Miller does not get it. Let me try another way to explain it than TLD's simple mocking - not that TLD isn't right, because he is. By using Kelly here, you are doing two things:
1. You are varying your wager size depening on your probability of success, whereas the flat gambler does not. It is trivial to see that this means that the Kelly man will get a better return on money wagered, because he gets his money in better. In particular, think about when the deck 'goes negative' and expecation is less than 0. Miller would say to keep betting, and it should be trivial to see that wagering any money with the worst of it is suicide.
2. Kelly tells you to increase the size of your wagers when you win, decrease when you lose. This lets you bet more, because it prevents you from going broke when you have a bad run. As a flat gambler, are you really going to keep the same unit size if your bankroll halved? What if it doubled? What if it shrunk to 0 because you didn't adjust your bet size and got unlucky?
In fact, the whole point of Kelly is that what matters is your ability to bet and grow a bankroll. Kelly is the way to bet the most money possible over the long run, in addition to getting it in with the best odds. If you overbet, you risk crippling your ability to bet later, and Kelly prevents that.
The times order of wins/losses matter is if there are simultaneous games: When you go 0-4 at 1pm on a Sunday, you can't adjust your bankroll between bets, so you lose an unfortunate % of your roll with a bad run. Kelly reduces bet size to help with this, but not enough to make it not hurt. If the games are one at a time, order doesn't matter because every wager is a % increase or decrease in your bankroll and multiplication doesn't care about order.
That's all in English. I've also looked at Kelly's math and proven to myself that his thesis is correct on that level. There are only three reasons I know of to not use Kelly. The first is that Kelly requires you to do a lot of math every time you wager, and there's a cost to that, so doing an aproximation of Kelly (and rounding down because it's better to underbet than overbet if you're full Kelly) can be better. Your time is money. The second reason is if Kelly is too risky for you, and you don't want those kinds of fluctuations. The third reason is if you don't trust your estimates of your edge and can't get good inputs.
Early in my gambling, I was full Kelly, even though I didn't know the math behind it, and risked large amounts (relative to bankroll) when I thought I had a large edge. Those were wild times, and I doubled up on the Super Bowl by betting on a middle that came in (since the maximum loss wasn't that huge). But that was when I was willing to lose: I was there to find out if I was good enough and if I lost my roll I was ready to pack it in. Now my roll isn't something I'm prepared to risk, so I'm much closer to half-Kelly.
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