It's well worth implementing and testing out the Kelly Criterion. It's super simple to code up in a Jupyter Notebook so that you get to enter an amount to bet each time. When I tried it, I found my own psychology changing as the bets continued, even when I knew the coin's bias. It's a really great demonstration of the difference between a) intellectually knowing the optimal strategy, and b) what actually happens.<p>A bet on a biased coin paradigm was actually tried in the real world with finance professionals, with a cap on the maximum payout. The results are described here: <a href="https://arxiv.org/pdf/1701.01427.pdf" rel="nofollow">https://arxiv.org/pdf/1701.01427.pdf</a>
It's pretty interesting. (Note though that the "average returns" reported hide a lot of variation.)
I wonder how professional gamblers approach bet sizing. It seems to me that for most applications the Kelly Criterion is not the right choice. The utility of money is asymmetric; gaining $25000 is worse than not losing $25000. Relatedly, most actual gamblers want to ensure good returns while not going broke, so minimizing risk of ruin is often more important than maximizing return rate. Further complicating the matter is that in real life you don't know your actual probability of success, but you may have an estimation. And finally, though this is less commonly significant, your rate of return in a given game might depend on your the amount you bet.<p>From what I've seen in the poker community, no one has really approached this type of bet sizing from a rigorous perspective beyond the relatively simple Kelly Criterion.
Perhaps I'm misunderstanding, but the post says that the optimal bet size f = 1-2p (where p is the probability of winning). But, this seems backwards. As p goes up, you should be betting more.<p>Shouldn't the optimal bet size, f, be 2p-1?
Fortune's Formula by William Poundstone is a fun read on the origin of the Kelly criterion, as well as the role of gangsters and bookies in the funding of the early communications infrastructure in the US.
Used an abbreviated version to of the kelly criterion along with Markowitz portfolio optimization and applied it to sports betting. All I can say is that past results do not indicate future returns
How you will go bust in favorable bet by N N Taleb - <a href="https://youtu.be/91IOwS0gf3g" rel="nofollow">https://youtu.be/91IOwS0gf3g</a>
A great investing blog I follow is <a href="https://breakingthemarket.com/" rel="nofollow">https://breakingthemarket.com/</a>. He talks about the Kelly Criterion and extending it to making correlated bets (investments).
This is so timely. I made this with a buddy of mine to help us figure out optimal allocation for stocks in a portfolio using Kelly.
<a href="https://engine.oracled.com/" rel="nofollow">https://engine.oracled.com/</a>
You need to very carefull to apply Kelly Criterion to stock market, as you cannot precisely calculate the p of your investments. If you assume a too high p then you will overbet and its only a matter of time to go bust (see N. N. Taleb MOOCS on Kelly). Thus the Kelly Criterion should be your UPPER bound for real-life investments with uncertain p, stay well below the betting amount what Kelly Criterion would suggest so that you stay longer in game.<p>Related to this, the best investors in the world are quite old guys. Why? Because they lived long enough to accumulate enough wealth to be of public interest.
> Notice that when p is 0.4 G is 0. What this basically means is that you should never bet if the odds are against you.<p>Unless if you have a higher or other goal. For example, because you want to impress a woman, because your name is James Bond, or because (more likely) you earn as a result of the related drama of an outlier. This is why sometimes we see people losing and they gain from it on the longer term; they gain from it via advertising, for example. Influencers, advertisers, marketeers, terrorists -- they all abuse this mechanism.
I read about this on HN and then lost it for months when I wanted to apply it to a crappy game on a random discord server.<p>The game lets you bet on chicken fights and tells you the probability your chicken will win (starts at like 62% chance to win), so this kelly criterion is perfect. It's a bit incredible how reliable it is.
There's a loose vs lose typo in the second paragraph. It's like school teachers whipped they're, their, there into our heads and where one typo door closes another opens.
The Kelly criterion is to financial math as the Fibonacci sequence is to mathematics. Yes it's neat, no it's not special, please stop bringing it up all the time.