Wasn't Kelly's work centered around binary outcomes that essentially amounted to total win/loss scenarios. That is rarely the case for a trader.
After two successive losers in a row, I would think the prudent thing to do would be to cut your position size way back. When you get that money back and put together a few positive days in a row, go ahead and scale your position sizing back up to where it was before.
I think another great topic to discuss is position sizing increases. I am personally fond of a system where you reward yourself for putting together a consistent string of positive days with a very modest bump up in sizing. You reward consistency. Make $10 or make $10K - if you are net positive then reward yourself. The bump up in sizing should be your smallest increment IMHO.
There are adaptations for non-binary outcomes as well, check out research papers by e.g. Ed Thorp etc.
=================== Yes.old time ; done it also-but the best results have been cut back quick when losing.Your title makes me cringe,2.NYSE scalper is right. No i dont reduce positions [generally speaking, unless my guts have been screaming at me for a long time to get out, ,silver around $50 bucks, i tightened up my silver stops] The reason, why cuting back works so well is equity trends , like markets trend do.Proved it. Frankly , no ofence, but since trends go on more than i figure[+ i study trends a lot, study trends a lot], i like to get out of trends late, not early, generally speaking.Proved it. So, no to your title. Of course a mutual fund that gets paid on gross asets , new money coming monthly; that may work/may not work over long term[index, investing], also called cost averaging. And ''long string of losses'' which can happen to any, i prefer sooner[well planned/proved ] than later for exits. Dont leverage or size up mistakes Proved it. Of course sizing up a mistake/ bankrupt co like GM, Enron, Bear ,LEH is even much worse that my silver example.....
Yeah, Martingaling for stocks is definitely a bad idea. I like the answer of increasing your size after some profitable days. That seems like it might be a good idea. It's tempting to increase after a loss, but your loss might be a sign that your system is no longer working. If that's the case then you're setting yourself up for failure.
Very dangerous system buying into the drawdowns unless you are pretty certain what you are doing. Hoping you are not still doing it except on demo OT. I used to put the same on in a drawdown, then double stake if it goes lower with a triple on the next one - then out. Of course it usually worked but when it didn't, that was any previous profits gone down the toilet. I like Buffett's strat but it's too slow and I haven't the cash to buy a company. Not sure he would get away with it anymore anyway. Some sort of incestuous spaghetti tangle of companies owning each other.
The problem with this strategy of adding to losers or increasing size during drawdowns is that the same trader, from what I have seen at least during my own career, doesn't add to winning positions or winning streaks with the same zeal and leverage.