Join Date: Aug 2011
Posts: 5,081
1. The growth-optimal strategy is to recalculate kelly for each individual wager.
However, kelly-betting doesn't guarantee that you'll never go broke in the real world. IRL there are min wagers and even if there weren't, having only $1 is essentially the same as being broke. Fortunately, the risk of ruin when kelly-betting is low IF your inputs are correct: the chance of being reduced to x% of your bankroll is x%. The bigger risk is that your probability estimates are over-optimistic (ie that you're accidentally betting larger than kelly), which would make your actual RoR higher. In fact it's possible to make all +EV bets and still have a near 100% chance of ruin (as close to it as a finite lifespan allows).
2. Multiply your initial bankroll by (growth factor)^n. For instance if you have a 55% chance of winning a sports bet laying -110, then the kelly fraction is 5.5% and your growth factor is the geometric mean outcome: 1.055^.55 * .945^.45 ≈ 1.004
If you start with $1000, then after 100 of those bets you'll have 1000*1.004^100 = $1490 + change