If the LAG runs bad they have a better chance of winning a lot of small pots to bounce back.

Second, not only your play style but also your opponents play style is key in determining variance. If you always have a guy that goes all in on the flop at your table you're going to be playing for stacks a lot more often and you're going to be taking top pair spots and having to dodge a lot of big bullets. Regardless of your play style you could get crushed. In live poker the hands per hour is just so slow that if you get QQ+ cracked a few times even though you were super +EV with an overpair each time your graph is going to suffer big time.

Third, do not underestimate how "unlucky" you can get. The 63o example is funny until it cracks your AK on an A63 flop.

Lastly I'll try to add some 1/2 graphs. I don't consider myself a crusher as I typically play less than 500 hours a year as more of a serious hobby but I win at a decent rate. My main poker tracking App doesn't have graphs so I only have data from 2018+ in the new app. Here's how wild the data points are:

2018: I played mostly 2/5 that year so only 23 hours of 1/2
23 hours 8 minutes - win rate 39.93 BB / hr

Also hit a $500 high hand not counted in win rate. This is what running good looks like.

2019: I played about half 1/2 half 2/5 last year
207 hours 21 mins - win rate 10.7 BB / hr

I had the worst downswing of my poker life last year that spanned across 2/5 and 1/2. Epic downswing that had me questioning everything. I've been playing since 2004 ish and tracking sessions since 2014.

2020:
6 hours - win rate 14.33 BB / hr

Only one session at 1/2 so far this year.

Whole graph from 2018 filtered to only 1/2 games to follow

Here's the graph. Session count along the bottom. I was invincible in 2018 then didn't even really notice the downswing for 1/2 started in Feb 2019 since I was still winning at 2/5 to cover it up. In June I started losing at all levels and continued to get slammed until October. Then it was like none of that down swing ever happened and I went back to the same sort of rates. Total mind bender.

c0rnBr34d said:

Here's the graph. Session count along the bottom. I was invincible in 2018 then didn't even really notice the downswing for 1/2 started in Feb 2019 since I was still winning at 2/5 to cover it up. In June I started losing at all levels and continued to get slammed until October. Then it was like none of that down swing ever happened and I went back to the same sort of rates. Total mind bender.

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Wow, this is some solid info. Thanks so much for sharing. It’s amazingly strange how amongst all the little variance squiggles there are sometimes huge up- or down-swings that seem to defy randomness, yet randomness can take on any shape, form, or size. Regardless, I firmly believe that a poker player’s mindset influences their performance on a subconscious level, it could be something as simple as suddenly defending a certain hand that you don’t normally defend (and not noticing you’ve even started doing it). From personal experience I’ve noticed that that’s when I start having downswings. And there could be hundreds of reasons why someone might start doing this; from new cognitive biases that persist while you think your playstyle hasn’t changed at all, or just from a sense of impatience or worry. For example, when I worry my opponents are better players than me, my win-rate starts to decline, regardless of whether or not my assumption is correct.

Do you think there might be anything that led to that downswing? Or is it truly random in your opinion? I’ve always noticed upswings want to stay on the upswing, and downswings want to stay on the downswing, and I always found it peculiar.

Perhaps this is a cognitive bias of my own of looking for order in chaos, which is an unavoidable part of being human. Or maybe there really is a psychological reason for it. Perhaps downswings are a form of self-sabotage stemming from failing to believe in one’s-self, which in my opinion applies in many aspects of life, not just poker. You may start taking -EV actions without even realizing you are doing them, and start going against strong instincts and such. And the opposite is true too for upswings and for positive life outcomes... Or maybe it is just random.

I think as an experiment, observing the graphs of a GTO bot playing against other bots (and comparing them to a human player playing against those same bots) might provide an indication of whether these bigger swings are psychological or truly random.

Also, hearing that there is mathematical proof for LAG play having less variance than TAG is pretty exciting. I always thought the opposite and would lean towards tighter play when building bankrolls from nothing. I've noticed this myself playing LAG, I may lose a huge amount in one pot but I noticed when I'm playing small pots my stack size is usually trending up. One more excuse to play LAG

ventrolloquist said:

Wow, this is some solid info. Thanks so much for sharing. It’s amazingly strange how amongst all the little variance squiggles there are sometimes huge up- or down-swings that seem to defy randomness, yet randomness can take on any shape, form, or size. Regardless, I firmly believe that a poker player’s mindset influences their performance on a subconscious level, it could be something as simple as suddenly defending a certain hand that you don’t normally defend (and not noticing you’ve even started doing it). From personal experience I’ve noticed that that’s when I start having downswings. And there could be hundreds of reasons why someone might start doing this; from new cognitive biases that persist while you think your playstyle hasn’t changed at all, or just from a sense of impatience or worry. For example, when I worry my opponents are better players than me, my win-rate starts to decline, regardless of whether or not my assumption is correct.

Do you think there might be anything that led to that downswing? Or is it truly random in your opinion? I’ve always noticed upswings want to stay on the upswing, and downswings want to stay on the downswing, and I always found it peculiar.

Perhaps this is a cognitive bias of my own of looking for order in chaos, which is an unavoidable part of being human. Or maybe there really is a psychological reason for it. Perhaps downswings are a form of self-sabotage stemming from failing to believe in one’s-self, which in my opinion applies in many aspects of life, not just poker. You may start taking -EV actions without even realizing you are doing them, and start going against strong instincts and such. And the opposite is true too for upswings and for positive life outcomes... Or maybe it is just random.

I think as an experiment, observing the graphs of a GTO bot playing against other bots (and comparing them to a human player playing against those same bots) might provide an indication of whether these bigger swings are psychological or truly random.

Also, hearing that there is mathematical proof for LAG play having less variance than TAG is pretty exciting. I always thought the opposite and would lean towards tighter play when building bankrolls from nothing. I've noticed this myself playing LAG, I may lose a huge amount in one pot but I noticed when I'm playing small pots my stack size is usually trending up. One more excuse to play LAG

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No prob, glad I could help. Keep in mind this is a small sample size of a rec player who does some limited game "study".

As far as reasons for the downswing, I wish I could explain it away. I really do. I'm not going to sit here and say that I played perfectly through any portion of the graph. I've played poorly and won and played well and lost plenty of times. My hours per year went up significantly in 2014 so I'll start there. My usual volume was about 500 hours per year so about 40 hours a month. Losing months happened but most months were winning. Back to back losing months were rare. Only once did I have 3 losing months in a row in 2017 and two of those months were nearly break even. I lost 4 months in a row exactly twice. The first time was 2015 when I first started trying to move up to 2/5 and was just getting out played a ton. But it still wasn't nearly as bad is last year when I got crushed for 4 months in a row. I had a great 2018 so last year I was journaling and blogging and reviewing big hands after each session. So while I'm sure I made some mistakes and the run bad may have effected some plays I'm sure I wasn't systematically changing my game to try to get out of the rut. In fact I studied more. I moved down and played more 1/2. I payed closer attention and I still kept losing. Some of it is just the mercy of the poker gods. Maybe the first month I could attribute to overconfidence or entitlement tilt. But the next 3 months don't happen by accident. People were consistently hitting draws on me and I got a ton of super strong hands cracked. I used to think those down swing stories were over blown but now I respect them a lot more.

I wouldn't go as far to say there is mathematical proof of the LAG vs TAG argument. But the data shown was pretty convincing to me. Could still be incorrect for all I know since the data set and analysis are not necessarily representative of all LAGs / TAGs and could have errors. The other HUGE sticking point is that in my opinion is exponentially harder to be LAG vs TAG at a given high win rate. For the same reason that some argue variance and win rate converge quicker there are a ton more decisions to make in more marginal spots so if you have leaks they will be exposed more often. And there will be spots that a TAG just doesn't find themselves in as much that you'll need to know how to navigate profitably. You will be playing against wider ranges for some and others will tighten up against you. You have to keep track of how the whole table is reacting and make so many more correct decisions per session vs a TAG. You'll also undoubtedly put some on tilt causing them to spew off which can be hard to detect if they were playing solid before that. Also if the rest of the table is already LAG-ing it up the correct adjustment would be to tighten up so depending on game / table selection it may not even be optimal to try.

ventrolloquist said:

.. higher winrate lowers your variance and the length/size of your downswing.. Is this reduced in live low stakes games vs. softer competition..

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Good question and interesting responses.
From my limited experience, my rate of winning is correlated to how far into the hand I play and the amount won/lost accordingly (showdown or folding a bluff). By "softer" if you mean I can win more often with marginal hands (via aggressive betting) then the change over time of (potswon/time) is reduced due to the certainty of a payoff with certain players.

ventrolloquist said:

Lmao. 63o all in pre sounds like playchip games. Sound very lucrative . For the sake of my question, let's assume you play ABC poker with the multiway maniac pots, and only bet on safe board textures with 2 pair or better to increase EV edges. Multiway pots are a variance nightmare.

Where do you play out of curiosity?

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It's a small poker room in my hometown. That is actually the first place I ever went for a live game, and I enjoy playing there still. The overall quality of the players is quite low, therefore, blinds shoves pre, or blind calls pre are not too uncommon, which means it can be very profitable with enough patience.

I'd say that multiway pots are always a nightmare from whatever point of view.