Not sure if this is a probability question as such, but I guess I am asking what bankroll is required for x average buyin to give 0% probability of busting. Assume you would need ROI and standard deviation figures? Feel free to choose them - I don't even know what is realistic.

I'm looking for something like this: http://pokerdope.com/poker-variance-calculator/

But for MTT's. I'm not even sure that is mathematically possible to calculate banroll of MTT's? But I have an old excel spreadsheet that had a macro:
https://gyazo.com/467444b5e5edbe7e834aeffd35e6a494
That for whatever reason doesn't work any more.

I've been told that a 2000 average buyin is a good mtt bankroll, but I'd like some mathematical 'proof' or some kind to suggest that, because it's signficantly going to determine whether I bother playing more MTT's as opposed to just cash games.

Thanks!

From the screen shot of the spreadsheet, the 2000 buy-ins assures no bankruptcy if you are playing 2000 tournaments and you don’t cash in every one. A silly approach to bankroll management. Think about it – if you were playing $50 MTT’s, you need a bankroll of $100,000!

Most bankruptcy analyses, assume you can live with a low but not 0 risk of run, say somewhere in the neighborhood of 3 to 5%.

For some time now, I’ve been sitting on a draft book containing 64 hold’em tables and analyses. One of the tables addresses your question for a STT SNG. It determines the risk of ruin (bankrupt probability) for a specified bankroll. Here is a copy of the applicable section without the fancy table formatting or accompanying graph..

Table 50. SnG: Bankrupt % (ROR) vs. Buy-Ins
Here we present the probability of going bankrupt for a specific tournament, namely a 9 man sit’n’go with a payout structure of 50/30/20. The bankrupt risk is for 500 tournaments. The buy-in = prize pool + fee is $10+$1 and it is assumed that is achieved with equal placing in 1st, 2nd and 3rd. We show the results for ROIs of 10%, 15% and 20%. It is seen that to have a less than 5% risk of ruin with a 10% ROI, a bankroll of more than 30 buy-ins is required, whereas this reduces to about half as many buy-ins with a 20% ROI. It is noted that the placing distribution determines the profit standard deviation, which is a factor that affects how often you bust. For example, with ROI= 20% and 15 buy-ins, ROR =7.3%. If the cashing player always finishes in the same place, say always 3rd, the risk of ruin becomes essentially 0.

SnG: Bankrupt % vs. Buy-Ins
9 Man 50/30/20 $10-$1 Equal Placing- 1,2,3

	Probability	of Going	Bankrupt
# Buy-In	$ Bankroll	ROI=10%	ROI=15%	ROI=20%
1	11	91.2%	87.5%	83.4%
5	55	62.9%	51.3%	41.8%
10	110	39.4%	26.3%	17.4%
15	165	24.5%	13.4%	7.3%
20	220	15.1%	6.9%	3.0%
25	275	9.3%	3.5%	1.9%
30	330	5.6%	1.8%	0.5%
35	385	3.4%	0.9%	0.2%
40	440	2.0%	0.4%	0.1%
45	495	1.2%	0.2%	0.0%

Example: With a 15% ROI, the chance you will go bankrupt within 500 tournaments if your bankroll is 30 buy-ins is 1.8%.

I very much appreciate your reply.

Would a 9man 50/30/20 bankroll be comparable to an MTT bankroll?
45buyins seems intuitively low to me for a 1.2% risk of ruin(for 10% roi).
I read that Shaun Deeb went 52games without a cash.

If 10% ROI and 10% ITM is a reasonable estimation, would those two things be enough variables to calculate a x buyin bankroll for y risk of ruin, or would one need the prize payout?

I don’t know how these results compare to an MTT but I would think an MTT has, on average, a much higher variance thus requiring a larger bankroll for a given ROR.

The standard deviation is an important ROR factor and it depends on both the prize structure and placing, so just ROI and ITM are not enough.

200-300 bi's is pretty standard ds in mtts, 500 bi's when things are really rough (only occurs every few years from my exp.) 1000 bi's is a safe number to never go broke. if your mtt roi is only 10% then im not sure that even 1k bi's is safe

My ROI is most recently 80%
But obviously that isn't accurate.
10% seems like a reasonable estimate given what I've seen/read about other MTT pros.
So back in circles to the 1k-2000bi bankroll again

standard deviation bb per 100 hands is 65.98.
Assume a standard mtt prize structure.
Now its possible to caluclate risk of ruin?

http://pokerdope.com/tournament-variance-calculator/
I just found this on the same cash game site.

Probability of loss = 27% after 2000 tournaments with ROI 10%. But that loss doesn't seem to be more than around 700 buyins if I interpret the results correctly. I.e. near 0% risk of ruin is 700 buyins. (for the specific mtt parametres I entered)

Therefore 2000buyins is too big as assumed. 45buyins however is way to small as I thought.

Two points
1. That calculator does not estimate the probability you will go bankrupt for a given bankroll. It doesn’t even ask what your bankroll is. If you enter my SNG values for 1 tournament , you get a mean profit of 1 and standard deviation of 16. I consider placing distribution and got 1.1 and 16.4 (the site probably rounded). In any case, apply these values to a well known ROR formula and you get my result of ROR=1.2%

2. The 45 buy-ins I stated for a 10% ROI was for a 9 man SnG. I previously noted that MTT’s have a higher variance and thus would require a larger bankroll, possibly much higher depending on the structure and number of players.