KTU answers all your questions about bankroll management strategies

Hey and thanks for creating the thread!

I've been thinking along similar lines recently, and I'm going to test your holiday approach in an upcoming Twister challenge

I'll write out my BRM framework here later. I've also concluded that BRM should be looser (for established pros) than many people think (I even know someone who has successfully got out of a $6.5K gambling debt, starting from his last $500 and taking loose shots at PLO25-100, not without luck, though), but my general thinking process in risk management is different.

Hey,

I am really interested in your framework!

I think there is no "correct" BRM. It depends what you want to optimize and what are your requirements:

• Risk of Ruin - How often should it work out?
• Hourly Rate - Where do you have your biggest edge? How can you maximize to play hands in these games?
• Take-Win or endless game - Do you want to play and endless game or do you want to set yourself a clear goal.
• statistical significance that you are a winner on a given limit - Are you sure that you are a winning player? Otherwise you need sample size to have a proof
• How comfortable are you with moving up and down the stakes from psychological point of view?
• Do you need to cash out on regular basis?

Is that helpful?

Cliffs: imho, BRM is rather not about variance, but about having room to explore which games one can beat.

Before I start ranting even more, I'd like to know more about your 'model player' and the assumptions you make about him, such as his non-poker income, expenses, assets, liabilities, poker track record.

If he's an 'ambitious amateur' who has a real job, then I assume that the job has a potential to pay €2K+ a month at least eventually, because otherwise, given that you assign him 37% ITM in the €10 Twister (when 1-tabling, I assume), it's +EV for him to take a sabbatical year and print money while the games are still good, having 36% ITM 4-tabling.

But if he does have a decent salary, he can cut the life expenses a bit (if he's not saving money up yet) and 'inject money into the bankroll', thus being able to play the same optimal stakes (hourly-wise given his skill level - don't forget that if he moves up too far, he'll get beat up by regs) without the need to move down. If he 'goes bust', he can just wait for a month and start out fresh. By playing lower stakes than optimal, he wastes time that would be spent on extra working hours or just recuperation.

It's an adage among live poker players (whose winrates converge slowly and downswings last for months because of small numbers of hands played, you know) that the bankroll is the amount that one is ready to invest into poker lifetime, almost regardless of whether it's available right now or will come in after salary is paid.

Not only is it true for online poker too, but I'll widen the bankroll definition even further (making it sound like a heresy for the generally overly conservative poker players, lol):

The bankroll is the total value of liquid assets that the player can acquire within a reasonable time and is ready to invest into poker.

Stories like the one I've linked above (note that the guy didn't even have to sell a $10K car, and many of us have such hardly useful things that we can sell in emergency, incl. the laptop that I'm typing this on) show that, even after the Black Friday, poker can quite reliably deliver such a big 'interest rate' on investments that it's +EV to even borrow money or simply get a stake in the poker community (a few hundred suffice) and pump it into the grind if one has a recent history of beating the same games comfortably (which seems to be an assumption behind your loose BRM strategies).

I don't do business, but I've seen entrepreneurs opine that poker players are in heaven because the latter enjoy lower risks of ruin while having an opportunity (and even striving) to be 100% solvent, while real-life businesses usually have to be chronically in debt and face 2-figure risk of ruin percentages to have a shot at success.

That said, moving down for a while might be appropriate because it saves extra time for the grind that would be wasted on seeking a stake or a consumer credit. But it's not really quantifiable, boils down rather to personal preference than to risk simulations.

Myself, I'm 100% solvent, but that's because the stakes that I can beat at all are so low that they put little pressure on my net worth. I'm not getting my feet wet in Amaya's $15s+ because I'm pretty sure I'd get beat up hard there, not by the variance alone, but by a combination of variance and stronger regs.

It doesn't mean I have no BRM at all; in fact, I've dropped a few K just to learn which games (incl. MTT staking) I can beat and which I can't; moreover, I would have dropped more if I followed standard BRM guidelines, but I'm one of a kind as far as personal issues. Probably that's the main reasoning behind BRM nowadays: some amount of money is required to measure one's winrate in a certain game reliably. This process is becoming easier nowadays, though, because, in PLO (esp. 5-card) and hypers (esp. lottery), all-ins and prize pool multipliers account for such a big portion of overall variance that all-in adjusted chip winnings are a measure of skill that converges fast before a huge monetary downswing happens. In 2006, when the seminal book 'The Mathematics of Poker' with BRM chapters came out, HUDs weren't widespread and I'm not sure if the all-in EV was a thing at all, people were judging their skill by actual results (they still do in live poker).

I like your post and you have a lot of good idea when it comes to maximing profits. I agree with your logic that people that have a good job could maximize their winnings if they "inject" money regularly.

But from psychology point of view I see few problems:
• People like knowing their risk in total.
• Most people are not that sure that they are really a winner when things go wrong. Lets think about a guy who has a good job and thinks he is a winning player on 200NL. He deposits 1k every month to see if it works out for him. If he loses 3 month in a row he might starting to feel unsure about his skill and feels less confident that depositing another 1k is a good idea at all.
• It is good to have a clear mission with a clear goal. This motivates way more than just playing to make as much money as possible if you are short in time.

But of course: The super intelligent emotionless robot would completely agree with your post.

The point is that the guy has to become as close as possible to an 'intelligent emotionless robot' anyway (more precisely, know when to stop playing when negative emotions show up) in order to be a successful poker pro. Playing with conservative BRM cures the symptoms of mental game leaks, but not the root cause. If the numbers in the cashier matter too much to him, he's better off studying the mental game (possibly investing money into a coach) and gradually applying it at the 200NL tables (outside of the comfort zone) than going down to 100NL (where he's not motivated because he has a lower hourly than at the job) and probably spewing the same $3K off anyway because of the unfixed issues.

If he has OK nerves and just wants to know whether he has, say, a 5 bb/100 or close winrate at 200NL (which he's determined as a cutoff for considering going pro), then he can invest 15 BIs, safe in the knowledge that, if he loses them within 30K hands (despite having 'busto periods' that he can use to study the game and review the sessions), he's likely not good enough to go pro at this point (note that he also has the all-in EV figure, which measures the skill a bit more accurately than actual winnings even in NL cash):

How to use SwongSim (free SNG/Spin variance calc) to get probabilities of hitting of low points in cash games

---------------------------------------------------------------------------------------
Effective	Specified		Simulation
Place	Finish Distribution	Finish Distribution
1	50,3%          	50,299287%
ITM	50,3%          	50,299287%
---------------------------------------------------------------------------------------
10000  simulations of  30000  games
Expected ROI (with 0% rakeback): 0,6%  ($2880)
---------------------------------------------------------------------------------------
99% 	had ROI below   1,95%	($9344)
97.5% 	had ROI below   1,74%	($8352)
95% 	had ROI below   1,56%	($7488)
90% 	had ROI below   1,35%	($6496)
80% 	had ROI below   1,09%	($5248)
70% 	had ROI below   0,91%	($4352)
60% 	had ROI below   0,74%	($3552)
50% 	had ROI below   0,60%	($2880)
40% 	had ROI below   0,45%	($2176)
30% 	had ROI below   0,29%	($1408)
20% 	had ROI below   0,10%	($480)
10% 	had ROI below   -0,15%	($-704)
  5% 	had ROI below   -0,36%	($-1728)
  2.5% 	had ROI below   -0,56%	($-2688)
  1% 	had ROI below   -0,77%	($-3712)
---------------------------------------------------------------------------------------
  99% 	had a downswing greater than   $1152
  97.5% 	had a downswing greater than   $1264
  95% 	had a downswing greater than   $1376
  90% 	had a downswing greater than   $1520
  80% 	had a downswing greater than   $1728
  70% 	had a downswing greater than   $1920
  60% 	had a downswing greater than   $2112
  50% 	had a downswing greater than   $2320
  40% 	had a downswing greater than   $2544
  30% 	had a downswing greater than   $2816
  20% 	had a downswing greater than   $3200
  10% 	had a downswing greater than   $3824
  5% 	had a downswing greater than   $4432
  2.5% 	had a downswing greater than   $4976
  1% 	had a downswing greater than   $5744
---------------------------------------------------------------------------------------
  99% 	had a low point lower than   $0
  97.5% 	had a low point lower than   $-16
  95% 	had a low point lower than   $-48
  90% 	had a low point lower than   $-128
  80% 	had a low point lower than   $-272
  70% 	had a low point lower than   $-432
  60% 	had a low point lower than   $-624
  50% 	had a low point lower than   $-848
  40% 	had a low point lower than   $-1104
  30% 	had a low point lower than   $-1440
  20% 	had a low point lower than   $-1904
  10% 	had a low point lower than   $-2640
  5% 	had a low point lower than   $-3280
  2.5% 	had a low point lower than   $-4000
  1% 	had a low point lower than   $-4800
---------------------------------------------------------------------------------------

Of course he could play 100NL and get info not only about his winrate there, but some prediction of the potential 200NL winrate as well. And playing very low stakes is the way to go for totally new players who don't know at all where they're standing. But our premise is that the model player has some history of beating decent stakes ('thinking' and 'being almost sure' that he's a winner are different things) and/or some solid fundamentals that allow to beat them (has invested time and possibly money into being coached).

Hi, KTU.
First of all, congrats for the BRMs, seems really interesting.
I have a question about the Tankroll one.
Well, I love zoom. Its a really dynamic game and I always play it. But, u suggests to migrate to regular tables in NL50 and NL100.
Zooming those limits is out of question for this brm to work?

Originally posted by Afulibador
Hi, KTU.
First of all, congrats for the BRMs, seems really interesting.
I have a question about the Tankroll one.
Well, I love zoom. Its a really dynamic game and I always play it. But, u suggests to migrate to regular tables in NL50 and NL100.
Zooming those limits is out of question for this brm to work?

Hey Afulibador,

It is very hard to maintain a good winrate on NL50/NL100 Zoom. Variance increases and it becomes less likely to win the challenge.
On smaller limits your average opponents will make enough horrible mistakes in order to make Zoom very profitable. But when moving up in stakes your opponents will increase in skill and you should take your time to pick up reads and avoid too strong opponents at all.

Cheers,
Arne

Thanks for the answer, Arne. Make sense ♠_thumbsup:

Btw, in this time between I really had too much fun playing w ur beginner strategy on spins. Its not the main point on this topic, but yeah... Nice job!

Hi Arne!

As Pokerstrategy has recently asked LemOn36 to advertise Tankroll BRM massively, I've been trying again to understand the underlying math (the Bellman equation, in case you're interested; I'm thinking of writing a formal arXiv.org preprint about BRM when I actually create a mathematically feasible model and solve it), and I still doubt that the strategy is sound from the player perspective (of course it serves Pokerstrategy's affiliate interests )

I'm not sure how optimal your strategies are, but they have little credibility without peer review.

In a sound BRM strategy, the number of buy-ins needed for the next stake should grow significantly as the stakes grow because the games get tougher.

As a corollary, there's no need for a solid foundation at NL5, especially because, though Pokerstrategy probably wouldn't like their players to rake less and earn money at a real job instead - to return later with a decent bankroll - it's necessary if the balance is low. Grinding nanostakes just doesn't provide a bigger hourly than a McDonalds job.

As a consolation for you, the bankroll strategy for NL50 or whatever should be tighter than Tankroll but looser than classical (I guess, 20 BIs at NL20 to 40 BIs at NL100, or maybe even looser, though I haven't run the numbers), exactly because falling to the (positive) low bankroll cutoff point where poker becomes a worse option is not a tragedy - one can earn a bit of money on the side and then come back and most likely spin the bankroll up from the soft micros in the second or third attempt.

So I stand by the opinion that Holiday BRM is a much better approximation to the ideal than Tankroll BRM.

Meanwhile, I'd be glad to see the assumptions about winrates and standard deviations at each stake and table count* (and the game modality if you're such a fan of Zoom, though I wouldn't recommend to play it ever) that you made when you were designing the BRM strategies. I.e. a list like 'WR X bb/100 9-tabling NL5, Y bb/100 4-tabling NL10, Z bb/100 1-tabling NL20'.

* Varying the table count is a way to make the range of stakes 'more continuous' - 9-tabling NL10 is intermediate between 4-tabling NL10 and 4-tabling NL20, in terms of both the hourly standard deviation and the hourly winrate, which is far not proportional to the table count because people miss profitable spots when multitabling.

Caveat: post-rakeback hourly winrates need to be given not for the best / average regs of a stake, but for the same player at the same stage of his development put into different player pools. E.g. someone who wins 15 bb/100 at NL5 will probably be a -2 bb/100 loser at NL200 or a 1 bb/100 winner at NL100 if put into those pools immediately.

The skill level can be incorporated separately as a function of time* (as the player learns, he'll be winning more at NL100 but would be also crushing NL5 with a bigger winrate if put there), but strictly speaking, it's illogical to consider it a function of the bankroll (someone who goes on a heater might be unprepared to beat the higher stake).

Note that there's always an optimal stake level that maximises the hourly winrate for the given player at the given skill level; the player shouldn't move above it even if he's 'overrolled', until time passes and he improves.

Both life expenses and (for part-time players) side income can also be incorporated into the equation easily, either as a drain for the BR or as an injection into it happening at a constant rate.

* I'm not sure if the optimal control problem will remain analytically solvable then, though.

I would just like to post about my experiences with the Tankroll management Strategy. This strategy CAN work. However, I highly recommend heeding the advice given by KTU. Especially regarding table selection at NL50+. Additionally, I think it is important that the intial $150 is dispoable (worst case scenario you lose $150. $150 for the chance to win $1000, seems pretty good to me). Also, moving up and down limits as prescribed by the strategy should not affect you mentally (on or off the felt). I had to do this on a number of occasions. Fortunately, I was still playing at limits higher than normal so even if I had to move up or down I was still motivated.

I started with about $160 / $170 at the beginning of September and hit $1k last night. Be warned. I ran very very hot during this time but I think I still played reasonably well also. For example on a couple of occassion I got KK in v AA 100bb in a standard spot BU v blind and BvB vs unknowns and binked a K both times. I also cold decked people a couple of times and got gifted some stacks as well when villains spazzed. Accoring to PT4 I ran $385 above EV although this "run-good" was predominantly at NL50+.

You could argue that I should be looking to hit $1160 but since KTU advocates the "take-win" approach I have opted to go forward from here with the Holiday BRM. My target being to make some money for a holiday to Thailand in April next year, whilst at the same time growing my bankroll. I plan to cash out 50% of monthly profit to go towards the goal so that 50% of any profit goes towards growing my BR.

Wow muel294! Congrats ♠_grin: