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Deriving the Kelly Criterion to Maximise Profits

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Re: Deriving the Kelly Criterion to Maximise Profits

#21

Post by nonameiguess »

CrazyStat wrote: post #18

I had never paid much attention to Effective Altruism or SBF before FTX blew up, but when that happened I spent some time reading old EA forum posts and SBF tweets and interviews. One of the things that absolutely shocked me was the dismissal of the Kelly criterion by SBF and other EAs. The argument was that the Kelly criterion was only rationalized by a logistic utility function, and if you were going to use your mo…

I don't want to denigrate the whole community or anything as quite a lot of thought-provoking and interesting reading has come out of it over the years, but I can't help but recall very serious defense of the notion of quantum immortality on LessWrong after Eliezer's fairly convincing rants that any serious scientist has to conclude multiple worlds is the only sensible interpretation of quantum mechanics. If you honest to God take this to its logical conclusion, then wiping out all life in your particular branch of the multiverse may very well be the right move if it doubles utility in 51% of all possible universes.

I don't actually buy that argument and think it's insane, but it would not remotely surprise me if SBF believed it, and if you do, then you don't really observe the Kelly criterion. You take the ruin for the larger team of other yous that collectively wins. If the density of quantum branches in which he funded colonization of the galaxy is greater than the density in which he is serving life in prison, it was worth it.

Re: Deriving the Kelly Criterion to Maximise Profits

#22

Post by whatshisface »

CrazyStat wrote: post #18

I had never paid much attention to Effective Altruism or SBF before FTX blew up, but when that happened I spent some time reading old EA forum posts and SBF tweets and interviews. One of the things that absolutely shocked me was the dismissal of the Kelly criterion by SBF and other EAs. The argument was that the Kelly criterion was only rationalized by a logistic utility function, and if you were going to use your mo…

In some way, I think everyone was so used to founders saying dumb things for attention that nobody realized SBF was actually going to do it..

Re: Deriving the Kelly Criterion to Maximise Profits

#24

Post by bayesianbot »

bdjsiqoocwk wrote: post #13
gwbrooks wrote: post #4

A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations. Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1…

I would like to understand in detail what you just wrote. "$1 per coin game" is this a game where you put in $1 to play and get paid either $2 or $0 with 50-50 probability (0 expected). And the what does it mean %1 edge? Does it mean the probabilities are such that the expected payout is 1c per coin flip?

He means video draw poker machines, where you get paid a multiple of your bet depending on your final hand. Most online casinos used to have bonuses where the required wagering amount to clear the bonus multiplied by the return value of certain games led to a positive expected value for the player. So as example you'd deposit say $100, get $100 bonus, wager on video poker for $2000, getting back 99% of the wager for average of $20 loss from the wagering and $180 cashout. Much more rarely there also were some games that when played optimally, would give slightly over 100% return for your bet. The casinos were banking on most players playing them suboptimally and/or getting hooked.

Even though it's +EV for the player, you'd need some bankroll to ride out the variance as you could lose on X casinos in a row. Ages ago these were really +EV and you could usually just autoplay them with small bets, so the bankroll requirements weren't that harsh. Later on the wagering requirement on the bonuses grew, often making the small bet grind unprofitable, but you could still find profitable situations when played with correct bet sizing. But those needed much bigger bankroll as usually it was more +EV the bigger the bets you made, so you'd often play many casinos for just a few minutes with big bets losing your deposit and bonus, but sometimes winning big and covering the losses with profit left over.

Re: Deriving the Kelly Criterion to Maximise Profits

#25

Post by gwbrooks »

bdjsiqoocwk wrote: post #13
gwbrooks wrote: post #4

A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations. Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1…

I would like to understand in detail what you just wrote. "$1 per coin game" is this a game where you put in $1 to play and get paid either $2 or $0 with 50-50 probability (0 expected). And the what does it mean %1 edge? Does it mean the probabilities are such that the expected payout is 1c per coin flip?

Single-line (that is, five dealt cards) video poker can be played with 1-5 coins. However, there is a disproportionate payout for a royal flush (A-K-Q-J-10, all suited) with five coins played. There are no video poker games you can play with less than five coins that are anything near breakeven payout.

Every video poker game in Nevada is required to be truly random. And every game has the payout for every possible poker hand shown on the game. A bit of math allows you to calculate both the correct strategy for any five cards dealt (which you memorize, just like proper blackjack strategy), but it also tells you the theoretical return of the game with perfect play.

As an example, 9/6 Jacks or Better (a game that pays nine coins for each coin played for a full house and six coins for each coin played for a flush) has a theoretical payout of 99.54% with perfect play. This puts it in the range of blackjack. And, like blackjack, you will eventually go broke because it's still not over 100%.

Unlike blackjack, you can't count cards. But what you can do is seek out returns in other ways. In the 1990s and 2000s, some casinos would compete on cashback comps. Add 0.33% or 0.5% cashback to the game I just described, and you're close to (or barely over) 100% payback. Find a game with a baseline payout of over 100% (full-pay Deuces Wild is 100.76, as a [rare] example), and you're deeper into the profitability zone.

Small returns unless you're playing higher denomination returns with a giant bankroll. Most people who do this make it a bit of a lifestyle -- pushing tens or hundreds of thousands of dollars through the machine gets you noticed by the casino, leading to free rooms, free meals, invitations to parties, etc.

Others look (or looked -- it's rarer now) for poorly planned promotions where a scarce hand pays off grandly and changes the math. Most of the life-changing wins in this space came from those sorts of situations.

Re: Deriving the Kelly Criterion to Maximise Profits

#26

Post by jiggawatts »

gwbrooks wrote: post #4

A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations. Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1…

Isn't that a pretty good return? Multiply by 100: this is the equivalent of $3,000/hour on $1.2M of capital!

Re: Deriving the Kelly Criterion to Maximise Profits

#27

Post by nighthawk454 »

jiggawatts wrote: post #26
gwbrooks wrote: post #4

A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations. Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1…

Isn't that a pretty good return? Multiply by 100: this is the equivalent of $3,000/hour on $1.2M of capital!

Not if you’re throughout limited with $1 games

Re: Deriving the Kelly Criterion to Maximise Profits

#28

Post by jiggawatts »

nighthawk454 wrote: post #27
jiggawatts wrote: post #26

Earlier quoted context omitted.

Isn't that a pretty good return? Multiply by 100: this is the equivalent of $3,000/hour on $1.2M of capital!

Not if you’re throughout limited with $1 games

Play 100 accounts in parallel.

Re: Deriving the Kelly Criterion to Maximise Profits

#29

Post by [deleted] »

diab0lic wrote: post #14
roenxi wrote: post #8

A word that is good to know here is ergodic [0]. Which I must admit to not really understanding although it is something like the average system behaviour being equivalent to a typical point's behaviour. If a process is non-ergodic then E[X] is usually not as helpful as it seems in formulating a strategy. [0] https://en.wikipedia.org/wiki/Ergodic_process

An example that may be useful to aid in understanding… Casinos are non ergodic. A million players each placing a single bet will have an expectation of losing the house edge. A single player placing a million bets has an expectation of $0. The fact that the aggregate and the single entity Experience different expectations despite both placing a million bets is what makes this ergodic.

[deleted]

Re: Deriving the Kelly Criterion to Maximise Profits

#30

Post by mudita »

nighthawk454 wrote: post #23

A few links through, this Ship Investor simulator is a great super-simple game to test some intuition: https://xkqr.org/ship-investor/ship-investor.html

The game is a bit weird. It often offers very bad deals, without an option not to invest. For example for the Gibraltar strait, the game gives the information that the probablity of success is between 90% and 100% and that it’s been traversed 31 times with a 90 % success rate. Then it offers me the choice between an investment of different sizes, where I cannot win back more than my investment, so I have to risk money for no possible gain (invest 167 ducats in shipment worth 167 ducats).
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