Bankroll Management and Variance
Posted by Espen Sørlie
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Espen, really like the way you tackled the topic. Just wanted to point out something else that you sort of touched on but didn't use in your analysis of your downswing (BTW massive props for opening up about that) - the buy-in and field size spread.
On pokerdope you can "add another tourney" so you could break down the 6193 mtt's you played into ranges, which let's you construct a balance of safety and shot taking.
Some screenshots of a theoretical split:
Combined results:
Compare Tournaments view (shows the effect of each mtt type):
Edit: that last one is kid of unreadable, and there is also other analysis - but hopefully you get the idea.Cool man! Did you find what I suggested, that swings are bigger when you sort it like that?
Not in the way I split that sample. The large number of lower BI's with higher ROI helps to stabilise the swing.
Interesting! I will try and play around with that too when I have time.
awesome vid
Great vid espen!
thanks guys^
Loved this vid. Added pokerdope to my fav sites.
At 24"41sec you say "1 thousand" wanting to say 1 hundred right ?
Can you just confirm what you want to say for those 2 things; 100 ABI and 300 for the top please because its not so obv 4 me ty...
oh wow, that is a typo in the slide. What I mean is having around 1000x what your average buy in is in your bankroll. If you have $20 average buy in, you might need around 20k to make sure you don't go broke. If you have $100 average buy in, I would need 100k to feel safe. Note that peoples situations are very different so maybe you can have 5k-10k and play $20 average buy in and feel comfortable. You can then easily go broke on a bad streak though...
can somebody on runitonce tackle this topic for cash games?
There is stuff on this in 'The Intelligent Poker Player' by Newall - he uses it in terms of big bets for LHE but shouldn't be too hard to work out for NLHE
Is there any way to use Kelly Criterion to determine the ideal buyin? In mathematics of poker (book), they only show a way to estimate the ideal cash-game buy-in based on your BR.
Sorry, Im not familiar with Kelly Criterion
LOOL 1000 BUY-INS ..? 20K to play a 20$ dollar MTT. 100k to play a 100 ? Dont know if its a joke or if im a joke really loool
Im just talking about my experience and what I would prefer as a professional. As you can see from the variance calculations I made, it is very possible to lose loads and loads of money purely because of variance. If you don't have any other source of income you need to guard yourself as well as possible from it. fwiw, I didnt say you need 20k to play a $20 mtt and 100k to play a $100 mtt, but to have that as your AVERAGE BI. 300 for the top means in order to play a $20 mtts as part of your main schedule you need 6k.
okay. What do you mean by your main schedule ? Not sure i understand your 300 ? Your 300 was supposed to be the number of BI for the top BI of our MTTs we can afford right ?
By main schedule I just mean things you are playing on a daily or a weekly basis. In huge value series like scoop or wsop we might want to take some well calculated shots.
And yeah I think you got what I mean about the 300 for the top now
loved the vid thx for the advise! ive never heard brm explained this way
Lord knows why SKYHIGH even signed up to this site, laughing at a fairly obvious BRM rule. LOLDONKAMENT PLAYERS.
That seems a bit harsh. The target audience for RIO has got to be people that don't know everything.
And even when you know a lot, there are other things you can find out or topics you can change your thinking about by interacting here.
+1: have to learn things somewhere
"admitting ignorance is the path to knowledge"
I'm using the same BRM. 1000x the AVG Buyin is pretty perfect imo. Lets you stay relaxed without having pressure when things aren't going well for a while.
Only at the 4:00 mark, but you are explaining why you think its good to have a low variation in your ABI (a smaller distribtuion range btwn top and bottom BIs).
While it is correct that the higher BI tournies have a much more significant effect on your BR and will be a heavy determinant of your results that is not a reason to have a low variation in BIs. In fact quite the opposite imo.
Firstly your ROI at SSMTTs should be much much higher than MS/HSMTTs, your variance may be higher due to larger fields, but your risk of ruin and P(ROI < 0%) is going to be much much smaller. If you are a MSMTT player who wants to be playing some higher BIs, esp sunday majors, it makes a lot of sense to play a wide distribution of BIs, lowering downside variance of playing only higher BIs (which had a MUCH higher downside given decreased ROI). Haven't run statistics on this, but I'm fairly sure having a wide distribution of BIs decreases overall variance rather significantly.
EDIT: Additionally, by playing a mix you also get to play vs tougher fields and improve. I've been b/e playing a mix of SS-HSMTTs over a year, but my SSMTT ROI has drastically and noticeably increased by playing HSMTTs, and playing SSMTTs occasionally reminds me of some thing i forgot fish are doing (if i forgot and was playing a fish in sunday mil)
You are wrong. I made a very easy example where in one scenario we have $20+2 BI over 10k tourneys, in the other we mix with 5k $30+3 and 5k $10+1. I put our roi in the first at 25%, and in the 2nd at 15% for 30+3 and 55% for $10+1. This adds up to an average roi of 25% and we have the exact same expectation.
HOWEVER, the point of this was to figure out the biggest variance way. You argued that the high roi of the lower stakes would even out the variance of higher stakes, but as you can see that is not the case. the standard deviation is higher with a spread of BIs and our probability of loss is also higher. of course there is two sides to variance, so our best run in the second sample is also ofc better than in the first.
Your argument about becoming better by playing better opponents might be true, I didn't really talk about that.
You sort of set up the answer by assuming that ROI scales to BI size to the AVROI remains constant (in order to underline the change in variation of outcomes I presume). Which is fair considering the last sentence of my claim, although I should've stuck with the start of it concerning decreased P(<0) as compared to other EV maximizing BI schedules which would suggest higher BIs. Regardless, if you keep avROI constant by adding lower ROI high BIs and higher ROI low BIs and then compare it to AVBI and AVROI then of course variation in the mixed lottery is higher with no EV gain.Anyhow, when choosing a schedule our ROI for each BI doesn't scale so linearly and minimizing variation is not our only goal, we also want to max(EV) obv, and when BIs and AvROI don't scale linearly you can be sacraficing a huge amount of EV by not mixing, and it allows you to play higher BI games by mixing, b/c you are not rolled for those games. So in your BRM there should be an acceptable RoR %, for X size BR (or not if you're on the professional side or nitty recreational side), although I think for most anyone there should be b/c you can move down instead of actually playing it out at higher BIs. Then max(EV) within that. Mixing will best accomplish this if your ROI doesnt scale, I posted a version of this below using 11$ and 55$ as the mix in for 5% of the games. Notice the 6% increase in EV, large upside changes in the confidence intervals for relatively small downside risk.
I definitely phrased my argument poorly, but imo you captured a specific instance of when mixing is bad if you can find all the same games at AV ROI of the mix. However the tournies ppl are usually mixing in are high BI majors that they have high ROIs in (like Mil, Biggers, Hotters, etc) and thus are probably closer to teh non-linear scaling of ROI that I described. If you're considering adding in some random higher BI that your EV drops significantly in then yeah, obv increases your variance way to much to be justified.
EDIT:For added fun, and this I think makes the argument for mixing more compelling, lets say that first set of charts I posted had a 45% ROI if the person wasn't mixing, then by playing a bunch of 50s and having to think about their game a lot more they had a nominal 5% ROI boost to 50% (so the second version of the charts. Below are the statistics for 1k games of 10+1$ at 45% ROI (unimproved)
That is around a 20% increase from this version of the 11$ schedule to the mixed version! granted if your mixing in higher BIs more heavily the efficacy of this decreases, hence my phrasing about 'a proper mix'. This clearly only works if thought through....but that effect is too substantial not to be notedLast EDIT, I promise, Also just fwiw
I think we can easily agree that you can gain a lot of EV by playing higher if your roi doesn't drop drastically, and Im pretty sure at this point we agree on everything else too. The only point I wanted to stress was that you increase your variance by playing a $100 mtt and a $10 mtt compared to two $55s. Sure you can increase your overall EV if it's the right time for it, but it was more meant for a tip for players who are just looking at their average BI and using brm rules with that. Just pointed out that there are more to the story than that.
Ah fair enough, I think I just mis-interpreted you in video as advocating for a narrow band of BI's w/o further qualification. Glad you agree at least partially on that as it's one of those things I thought I had applied well from my econ/stats background and yet may have screwed up in thinking it was a relatively simple lagrange max notion w/ BR as constraint.
Fantastic Video! Having suffered a 3000 game down swing (which is still continuing) this really brought home how much variance impacts your results. Its something that mentally I have tried to digest but I still cant help but doubt my ability when things are not running well. This has really helped me clarify things in my own mind. Thank you!!!!!!
No problem :) As I said, some times the human mind can't even comprehend how bad it is possible to run. So in massive downswings, while you should ofc study to get better, it can easily just be an insane run of terrible luck..
Really enjoyed the video, will read the comments later. I started playing around with the tournament variance calculator and it seems interesting, thanks for sharing Espen.
Great information here, really enjoyed the pace.
I would consider rating myself on how aggressive want to be in a scale of 10. ONE stands for the 1000BI and TEN stands for 100BI. I would rate myself 4.5 so i would probably had to build 5K to play the $11 tourney regularly.
Good luck on and off the tables
That makes sense, however I don't think the scale should end at 10, it is def viable to have more than 1000BI ;) GL U2!
yeah i get it now cause it makes much more sense having more than 1K given the distributions you presented in the above video
Hi Espen,
Been wondering this for a while and this seems like a good thread to ask.
Do you think it's ok to allow less buy ins if a tournament is a KO? Does this change anything?
Let's use the PSKO's on stars as an example. The are $12.50 + $12.50 + $2.
Do you think it's ok to treat those as 2 separate buy ins? So 1000 Buy ins here would be $12,500?
The progressive KO is a bit different because it is super first place heavy when only the winner of the tournament gets 100% of the bountys he gained. say in a normal $21 superko ($10+$10+$1) it seems reasonable!
Great vid espen! What about dropping down limits? lets say i have 30k $ BR and my avg BI is 33$, so if I get down to 15k, do I drop the BI? or what is the formula here? :)
yeah, then drop down to $15 abi I guess
Brilliant video espen! I was just wondering what your thoughts are about rebuy tournaments and how it affects your BRM rules, as there are a lot more variables when compared to a freezeout (How many times you rebuy, how much the prizepool fluctuates within the same number of entrants etc). In addition, is there a way we can legibly input rebuy tournaments into pokerdope? I would imagine some days I will rebuy more than others, as would my opponents; as there's no prizepool section on the tournament variance calculator I would imagine its easier said than done though. What are your thoughts on this?
The way sharkscope does it is just taking prizepool/amount of people to find the average BI. This is ofc not representative of everyone, so I would just assume it to be around 3-5x and do BRM from that.
Ahh sharkscope, I'm using a lesser tournament tracker which doesn't take the average buy in into account. I shall switch at once.
thanks espen, this helped me a lot...
now im sure that it` s not only my Play that affects my winning quote these weeks...
do you know how to get the roi ?
without having to publish it on "officialpokerrankings" or such sites?
or is it just an estimation of what your edge is?
or should i just calculate it after i plaid a decent sample size?
for example 5000 tournaments or so...
greetings from Austria, mansislav :-)
roi is hard to estimate, and it depends on a lot of different things. all you can do is make an estimation based on results from before. the obvious problem with this is that because of variance, you need a huge sample to get an accurate roi. the time it takes to acquire such sample, means that your roi probably has changed in the meantime (you have gotten better, tournaments have become tougher etc). 5000 games isnt going to be enough to be accurate, but most of the time it will give an indication. It is very possible for professionals to have 5k and even 10k games losing streaks. it doesnt mean that is their true roi and that they are losing players.
thanks man !
This video has been unbelievably helpful for me. This video may have single handed saved my poker career.
Wow, that is very cool to hear! Good luck in the future
hello Espen, I have been a winning player for several years and suddenly can't win for 6 months in a row. I started to think about corrupt software and stuff like that but by showing your two down swings over two 6 month periods gave me my confidence back.
I am a cash player but taken your sample over more then 6000 tournaments , this estimation can speak for cash games two. I admire that you had the gutts to show youre down swings and on the contruary, it speaks for you to post it and I'm shure it helped a lot of viewers including myself.
Cheers!
Im glad to hear that and wish you good luck in the future :)
this is the most depressing and valuable training video ever )
what stakes on PS do you recommend a new MTT player transitioning from cash to start off at? If bankroll/variance wasn't an issue? I'm a cash player transitioning over to learn and improve mostly. I'm very new to MTT learning and playing from the ground up. Would I just get completely crushed at $109-$215 levels?
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