The Market Game

The Market Game is up and running!

While testing it I got some very interesting surprises. The original objective was to show how a level playing field soon becomes asymmetric following the Pareto principle or 80/20 rule. That certainly happens but at different speeds depending on the starting conditions, for example, the larger the wager size in relation to the player’s bankroll the faster he goes bankrupt and the quicker the 80/20 position is established. This brought to mind the Kelly criterion which seeks to establish the ideal bet size. Once only a few players remain with a large bankroll from winnings, the system enters a steady state as it becomes increasingly difficult to bankrupt anyone without increasing the bet size (my demo can’t do that in the middle of a game). Another fast moving starting condition is a large number of players.

While The Market Game does not help with stock picking I think it is instructive for portfolio management, for example for finding the optimum number of stocks to have in the portfolio. I have the gut feeling that the Kelly criterion could be useful for figuring this out. I think it also points out the danger of risky positions but one needs to be very careful how one defines risk.

Try it out and let me know how goes!

The Market Game

If and when I write it up I’ll add a link to the rest of Software Times. I’ve been thinking of adding a second “game,” a trading game, to see how that changes the landscape.


Denny Schlesinger

PS: How predictable is random? With this starting position

Players: 25
Bankroll: 500
Bet: 50

after the first ten hands a minimum of 15 players are bankrupt! With ten hands played, if every winner is distinct, 15 have not yet won. But having bet $50 ten times, their bankroll is gone. This first winner, after the initial hand, has a bankroll of $1,700 [500 - 50 + (25 * 50)]. It is very unlikely he’ll be out of the game. This is what the Kelly criterion deals with.


Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin

What would you do if you were invited to play a game where you were given $25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61 young, quantitatively trained men and women to play this game. The results, in a nutshell, were that the majority of these 61 players did not place their bets very well, displaying a broad panoply of behavioral and cognitive biases. About 30% of the subjects actually went bust, losing their full $25 stake. We also discuss optimal betting strategies, valuation of the opportunity to play the game and its similarities to investing in the stock market. The main implication of our study is that people need to be better educated and trained in how to approach decision making under uncertainty. If these quantitatively trained players, playing the simplest game we can think of involving uncertainty and favourable odds, did not play well, what hope is there for the rest of us when it comes to playing the biggest and most important game of all: investing our savings? In the words of Ed Thorp, who gave us helpful feedback on our research: “This is a great experiment for many reasons. It ought to become part of the basic education of anyone interested in finance or gambling.”



Excellent paper and spot on!

Furthermore, most investors believe the stock market is not a successive set of independent flips of a coin, but that there are elements of mean reversion and trending in stock market behavior, and of course, outlier events happen with much higher probability than would evolve from a series of coin flips.16 (Page 6)

Coin flips have a normal (bell curve) distribution while stock market prices have a power law (Pareto) distribution. Normal distribution mathematics don’t work well with power law distributions. Using the wrong maths really screws up quants’ results!

Given that many of our subjects received formal training in finance, we were surprised that the Kelly Criterion was virtually unknown and that they didn’ t seem to possess the analytical tool-kit to lead them to constant proportion betting as an intuitively appealing heuristic. (Page 7)

Purists don’t want to associate investing with gambling but casino mathematics can be very useful in the stock market.

What do the results of this experiment say about the prospects for reducing wealth inequality, or ensuring the stability of our financial system? (Page 7)

First of all, the coin flipping experiment has the same flaw as my simulated poker game, both are normal distribution based and that’s not how the stock market works. I’m thinking how one might simulate trading in the market. In coin flipping results are independent of previous outcomes but in the market each trade affects the price and the utility of buying a stock. Much more complicated and causing the Pareto distribution.

It might reduce the losses of losers but the Pareto distribution of wealth should remain, although the bias should lessen somewhat.

I foresee two applications, 1) portfolio diversification, determining the ideal number of positions to have and how much to invest in each, and 2) as an extra input to stock picking, mainly as a help in avoiding poor picks. While all this makes perfect intuitive sense to me, I don’t know how to convert it into practical use.

Denny Schlesinger