Kelly Criterion Simulator | Hacker News Reader

Kelly Criterion Simulator

kellysimulator.com

73 pointsaleyan30 comments

I made a 'game' to help me son get some intuition for bet sizing: https://tools.encona.com/investor

Good game, but the fact that there is a target that you have to achieve in a fixed number of rounds changes the math.

For instance, if all I care about is satisfying your win conditions, and I am above $20,000, then I should just pass till the end. Similarly, if I have been unlucky (even with Kelly bets) for the first 14 rounds, I should go all in on the 15th round.

You are right! It's stupid to have a target.

The target wasn't there in the original version... I'm embarrassed to say I asked Claude to do a bunch of general 'make this better' on a few of the items on that site, and didn't check the output closely :(

Fixed number of rounds with a target should use DP for solution, not KC.

What is DP?

Dynamic programming. Although if you don't know the distribution of how the bets will look beforehand, there's no real optimal strategy. Think you see first bet has 99% chance of giving you x2. Do you bet everything and take it? It could either be the worst bet of the 20 bets, in which case you just took 1% chance to lose everything unnecessarily, or it could have been the single bet that would be winning money, in which case betting it all would be the only strategy that could win.

Interesting, I recently learned about this.

So there is a term called "Full Kelly" which is were you actually wager the amount given by the formula. This is pretty aggressive and not for the faint of heart. Usually, you do something like a "half Kelly" where you halve the suggested bet amount. Usually because you assume you might be incorrect in your estimated advantage.

What I haven't found yet is some mental math rule to apply this. Given some assumed advantage, what percentage should I "wager"?

Optimal bet size is 2x the coin bias. Dérivation here: https://www.edwardothorp.com/wp-content/uploads/2016/11/TheK...

https://www.lesswrong.com/posts/TNWnK9g2EeRnQA8Dg/never-go-f...

Kelly is nice if you know the odds.

and if you have a lot of bet opportunities.

And if your bets aren't correlated.

also helps if you're not betting with your own money

A similar calculator created many years ago is at https://www.albionresearch.com/tools/kelly

What bet you can make consistently gives you at least 51% odds? As far as I know, the best you can do in a casino is 48%. If I plug 48% into the simulation, it states there is no Kelly edge for that bet.

The first time I ran across Kelly it was WRT card counting. There is some rare positive off the top video poker out there.

As far as casino games, you might find yourself in this situation with a half-decent poker hand or if you're counting cards in blackjack. Casinos don't hand out advantages over the house, which is why the former is coming from other players and the latter is against the rules. As the sibling comment notes, it is generally irrational to participate in casino games and the simulator is correct to tell you not to do so.

This comes up more when you have (or at least believe you have) information that the counterparty doesn't have.

On a casino? Play good poker and go for a low rake. Playing the house is always negative EV, by definition.

Bets with a positive edge can be found most commonly via sports betting, poker games, and the stock market. Although note that most bets you can find via such methods do not have a positive edge, and the edge is not labelled.

More generally, look for any area where bets can be made, and professionals exist who make their living winning such bets. There are professional poker players and sports gamblers; there are not professional roulette players.

The problem with sports betting is that if you really want an edge (at least in something like soccer) you could easily end up dropping six figures a year on data licenses to have a decent model and be able to find worthwhile bets across all competitions. That puts a lot of pressure on the amount of capital you need to deploy, which rules out a lot of bookmakers. As you graduate to markets with more liquidity (i.e. Asia) you’ll also find your edge shrinking. Still obviously very doable, but it’s hard to guarantee stress free passive income this way.

the first lesson here is that betting is easy when you believe that you know the important variable, your edge.

the second lesson is that, no matter how poorly you perform, you are going to be able to make the case to your stakeholders that, contrary to all evidence, you do in fact have an edge and you are in fact exploiting it correctly.

the lesson not here is that, in practice, continuing to believe that you know your edge is going to be virtually impossible in the long run, partly because of volatility, but mostly because, in practice, you do not know it.

In case the author is here:

What's the difference between "win probability of win" and "odds", please? The seem the same thing to me.

And also, what are "decimal" vs. "american" odds, please?

Thanks.

‘Odds’ is the payout, the price of the bet, the prize you may win. And the ‘win probability’ is the probability of winning as the name suggests.

Decimal odds give the total payout (including stake) if you win a bet of 1. So if I place a bet of $1 at decimal odds of 2.5 and it pays out I receive 1 x 2.5 = 2.5. So payout = stake * odds.

American odds (also sometimes called “moneyline” odds) have two presentations.

- If the odds quoted are positive it indicates the net payout (excluding stake) from a bet of $100 dollars. So I place a bet of 1 dollar at moneyline odds of 150 it pays me 1.5 plus my original stake back. 150/100 * 1 + 1 = 2.5. So payout = stake + (odds/100 * stake) . A positive moneyline odds number means an underdog.

- If the odds quoted are negative it’s how much you need to bet to win $100 (excluding stake). So if I place $1 at moneyline odds of -150 and it pays out I get 1 * 100/150 + 1 =1.667. Therefore payout = stake + (100/abs(odds) * stake). A negative moneyline odds number indicates a favourite. The higher the absolute value, the bigger the favourite as far as the house is concerned.

Back in the day when I played HU Hyper-Turbos on Pokerstars I created one of these in Mathematica (not as fancy with Monte-Carlo)

This woulda been helpful for Leo and the 3% of Korea that got liquidated

Their estimates: Win probability 100% -- Odds / payout 100-1.

The Situational Awareness situation was the reason I wanted people to be aware of the Kelly Criterion and submitted this link.

Excellent work! The chart is gorgeous.

I added a Kelly simulator to my own personal stock tracker after seeing this

Graph needs a log scale

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