Just a few questions from the perspective of an interested current investor:
1) Can Ryan explain the difference between EV (which I take to be expected value) and expected bankroll growth?
EV = Expected Value. It's the easiest to understand, it's basically the average you'd make over a VERY LARGE amount of bets. e.g. If we flip a coin, with fair odds the EV is going to be 0, even though in reality you'd either have made money, or lost money.
But lets say someone offers you good odds, 2.01x if you win, and 0x if you lose. That's a great deal! You should take it, it's +EV. But the question is, how much should you bet? Well, you don't want to bet too little, because you're missing a great opportunity. But you also don't want to bet too much, because you risk losing too much money and will be very slow to recover (if you recover at all). The paper and surrounding stuff goes into great depths to explain why you should optimize for bankroll growth, not EV.
So if you plot it, you'll see it probably looks like this:
So risking a 1x kelly is mathematically ideal, and what every casino should do. But reality is not so clean:
a) You can't force a gambler to do it (almost most of the time, gamblers only want to bet a small amount and not what you tell them)
b) It might be worth taking a few 1-2x kelly bets, because otherwise you might lose the gambler to a competitor
c) Very few people actually do large bets, but everyone likes being able to do large bets.
d) Lots of investors are gamblers, so maybe they want to risk a wild ride
e) Variance sky-rockets with bigger bets. As I remember, Dooglus sanely dropped down from a fully kelly on JD (which had thousands of bitcoins in its bankroll) because of variance concerns
etc.
So when I said MP is in -expected growth territory, it means its risking even more than that 2x kelly so with an theoretical-angry-whale-attack it should expect it's bankroll to zero! Here's a toy simulator i wrote earlier:
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
---
So when I wrote MP, it was running at a 1x kelly for obvious reasons. Now it's apparently at a >3x. Which is fine, but I doubt investors realize what they're getting into. Probably a more honest name would be "+EV gambling", even if the site makes thousands of bitcoins (Which is very well might) it's still not (and can never be) safe with that risk level