Hi all!

I am aware that this is a very simple question with a very difficult answer, since there are too many factors to take into account (skill, opponents, prize structure and so on...), but I am thinking about taking MTTs seriously and I would like to ask you a few things:

- First, the simpler one: If I become a solid player and go for the average online MTT, how much ROI should I expect to be getting?

- How far away is the "long term"? I know this is a hard question, but does anyone have an idea of what the standard deviation of an MTT result is? Or, put in other terms, how many MTTs do I need to get certain guarantees of actually winning?

- Reaching this "long term" requires a lot of volume, so, how much can your ROI be affected by massive multitabling?

Might have better luck in 'beginner's questions'

I have a program that can determine the required sample size to be 90% confident you are a winning player for tournaments that have a prize structure of 3 winners.

It requires inputs of number of players, your ROI , prize structure and expected ITM distribution. The latter uses weights of 1-1-1 (uniform), 1-2-1 (symmetric), 3-2-1 (first most likely) and 1,2,3 (third most likely).

The average required sample size over these distributions for various ROI’s were as follows for an 18 man MTT with prize structure 50-30-20.

Sample Size to be 90% Confident
You Are a Winner in an 18-man Tourney

ROI	Sample Size
2%	21,000
5%	3,400
10%	900
15%	400
20%	250
25%	150

For larger tourneys, the variance is greater and so will be the required sample size.

That's an interesting solution, thank you very much!
I still fail, though, to know whether I should expect a 2% or 25% ROI when playing in real life. Also, I am mainly concerned with >100 player-pools

Expected ROI: I think it depends on the stakes and of Course on the amount of tournaments. something around 20-30% should be fine.
search function brought some older threads:
https://forumserver.twoplustwo.com/6...layer-1265127/
https://forumserver.twoplustwo.com/6...-site-1702667/

Long Term: An thread/post from (I think) shaun Deep Comes in my mind where he is calculating the amount of tournaments and the varianace in MTTs. not sure where to search for it, but it was a nice read. Maybe someone else knows where to find it
edit: found it, it was About shaun Deep: http://www.nsdpoker.com/2011/01/mtt-pros/

ROI affected by multitabling: this thread is worth a read: https://forumserver.twoplustwo.com/1...lenge-1726275/
he is Talking a lot About how more tables are bad for his Overall Play because he can't Focus 100% on all of them but with more tables played, his bb/100 is not suffering too much. he tried to find the Right amout between many and too many for the best possible ROI

also there are a some good threads to read if you have the time: https://forumserver.twoplustwo.com/2...isdom-mtts-48/

Thank you very much for your research!

On the ROI, there are a lot of different numbers there. Not unexpected as it's heavily dependent on table size, initial stacks, player pool, blind increases... Anyway I think 20% ROI is quite achievable.

With this data I'm going to build a simulation to replicate the results you linked about "reaching the long term". I'll share my results here soon!

About multitaling, this can also help. It's intended for sit&go, but conclusions extrapolate: https://www.super-turbo-poker-tips.c...ling-tips.html. I would get form here that we can allow ourselves to play a good amount of tables without worrying too much (we still have a ton of edge) and full-ring MTTs require less "average actions per minute" than hyper-turbo SNGs

Case 1:

Let's consider 4 players at a 110-men tournament where 18 people make it into the prizes. The payout structure (in buyins) is the following:

18, 14, 11, 9, 8, 7, 4, 4, 4, 2.75, 2.75, 2.75, 2.25, 2.25, 2.25, 2, 2, 2

This results in a 9,1% rake, now:

- Player A has an equal chance of finishing in any place at the tournament.
- Player B gets a 12.5% ROI by finishing an extra 30% of the time at any ITM position
- Player C gets a 12.5% ROI by finishing an extra 50% at any of the four top spots
- Player D gets a 12.5% ROI by finishing an extra 70% of the time at 5th-18th places.

First, for each player, we simulate 500,000 runs, each consisting of a thousand of these tournaments:

- Player A loses at 85.0% of the runs, while he does better than a 125-buyin win at 0.9%. He lost 434 buyins at his worst run.
- Player B loses at 10.4% of the runs, while he does better than a 125-buyin win at 46.9%. He lost 320 buyins at his worst run.
- Player C loses at 11.1% of the runs, while he does better than a 125-buyin win at 48.4%. He lost 301 buyins at his worst run.
- Player D loses at 9.4% of the runs, while he does better than a 125-buyin win at 44.7%. He lost 278 buyins at his worst run.

Here you have a histogram with the results



For contrast, let's try now 100,000 runs of 5,000 tourneys each:

- Player A loses at 98.9% of the runs, while he does better than a 125-buyin win at 0.9%. He lost 434 buyins at his worst run.
- Player B loses at 0.24% of the runs, while he does better than a 125-buyin win at 98.7%, and better than a 625-buyin win at 44%. He lost 322 buyins at his worst run.
- Player C loses at 0.28% of the runs, while he does better than 125-buyin win at 98.6%, and better than a 625-buyin win at 48%. He lost 277 buyins at his worst run.
- Player D loses at 0.12% of the runs, while he does better than a 125 buyin win at 99.0%, and better than a 625-buyin win at 40%. He lost 185 buyins at his worst run.



In conclusion, in 100-men tourneys, when we have enough of an edge, we can perform very well and avoid variance quite quickly, regardless of whether our edge comes from good final tables or good mid-late finishes. I will check again with different payout structures and with more populated MTTs. Conclusions will be posted here as well!

Case 2:

Let's try a different payout structure (with fewer players getting a larger chunk of the money). Once again, we will compare our four players:

- Player A has an equal chance of finishing in any place at the tournament.
- Player B gets a 12.5% ROI by finishing an extra 30% of the time at any ITM position
- Player C gets a 12.5% ROI by finishing an extra 39% at any of the four top spots
- Player D gets a 12.5% ROI by finishing an extra 113% of the time at 5th-12th places.


The results after 500,000 runs of 1,000 MTTs show:

- Player A loses at 80.2% of the runs, while he does better than a 125-buyin win at 2.6%. He lost 531 buyins at his worst run.
- Player B loses at 15.5% of the runs, while he does better than a 125-buyin win at 47.1%. He lost 358 buyins at his worst run.
- Player C loses at 15.5% of the runs, while he does better than a 125-buyin win at 48.5%. He lost 405 buyins at his worst run.
- Player D loses at 15.1% of the runs, while he does better than a 125-buyin win at 43.1%. He lost 322 buyins at his worst run.




Now let's try 100,000 runs of 5,000 MTTs

- Player A loses at 96.8% of the runs, while he does better than a 125-buyin win at less than 0.1%. He lost 531 buyins at his worst run.
- Player B loses at 1% of the runs, while he does better than a 125-buyin win at 96,5% and better than a 625-buyin win at 45,0%. He lost 358 buyins at his worst run.
- Player C loses at 1.1% of the runs, while he does better than a 125-buyin win at 96,4% and better than a 625-buyin win at 48.2%. He lost 405 buyins at his worst run.
- Player D loses at 1% of the runs, while he does better than a 125-buyin win at 96,3% and better than a 625-buyin win at 36.7%. He lost 322 buyins at his worst run.




We are already noting the effect of this steeper "payout ladder". Player D is suffering from less variance, but I don't think it's a good representation of reality. Most MTT winners would probably look a lot more like a midpoint between B and C. Still, I think these findings are quite encouraging! It doesn't take that long to "guarantee" good results (if we have what it takes to get the theoretical ROI)

In my next attempt, I will try to see how this translates to a tournament with more players, where variance is expected to be significantly bigger

Let's try it now with 1500 players and the following payout structure (9% rake):

190, 140, 100, 70, 50, 39, 30, 24, 21, (15,3), (13, 3), (11.5, 3), (10.5, 3), (9.7, 3), (8,9, 3), (8, 3), (7.2, 3), (6.3, 3), (5.5, 9), (4.7, 9), (4.1, 9), (3.6,9),(3.2,9), (2.9,9), (2.7,9), (2.55,9),(2.4, 9), (2.25, 9),(2.10, 9), (1.95, 9), (1.8, 27), (1.65,27)

In the last experiments, our three winning heroes gave very similar results, so let's also study the impact of ROI:

- Player A has an equal chance of finishing in any place at the tournament.
- Player B gets a 6% ROI by finishing an extra 30% of the time at the two final tables
- Player C gets a 12.5% ROI by finishing an extra 42% at the final two tables
- Player D gets a 19% ROI by finishing an extra 113% of the time at the final two tables.


The results after 500,000 runs of 1,000 MTTs show:

- Player A loses at 68.1% of the runs, while he does better than a 125-buyin win at 2.6%. He lost 665 buyins at his worst run.
- Player B loses at 43.7% of the runs, while he does better than a 125-buyin win at 37.6%. He lost 644 buyins at his worst run.
- Player C loses at 35.0% of the runs, while he does better than a 125-buyin win at 46.4%. He lost 656 buyins at his worst run.
- Player D loses at 26.8% of the runs, while he does better than a 125-buyin win at 55.8%. He lost 601 buyins at his worst run.




What about 100,000 runs of 5,000 MTTs each?

- Player A loses at 81.1% of the runs, while he does better than a 625-buyin win at 2.5%. He lost 2265 buyins at his worst run.
- Player B loses at 30.3% of the runs, while he does better than a 625-buyin win at 29.1%. He lost 1796 buyins at his worst run.
- Player C loses at 15.1% of the runs, while he does better than a 625-buyin win at 48.3%. He lost 1472 buyins at his worst run.
- Player D loses at 6.0% of the runs, while he does better than a 625-buyin win at 68.5%. He lost 1334 buyins at his worst run.




Long story short: Play BIG samples and have a ton of edge! Games with a lower number of playres give you more guarantees, but there aren't that many fish playing! If you can find a tournament when you smash the competition but without a huge player-pool, go for it!