Just randomly, I wanted to point out that your growth rate actually is NOT maximized by kelly betting; it is maximized by never downsizing.

As pointed out in Bill C. and Marc Ingenoso's "Risk Formulas For Proportional Betting", overbetting by using k > 1 (more than full kelly) will reduce your growth rate. That's because betting more than the optimal amount means that you will have relatively greater negative swings, and since your bets are a fixed % of the bank, the bet levels are reduced much more than if you had bet smaller and had a smaller negative swing.

However, overbetting by never downsizing (only upsizing) increases your growth rate because your bet levels never drop no matter what the circumstances, and so your hourly win rate can never decrease, only increase. Of course, with this method, there is an associated RoR, whereas any type of kelly betting has a 0 RoR (assuming fractional bets).

So, according to Bill C. and Marc Ingenoso, when you are overbetting with kelly betting, your growth rate approaches zero as k approaches 2, and your growth rate becomes negative when k > 2 (and RoR is theoretically 0 with any value of k as long as your top bet < 100% of your BR). Betting, say, 10%, or 50%, or 100% of your BR on positive counts (and never downsizing, only upsizing) would yield the highest positive growth rates and the highest RoRs (essentially 100% RoR when betting 100% of your BR).

I just wanted to point out that there's a difference between overbetting by using k > 1 and overbetting by never downsizing; this is the issue that had confused me until I read "Risk Formulas For Proportional Betting". Perfect full kelly betting maximizes your growth rate when you decide to bet a fixed percentage of your bank (i.e. when you want to maintain a zero RoR); betting with an initial % of your BR + never downsizing (only upsizing) maximizes your growth rate when you accept the RoR associated with that initial percentage (actually, I guess choosing an initial percentage that is anything other than a 1/x fraction of your bank (where x is any whole number) might give you a negative growth rate; like if you chose to bet 40% (2/5) of your bank and never downsize, then after two losses, you would only have 20% left to bet, or if you chose 75% (3/4), after one loss, you would only have 25% left. If, however, you chose 50%, you would cleanly be put out of commission after 2 losses; you could never have a negative growth rate).

Again, there's probably no point to this; I'm just pointing out the distinction since it wasn't initally clear to me.