Dave Orr

Google AI PM; Foundation board member

Calculating Kelly

It's too cumbersome and only addresses part of the issue. Kelly more or less assumes that you make a bet, it gets resolved, now you can make the next bet. But in poker, with multiple streets, you have to think about a sequence of bets based on some distribution of opponent actions and new information.

Also with Kelly you don't usually have to think about how the size of your bet influences your likelihood to win, but in poker the amount that you bluff both changes the probability of the bluff being successful (people call less when you bet more) but also the amount you lose if you're wrong. Or if you value bet (meaning you want to get called) then if you bet more they call less but you win more when they call. Again, vanilla Kelly doesn't really work.

I imagine it could be extended, but instead people have built more specialized frameworks for thinking about it that combine game theory with various stats/probability tools like Kelly.

The Math of Poker, written by a couple of friends of mine, might be a fun read if you're interested. It probably won't help you to become a better poker player, but the math is good fun.

Calculating Kelly

At this point I will admit that my gambling days were focused on poker, and Kelly isn't very useful for that.

But here's the formula as I understand it: EV/odds = edge, where odds is expressed as a multiple of one. So for the coinflip case we're disagreeing about, EV is .02, odds are 1, so you bet .02.

If instead you had a coinflip with a fair coin where you were paid $2 on a win and lose $1 on a loss, your EV is .5/flip, odds are 2, so bet 25%.

Calculating Kelly

The way pro gamblers do this is: figure out how big your edge is, then bet that much of your bankroll. So if you're betting on a coin flip at even odds where the coin is actually weighted to come up heads 51% of the time, your edge is 2% (51% win probability - 49% loss probability) so you should bet 2% of your bankroll each round.

I guess whether this is easier or harder depends on how hard it is to calculate your edge. Obviously trivial in the "flip a coin" case but perhaps not in other situations.

The Kelly Criterion in 3D

I agree with that, but I think that utility is not even log linear near zero.

The Kelly Criterion in 3D

The Kelly Criterion maximizes the growth of your bankroll over time. This is probably not actually the goal that you personally have for wealth, because of the nonlinearity of money. You (if you're like everyone else) care much more about preserving wealth, once you have some, than you do about growing it.

Some of this might be loss aversion, but mostly this is right -- going from $1M to $2M is nice but far from a doubling in your happiness or ability to do things; going from $1M to zero is a disaster. Kelly doesn't take that into account, except in the purely mathematical way that if you literally go to zero you can't make any more bets (which never happens).

For this reason, professional gamblers I know tend to bet half-Kelly to balance out bankroll preservation with growth. (Source: used to be a pro poker player.)

On the flipside, if you have another source of income, you can bet more aggressively. For instance, if you have a job that generates positive savings, you can count unearned savings as part of your bankroll for Kelly purposes. This is a huge advantage pure pro gamblers don't have. You probably don't want to be too too aggressive there, and how much to count will depend on the stability and/or fungibility of your income. A year or two of savings could be appropriate.

None of this should change your bottom line that you should take +EV longshot bets if you've been passing on them, just how much you should bet.

Bedtime reminiscences

One thing we did when the kids were small was called rose/bud/thorn. Each of us says something good that happened that day (the rose), something bad (the thorn), and something we were looking forward to (the bud). Sort of a starter gratitude journaling exercise.

No idea if it did anything useful, of course. Parenting is like that.

#unclogtheFDA: a twitter storm to approve vaccines

I think picking a weekday is better than a Sunday, because most of the influence will come from media coverage. A media cycle is easier to start during the week than on a weekend.

Covid 2/4: Safe and Effective Vaccines Aplenty

The reinfection rates for the SA variant are indeed concerning. Do we have any data on whether previous infection prevents deaths or severe infection? The vaccines in general seem to do a great job of stopping the really bad outcomes regardless of how well they do on preventing all infections, so possibly something similar could be going on with the SA variant. Any data either way?

Covid 1/28: Muddling Through

So actually the best outcome for the US is to ship with regular syringes, but then also ensure a ready supply of low dead space syringes so that those can actually be used?

I took a class based on Getting More and it was interesting and useful. This was offered by the company so I can't comment on general classes. There's evidently an online course based on the material, no idea if it's more useful than just reading the book.

I like GM more than e.g. the Carnegie book because it's just usefully framed as "understand what the other person wants and try to get it for them" which is like 90% of being a good negotiator, assuming you know what you want as well.