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Hey I know its to reduce variance, but the number of buy ins shouldn't depend on the field of players in a tournament? I mean: if you play the Sunday storm for example which has a field of at least 30k, my personal instinct tells me that having 100 buy-ins could not be enough to eliminate variance. And hence, if the field is very small, like 18 players, could it be lower that 100 buy ins? Do you guys ever wondered that? And also, do you kow if there's a formulae to calculate this?
Consult a statistics major for a formula for this but basically your instincts are correct. Let me give you a crass example to illustrate this theory at work:
Suppose you're an ordinary guy with a job making like $1000 a week, and you play the weekly lottery. And suppose there are two hypothetical lotteries, one which is conventional, you pick six numbers and if you hit them all you win a jackpot, but the house had a massive edge. One ticket costs $1, odds to hit are 1:10,000,000 and the payout is $5,000,000. So your EV per ticket is negative 50 cents. Millions of people play lotteries like this in real life all the time, and a lot of people consider them stupid for it.
The second lottery is a +EV lottery. This time, like before, its $1 per ticket and 1:10,000,000 to hit, only the payout for hitting is $15,000,000. Now your expected value per ticket is positive 50 cents.
Now, since you only make $1,000 a week at your job, the second lottery is only slightly less stupid for you to play with a significant amount of your money, in spite of the fact that it's massively +EV to play. Pretty much the only way to realize that amount of equity is to play a massive number of tickets with a massive bankroll, or to pool bankrolls with thousands of others like yourself.
That is what the Sunday Storm is. A very +EV lottery, that you need a massive bankroll to justify playing for non-recreational purposes. It is overwhelmingly likely that you would never make the final table of that tourney in a human life's span of playing it every week. Sharing 5% with 20 of your friends though could make it worth your while, though.
For big MTT some pros suggest you need a +500 BI to overcome the variance of the game, especially when your edge at the game becomes smaller.
I think it has no certain rule , but you really have to know how much variance the tournament you will play features . I think the variance includes : field , structure of the blinds , buy in, the level of players.
With this as base , can you get a sense of how to manage the bankroll
Use 700 BI and never go broke. I think 100BI isnt so much.
I personally use over 1000 BI bankroll management, but it depends on which kind of tournaments you play. Most important factors: size of the field and your average ROI%. Also prize structure matters: if you grind T$ from satellites that pay off lots of seats you don't need that tight bankroll management.
If you have like 200 BI bankroll play small-field tournaments which you have an good edge.
Your style of play could also dictate what type of variance you can expect, and thus the required BI bankroll. If you play very tight then you can expect to have lower variance than someone who play's loose and likes to get it in more frequently.
Most pros say that 100BI is just the minimum requirement for grinding. Maybe you're lucky and don't have to face huge downswing at the beginning of your career, so just go with it. In general, 500BI is more reasonable for huge field like the Sunday storm.