Get a cup of coffee.
In this thread, we'll analyze the "Devil's Card Game".
This is a super useful thought exercise. It can teach us several key concepts in economics, probability, betting, hedging, investor/market psychology, etc. pic.twitter.com/2VHx4iVkLk
— 10-K Diver (@10kdiver) April 13, 2022
One of the best threads I’ve seen in a while. It’s important because it shows how betting strategies vary based on your goals.
In the basic version, the “Devil’s Card Game” is constrained by the rule that you must bet your entire stack each time.
You can maximize:
- utility (in the real world Kelly sizing is the instance of this when utility follows a log function)
- the chance of a particular outcome.
At the end of the thread, we relax the bet sizing rules and allow the player to bet any fraction of the bankroll they’d like. This is a key change.
It leads to a very interesting strategy called backward induction. In markets, the payoffs are not well-defined. But this game features a memory because it is a card game without replacement. Like blackjack. You can count the possibilities.
The thread shows how the backward induction strategy blows every other strategy out of the water.
If we generalize this, you come upon a provocative and possibly jarring insight:
The range of expectations simply based on betting strategies is extremely wide.
That means a good proposition can be ruined by an incompetent bettor. Likewise, a poor proposition can be somewhat salvaged by astute betting.
I leave you with musings.
- Is it better to pair a skilled gambler with a solid analyst or the best analyst with a mid-brow portfolio manager?
- How confident are you that the people who manage your money would pick the right betting strategy for a game with a known solution?Maybe allocators and portfolio managers should have to take gambling tests. If analytic superiority is a source of edge, the lack of it is not simply an absence of one type of edge. It’s actually damning because it nullifies any other edge over enough trials assuming markets are competitive (last I checked that was their defining feature).