using the kelly criterion to build an mtt bankroll

[ph_il]

this is the formula I'm using based on an estimated roi and itm percentage, over a large enough sample size. the idea is to know when I can take calculate shots at bigger buy-ins, based on my estimated mtt edge.

f = roi * itm / (roi + 1 - itm)
f = bankroll risk %

I can then use 'f' to determine how aggressive I want my shot taking to be:

f * 100% = aggressive
f * 75% = moderate-aggressive
f * 50% = moderate
f * 25% = safe
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my roi and itm is a bit lower than it currently is for a few reason:

itm: most sites pay out between 15-20% of the field, this the average.

roi: its better to underestimate your roi than over estimate it. as I play more mtts and move up in stakes, I expect it to drop down its true percentage. I also think it's possible for me to maintain a 10% roi.
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as shown, I'm sticking with buy-ins in the safe to moderate-aggressive range. so, I can buy into mtts within that range. I can't go over the max, but I can go below my minimum. however, for bankroll building purposes, I want to stick within my buy-in range.

this means, that if I wanted to take an aggressive bankroll shot at 2.20 mtts, I can do so when my bankroll hits 154.93 or higher. which is a lot sooner than the normal 100x buy-ins or a 220.00 bankroll. as my bankroll builds, I can take more aggressive shots as it allows, while playing mtts within my buy-in range.

note: the buy-in range if for total buy-in. so, for example, i could play a 1.10 re-entry mtt but couldn't re-enter as the total would be 2.20, which is above my range.
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the main rule is that I have to recalculate my buy-ins with every bankroll change. this assures that I'm taking shots when allowed, moving down in stakes as needed, and following a brm plan that allows me to take calculated risks while not putting my bankroll in danger.
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unfortunately, I don't to properly apply this to multi-tabling. I 1-2 table so I probably won't worry about it as I'll just re-adjust my buy-in range after each entry.

 

[R.Holynskyi]

Uhhh
How difficult everything is. In order to play and enjoy the game, you don't need to be a professor of mathematics

 

[THGE10]

Very good worky. I will think about my bankroll. Thanks

 

[amatola]

I am guessing this only works if you constantly only play the same amount of MTTs at the same time and if you moved up from playing 2 to playing 6 - you would need to adjust.

 

[ph_il]

I am guessing this only works if you constantly only play the same amount of MTTs at the same time and if you moved up from playing 2 to playing 6 - you would need to adjust.

yeah, multi-tabling is the challenging part that I haven't figured out. as I said, I only do 2 tables at most, so its not a problem. but it's probably something I'm overthinking. if anything, it'll probably just be easier for a person to recalculate everything at the end of each multi-tabling session, rather than do it for each individual game.

the whole point of the plan is to know when I can take shots at higher buy-ins, when I need to move / down in stakes and what buy-ins I can play at to maximize my bankroll growth and minimize risk. it's just like any other brm plan, based off of my mtt edge and not just bankroll size.

 

[ph_il]

Uhhh
How difficult everything is. In order to play and enjoy the game, you don't need to be a professor of mathematics

it's not really complicated math and it doesn't take away from the game in any way. it just shows what games a person can play based on their edge, in order to build a bankroll and play bigger buy-in mtts. it allows a person to make calculated risks while practicing good brm.

it's not necessary, of course. it's just another way to approach bankroll building and risk taking.

 

[amatola]

and do you think an above-average but not brilliant player would have a better ROI in 100 entry MTT vs 1000 entry MTTs taking into account greater variance in larger MTTS- or does it all even out in the end as it's percentage based?

 

[fundiver199]

A bit to complicated for my taste. A much more simple system like using a 100 BI rule will work well enough for most people

 

[amatola]

Maybe is doesn't apply here - but if you were using this system to work out an average buy in - you would need to be careful. Dnegs 2023 wsop is a good example - he had plenty of cashes (must have been 20 or so), even a couple of deep runs - but they all happened on his "low" buyin sub $10k - whereas he did not cash in the $100k/ $250k - result down around $800k.

 

[quick]

It's not a bad idea, and looks like you are applying Fractional Kelly, but as others have said it might get a bit complex to manage, for a few reasons:

- The ROI estimate can vary of course. Are you factoring in the consideration of field sizes as well as the prize sizes as it relates to impacting ROI? @amatola alluded to this . You'd need quite a large sample to see how field size impacts ROI %.

- Changing buy in sizing requirements mid tournament (i.e. not rebuying in the same tourney you were rolled for before your lost your first buy in) is likely not practical and likely will leave EV opportunities ,which lead to possible increased ROI, on the table. It would depend on if it makes sense to re buy, how large or small remaining field is, average stack sizes, etc. But overall it would be likely -EV and missing out on possible higher ROI by not re-buying if it makes sense from a gameplay perspective in the specific tournament in that moment.

- Risk of Ruin (RoR) should be factored in. In Fractional Kelly calculations, the RoR is usually small as you go to smaller fractionals with Fractional Kelly calculations but it still plays a role here. Some might suggest running a Monte Carlo simulation to get a simulated sample of how a large number of tournaments would go for you ROI wise. I think the PrimeDope Poker Variance Calculator is basically the same way to do this. This would also show how high your ROI could go on a massive heater or how negative it could go on a massive downswing.

- In theory you could "probably" create different Fractional Kelly calculations for different game types and/or field size ranges but that would probably just get more complicated and harder to track. You generally need a bigger number of BIs if following BRM the larger the field of a tournament.

- It's my understanding that using the Kelly Criterion in gambling is more for games where there's a defined edge from the opponent that is static and/or more easily quantifiable than 6 or 9 opponents at a table. Possible HUSNGs might be a poker example. In general gambling it's my understanding the Kelly Criterion dictates essentially to increase your next bet after a win (i.e. because the win increased your bankroll) and decrease your next bet after a loss (i.e. because the loss decreased your bankroll) which works great for blackjack, Sports Betting, or slots but not so great for tournament poker. For one, because , again, if you stopped a rebuy in a tournament where the factors are favorable to a +EV opportunity that may increase ROI you miss out and have 0% ROI for that tournament if you don't rebuy when the factors are favorable to a rebuy. Additionally, as you noted in another comment, factoring multi-tabling into it also plays a role if using the Kelly method of moving up/down with bets (buy ins).

Overall it's an interesting topic.

 

[50centOverdraft]

Hey that was really insightful I'm going to use this tip as a bank roll manager

 

[Poker Orifice]

Kelly Who? Is she backin' ya?

I hope she's gettin' something out of the deal. I hate it when people use others.

Well best of luck anyways... even if you're losing but at least gettin' lucky with Kelly.

 

[Goggelheimer]

Kelly Who? Is she backin' ya?

I hope she's gettin' something out of the deal. I hate it when people use others.

Well best of luck anyways... even if you're losing but at least gettin' lucky with Kelly.

I am sometimes a friend of Google and sometimes Google is a friend of mine.
I have found this:

The Kelly Criterion Calculator

And there is a link to the original Article from J.L.Kelly in the internet archive.

If you have a mathematical degree that might be interesting but my old brain prefers simple math like the above samples.

 

[BetterThanAvgButNotByMuch]

OOOh my, I started getting a headache just looking at that!! lol.

There are much simpler ways to do that just require some common sense and discipline.

This is really "nuking"/ overthinking it. lol

But it might help someone so I gotta give you a like for trying.

 

[Poker Orifice]

I am sometimes a friend of Google and sometimes Google is a friend of mine.
I have found this:

The Kelly Criterion Calculator

And there is a link to the original Article from J.L.Kelly in the internet archive.

If you have a mathematical degree that might be interesting but my old brain prefers simple math like the above samples.

Did she make a calculator? Why does it matter if she has made a calculator when he is talking about a bankroll from her?
fwiw, I've never seen her play but I am guessing she must be a pretty good player if she is smart enough to make a calculator for poker.

 

[Goggelheimer]

Did she make a calculator? Why does it matter if she has made a calculator when he is talking about a bankroll from her?
fwiw, I've never seen her play but I am guessing she must be a pretty good player if she is smart enough to make a calculator for poker.

I think the she is a he.

J.L.Kelly

so blablub schwafel rhabarber.

I think the calculator, or the reason, was not poker, if I understood that right.
I think he worked on that for a friend that was a black jack player, but don't nail me on that.
He developed a mathematical calculation for bankroll needs in risk categories in general.
But it seems to work for other luck based games too.

 

[LaNimmer]

Holy moly! I can barely do the rule of 2 and 4!

 

[frazzle1991]

that's a whole lot of math, I booked marked to revisit when i can wrap my head around it properly

 

[TeUnit]

You just want to make sure your sample size is large enough given the format you are playing

 

[tagece]

Interesting. Works well if you put this is a excel sheet. Doing this you can calculate it for different kinds of game.

 

[uppression]

My goals in 2024 are to improve my game selection and bankroll management.

I've played around with the Kelly calculator for a while and I think I am finally making sense of it for MTTs. It seems reasonable to use past performance as a starting point.

In 2023 I played 175 events with a 37% ROI and 12.5% ITM.
My average buy in was $206 and average cash out was $2225.

I used the Albion research Kelly criterion calculator with the following parameters.

• Bankroll: 1000
• Odds offered: 2225:206 (my average cash over my average buy in)
• Estimated probability of winning: 12.5% (my ITM)
• Bets must be in multiples of: $1
• Minimum Bet: $200 (The buy in for the tournaments I play)

The results are to risk 4.4% of my bankroll at full Kelly, 2.2% at half Kelly and 1.1% at quarter Kelly.

 

[MTT Database Review]

First off - I am not reading all of that.
Second - Stop trying to make bankroll rules based on your ROI. You need HUUUUUUUUGE sample sizes for that. You skill level can change drastically before you get anywhere close to that. Put your hands into a tracker and look at your EV winrate in BB/100h. If you are somewhere around 4-7bb that means you are playing what you should. Higher than that and you can move up, lower you need to be more careful and expect big swings. Buy obviously if you are winning 2bb/100h at $500 avg, you are still a very good player.
As for the buy ins, several hundred. How much exactly depends on your financial situation and where you play. If its a lot of Sunday sessions on GG, then you can lose a lot of buy ins because the fields are huge. If you play some non-prime time sessions on smaller sites, its gonna be much less swingy. And if you are playing on some regulated sites in US like pokerstars Pennsylvania, New Jersey, or Ontario, something french, italian.... then you should have very small swings due to those fields being very small and extremely soft.

 

[dreamer13]

When using this method, the player faces the following problems: If the outcome is overestimated, the player will lose more money, and if the outcome is underestimated, he will not be able to get the profit he expected.When using the Kelly method, many factors must be taken into account, such as the level of risk, as well as possible losses and profits.The strategy seems to be the simplest and most effective from a mathematical point of view. expectations, always going for broke, will under no circumstances lead us to success. On the contrary, complete ruin can occur within a few rounds, and the probability of winning is extremely low.

 

[LektorAJ]

The formula is wrong because it doesn't account for variance when you are in the money.

I posted some tables of bankroll needed at

Kelly Criterion for MTTSNGs - MTTSNG -- Two Plus Two Poker Forums

After my 1000th post on average bubble factors was well received I decided to do another number crunching one for my 2000th post. What this is and why

forumserver.twoplustwo.com

Kelly for an mtt with 1000 people in is some like 6000/edge. If you have a 30 percent edge you need 200 bankrolls, more like 2500/edge for 180 man sngs, I don't play anymore (found this googling for my old post when coming across Kelly for investment) but I'll do you a calculation if you post a typical payout structure of what you're playing.

 

[Lena M]

Hi
I think it's too much
This is similar to the approach to the game of a NASA engineer.