I just ran some math on a situation I'm likely to actually encounter. For those of us who can't actually put together a fixed bankroll with a low RoR, small affordable buy ins played double up or bust seem to be an answer.
To run up a bankroll using this method, I used QFIT's goal calculator to get the percentages of doubling before busting starting at 20 units to 40 units.
For one 20 unit buy in (very shallow) you expect to double it ~%53 of the time. From 40 units to 80 (assuming a previous success and you don't withdraw from your winnings), you expect to double it ~%55 of the time. From 80-160, 71%, from 160-320, 85.56%, from 320-640 %85, finally from 640-1280 (not a bad starting bankroll if you plan on playing fixed) 97.24%
It works out that turning 20 units into 1280 units has about a 10% chance of working. While this is a small percent of the time, it obviously works out to be a positive expectation.
What this implies for those who wish to build a good fixed bankroll from small buy ins is actually promising. Assuming you can afford to lose your buy in (why did you gamble with it if you couldn't?), it will take about 10 tries to run up a good working bankroll with a low RoR.
To run up a bankroll using this method, I used QFIT's goal calculator to get the percentages of doubling before busting starting at 20 units to 40 units.
For one 20 unit buy in (very shallow) you expect to double it ~%53 of the time. From 40 units to 80 (assuming a previous success and you don't withdraw from your winnings), you expect to double it ~%55 of the time. From 80-160, 71%, from 160-320, 85.56%, from 320-640 %85, finally from 640-1280 (not a bad starting bankroll if you plan on playing fixed) 97.24%
It works out that turning 20 units into 1280 units has about a 10% chance of working. While this is a small percent of the time, it obviously works out to be a positive expectation.
What this implies for those who wish to build a good fixed bankroll from small buy ins is actually promising. Assuming you can afford to lose your buy in (why did you gamble with it if you couldn't?), it will take about 10 tries to run up a good working bankroll with a low RoR.