The fact that no two sessions are the same is the entire point of doing several simulations.

Winrates are point estimate statistics. They are no better or worse than confidence intervals, which are interval estimate statistics.

Every statistic has bias. Just as variance clouds every estimate, so does bias. The fact that bias is present is not a death knoll. It's standard.

Idk what you mean by "observed results" in italics. Or at the bottom with "vs. win rate."

Winrates are real. Given game conditions, player skill, etc., a win rate exists. It's just impossible to measure with 100% accuracy due to bias and variance errors. This is true of nearly every measurable thing in the world. And so we use statistics to create estimates of these phenomenon because it's better than nothing. By a lot.

I always assumed that running sims, like pokerdope was to get a sense on long term averages and BR requirements. Obviously each table will yield different win rates and SD for each player, but the point is to average out all the table conditions you'll face over a selected period of time.

Going to the main point of length of break even stretches, even those simulations show that if you have a decent live win-rate, it's improbable to have a year long BE stretch. Based on what I've heard from confirmed winning players I actually know in real life, it's hard to make no money over ~50,000+ hands.

Sometimes I think this thread misses what was the entire point of my last post: Winrates are statistics. Statistics, by definition, are estimates.

Section 5.1 of the wiki article on Statistics is prudent here. I have annotated it to suit or needs and desires:

"A statistic is a random variable that is a function of the random sample(YOUR SESSION LOG), but not a function of unknown parameters(SUCH AS YOUR REAL-LIVE TRUE TO GOD WINRATE). The probability distribution of the statistic, though, may have unknown parameters.(PROBABLY/CERTAINLY DOES)

Consider now a function of the unknown parameter(YOUR REAL-LIVE WINRATE): an estimator is a statistic used to estimate such function(IN OUR CASE, THE HOURLY IN YOUR POKER TRACKER APPS). Commonly used estimators include sample mean, unbiased sample variance and sample covariance."

To take it further, your TRUE REAL-LIVE WINRATE is an unknowable population parameter. Your observed winrate is a statistical estimate based off of a random sample that you collected by putting in hours at the 'sino. That's it. Don't try to make it more than it is. Live with the fact that you'll never truly know because things change. It's just a strong clue and nothing more.

Well put. Should probably go into that disclaimer page when this thread is fired up for the first time.

Big winners don't like admitting they run pure.
Small winners don't like admitting they play bad.

That said, my opinion is that many live poker markets are very crushable with very low variance.

This all depends on volume.

People toss around the term "year long BE stretch", but then for some players that means around 600 hours. That 600 hours is 18,000 hands. Which is pretty plausible for a BE stretch in a simulator. Let alone once you add the mental grind of going *months* without posting a noticeable profit.

50,000+ hands starts to become much less likely to be BE. But god help the guy that only plays 300 hours a year.

Told myself I was going to stop ****ing around this year and start to properly track my results. After a few breakeven to slightly losing months at PLO got back to holdem and having a sick little heater to kick off the year

Graph


Overall results: 1/3plo, 1/3nl and 2/5nl

Solid start to the year! Good luck & run good!

What if I told you that a 2/5NL player, who was at MGM in MD the day it opened & played 18-28hr sessions, went home & slept & then back at it again, went 2 months without a single losing session & won in excess of $50K, would you believe that was an unreasonable win streak?

Bryan Devonshire's losing 18 months, could have been: won X during the 18 months & lost X+1% of X. He didn't lose every session. Also, he plays tournaments, so he doesn't put the hours into cash games that a 2/5NL cash grinder does.

As Avaritia said, Devonshire played in larger games than 2/5; he didn't play full-time, as he is mostly a tournament player. He didn't say how many hours of cash he played during the 18 months. So much arguing going on, that I wish I hadn't mentioned it.

I've been tracking my hourly since July 2014. I avg $15-$17 pr hr @ 1/2NL, depending on where the variance swing is & that includes a 7 month heater where I avg ~$31pr hr due to 2 big winning sessions. I've only had a few losing months & none were more than $1K. I've had several 100+ hr months averaging <$10pr hour. I avg 110 hours per month.

I do not play for a living, as I'm retired & worked all my life, so I have absolutely no pressure to win. I could not imagine trying to grind out a living at 2/5NL at my age.

[QUOTE=GatorXP;53398178][QUOTE=browni3141;53398121]Are you trying to make a living off of poker? Quit PLO IMO.

It wasn't meant to bash you, but I would not play in a game where a 1200 hour breakeven stretch is reasonably likely to occur. After observing it it's more likely that it's "reasonably likely" than that it was just a freak occurrence.

I'm pretty sure a site like pokerdope would yield the exact same conclusions as the formulas I posted would. My formulas just don't give you those cute squiggly lines. They could be used to graph those confidence interval cones, though.

It depends. Is this guy a good player or just a degen? If he's playing close to every day and logged 1000+ hours over that period, then $50k might be pretty close to his EV, so it's not particularly remarkable. Even if he only played 500 hours it's not that remarkable. The impressive part is that he didn't have a single losing session. If we use the same SD/u = 10 as before, then it's roughly 77% chance to win a 25 hour session. (.77)^40 = about 1/35,000 if he played 40 25 hour sessions with SD/u = 10.

Even if this is accurate (it's probably not without knowing anything about his play or game conditions), it's pretty irrelevant. We shouldn't look to massive outliers to determine what could reasonably happen to an individual. It's like worrying about being struck by lightning every time you go outside because you heard about a guy who was struck 8 times over his lifetime.

@ Avaritia also, I was not talking about Devonshire, as he pretty clearly is playing in conditions different from someone who plays only 2|5. I was responding to this:

SD/u = 10 was not pulled out of thin air. It is pretty close to what I've experienced and it is higher than what a lot of other people have experienced. If you don't like my choice then pick your own value.

Mathematical models are not perfect, but they are far superior than personal experience and anecdotes from outliers at representing what could happen to an individual in the future.

So I'm planning a move to Vegas at the start of this summer to play poker professionally. Please don't bother with all the obligatory "dont do it!" and "nobody makes it" responses. I have results, I have a the bankroll for it, and I have the life situation to allow it. I would just like help/verification for 3 similar stats formulas to help me double check my budget and projected income for the next year. The more "plain english" you can make things the better. I saw a couple formulas I believe are correct, but the symbols in a few posts confuse me.

Formula 1) I have logs with hours and profits for all sessions. I want to generate confidence intervals on my hourly profit ie) I want to be 95% confident that my hourly is between X and Y. What is the correct way to calculate that?

Formula 2) I believe this is just a variant of formula 1. What is the formula to predict how "luck neutral" my results are likely to be. ie) If my results are 20bb/hr over 1000 hours, how likely is it that I could have achieved that result if my play "should have" earned me 15bb/hr.

Formula 3) Given a winrate of X over Y sessions with V variance, what are the chances that I would experience a winrate of Z if I played N more sessions?

Thanks in advance!

Also any recommendations of nice apartments (700-1200/month) within a 10 minute drive of the strip would be appreciated if anyone has some.

Plug your numbers into pokerdope variance calculator. You'll need to make sure your stdev is accurate.

cool tool. thanks for the tip

this is it I think.

2*(stdvhrsbb)/sqrthrsplayed

So for example.

You played 1000 hours and won 10BB/Hr cuz you been crushing/ runnin' good, and have a Standard Deviation of 73BB/Hr

2*(73) / sqrt of 1000

146 / 31.62

Means you have a 95% confidence interval of your true winrate thus far
being between

14.6BB/hr
and
5.4BB/hr

I'm not 100% certain this is correct, but that's how I understand it. Prob need some confirmation.

As for the other stuff, who knows? That's above my pay grade.

Search ITT for posts by bip! with the word confidence in them.

Also, why Vegas? Better poker destinations out there, imo.

This is correct. Change the 2 to a 1 for 2/3 confidence, and change it to a 3 for 99% confidence.

There are some important caveats that are always worth mentioning, things like our results are not true independent trials, and as we accumulate the hours our edge may(will) change - making the inclusion of results from long ago, questionable.

You can get a nice apartment near the strip for 700? :O

Thanks for the responses guys! Much appreciated!

Any good bankroll management advice for someone properly rolled looking to play in some occasional tournaments? I prefer the bigger tournaments because they rake less as a percentage and have longer levels / structure, but am curious if there is a rule of thumb on on the max entree fee per tournament in relation to my br.

There are formulas out there for tournament grinders, but I haven't seen one for a mix of cash and tournament. Consider selling some of your action to get you in to the beatable structures (time and rake) without risking too much of your BR.

I don't think a mix matters to the BR calcs.

You need BR $10k to play MTT's of size X.

You need BR $10k to play $2/5 NLHE.

If you've got the $10k you can play either.

Should be able to chuck in field size, ABI, rake, estimated winrate (crushers = 100% ROI in liveaments) etc into the poker dope tourny variance calc to come up with the numbers you want.

it's supposed to be 100 buy ins of your normal tournament size for a winning reg, but my guess would be that in the live setting approximately 0.1% of touring mtt pros/serous regs have this in their poker bankroll.

yeah but how many tourneys do they play with 100% of themselves? not many imo

Also it's completely different if you're playing 100 man fields or 5k runner main events. Completely different. You can't reasonably apply 100BI BRM to both formats.