If you bet 2x kelly of your fixed bankroll long term, you are guaranteed to bust!
heheh. That's fun to write a toy simulator for:
var kelly = 1;
function roll() {
return Math.random() > 0.495 ? 1 : -1;
}
var wins = 0;
var loses = 0;
function run() {
var bankroll = 1;
for (var j = 1; true; ++j) {
var bet = bankroll * 0.01 * kelly;
bankroll += bet * roll();
if (bankroll > 1e40) {
wins++;
console.log('Won all the money in the world. Won: ', wins, ' Busted: ', loses);
return rerun();
}
if (bankroll < 1e-40) {
loses++;
console.log('Busted! Won: ', wins, ' Busted: ', loses);
return rerun();
}
}
}
function rerun() {
setTimeout(run, 0);
}
run();
Sample output of running with a 1x kelly:
...
Won all the money in the world. Won: 189 Busted: 0
Won all the money in the world. Won: 190 Busted: 0
Won all the money in the world. Won: 191 Busted: 0
...
Sample output of running with a 2x kelly:
Busted! Won: 38 Busted: 83
Won all the money in the world. Won: 39 Busted: 83
Busted! Won: 39 Busted: 84
Busted! Won: 39 Busted: 85
Busted! Won: 39 Busted: 86
Busted! Won: 39 Busted: 87
Busted! Won: 39 Busted: 88
Won all the money in the world. Won: 40 Busted: 88
Sample output of running with a 3x kelly:
Busted! Won: 0 Busted: 191
Busted! Won: 0 Busted: 192
Busted! Won: 0 Busted: 193
Busted! Won: 0 Busted: 194
Busted! Won: 0 Busted: 195
