Elementary Game Theory Considerations for Trading Competitions
Disclaimer: I am not a financial adviser. This is not financial advice and intended for entertainment purposes only. Seek financial advice from a licensed and qualified financial adviser in your jurisdiction not a pseudo-anonymous person on the internet!
What is the goal of technical trading? It’s to make money! How, exactly, does a technical trader make money? They do so by making a series of +EV (expected value) ‘bets’. Consider the flipping of a fair coin, your odds of landing on heads are exactly 50pct. Now, assume when the coin lands on heads you receive $1.05, when the coin lands on tails you pay $1. If you were to find someone willing to take the tails side of this bet and flip with them an infinite number of times, you would eventually win all the money and they would lose it all.
With each trade, a technical trader assumes a finite amount of risk; R — this is $1 in the fair coin example — exactly the amount of money they lose should their trade be incorrect. The amount of money they stand to gain should their trade be correct is their Reward, or Payoff, I’m choosing to abbreviate it as Py — this is $1.05 in the fair coin example. The final statistic that determines the profitability of a trader is their winrate; W. This is just the percentage of trades that a trader “wins”; gains Py — this is 50pct in the fair coin example.
From R, Py, and W we can calculate a trader’s edge per trade; E. Simple formula:
(Py * W) - (R * [1 - W]) = E
Plugging in the numbers from our coin example: ($1.05 * 0.5) - ($1 * [1 - 0.5]) = $0.025 or 2.5 cents.
The goal of a technical trader is to maximize their E while using an R small enough (as a percentage of their total trading capital) to ensure they’re never in danger of going broke. The higher their E, the more money they’re going to make for as long as they’re in the game. Effectively managing risk such that a trader is never in danger of going broke is one of the most important parts of successful trading. Finding quality setups that are going to generate large E’s is useless if you have no trading capital.
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Now, suppose instead of just having the goal of maximizing our E while managing our risk such that we’re never going broke, we’re in a competition with 250 traders. The 250 traders are allowed to trade for 1 month and at the end of the month the top 5 gainers are paid a cash prize.
These circumstances — depending on the prize amount versus capital risked — are going to drastically change our incentives and thus our trading strategy. The game has changed. We want a strategy that is going to maximize our earnings, and thus we have to consider the likelihood a given strategy results in a top-5 finish (weighted according to payouts). Say the prize distribution looks like this:

Thus, the EV of our strategy is going to be pct of 1st place finishes multiplied by $3,500, plus pct of 2nd place finishes multiplied by $2,500, plus pct of 3rd place finishes multiplied by $2,000 etc.
Assume a given strategy is going to result in top-5 finishes 5pct of the time — 1pct 1st, 1pct 2nd, 1pct 3rd, 1pct 4th, 1pct 5th. The other 95pct of the time we finish 6th or worse. The EV of this strategy (assuming the net EV of our actual trading is zero) is +$100. Now, assume we finish 1st 5pct of the time and 6th or worse 95pct of the time. The EV of this strategy is +$175. More top-5 finishes = more EV, more wins = more EV. Very simple stuff.
So, if our goal is to maximize the amount of money we’re making from the prizepool, shouldn’t we just be maximizing our E? Well, the problem is we don’t have infinity number of trades, we have 1 month to trade then the scores are checked and the prizepool is distributed. We could hammer out a million $1.05 vs $1 fair coin flips and expect to make $25,000, but finding a million opportunities for a trade with similar R/Py ratio to the fair coin example is going to take us a lot longer than 1 month.
How, then, do we maximize our EV in this sort of competition? It’s a matter of taking trades with much larger Py. These trades naturally are going to have a larger R. Remember, though, the marginal utility of finishing 6th is zero. You don’t get a cash prize and nobody is going to remember who the 2nd place finisher was in a month, much less the 6th or 10th or 20th. Nobody cares. So, you want to make trades that, if successful, give you a chance to win the competition, rather than just giving you a positive edge and making money. Losing 100pct of your capital is — in terms of prizepool EV — the exact same thing as doubling it and finishing 6th.
Larger Py = more wins, even if your trades have poor winrates and patently degenerate levels of risk.
Consider the following two strategies.
- A trader makes 100 trades risking 1pct of his capital per trade with a 1-to-2 R-to-Py ratio and a 40pct winrate. He can expect, on average, to increase their capital by around 20pct. The best he can ever do is increase his capital by 200pct — over 100 trades he risked 100pct of his capital and won double his bet every time.
- A trader makes 1 trade risking 100pct of his capital on the trade with a 1-to-15 R-to-Py and a 6pct winrate. Even without considering the pure degeneracy of this risk assumption, this is not a good technical trade. The E of this trade is in fact negative (15 * 0.06) - (1 * [1 - 0.06]) = -0.04. This trader expects, on average, to lose 4pct of his capital each time he makes the trade. If a trader starts with $100, making this trade costs him $4 in EV.
Now, let’s say every time trader 2 is successful with his trade, he wins the competition. So, the EV of the trade is (0.06 * $3,500) - $4. He’s making $206 in EV employing this strategy. The guy who made 100 good technical trades that involve sound risk management practices ends up with $20 in EV — even when he triples up nailing every trade perfectly he finishes outside the top-5 and thus the EV is just his trading EV, he never wins prizepool money. I made these numbers up and I do not endorse either strategy, surely a strategy can be developed that results in higher EV with a far smaller risk of ruin than 94pct. My intention with these examples is to illustrate the point that max EV trading competition strategies are decidedly different from max EV trading strategies. Our goal isn’t to make money in the aggregate, it’s to make more money than everybody else at the highest possible frequency.
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Further considerations:
1) The larger the gap between initial capital invested and money up top, the larger the Py you should be aiming for and, thus, the more risk you have to be willing to assume.
2) If you’re given an opportunity to buy in for several different amounts, picking anything other than the smallest amount is unassailably wrong. Choosing a larger buy in necessarily decreases the amount of risk you’re able and willing to assume and thus the Py you’re able to shoot for, since as a percentage of invested capital the payouts are much smaller. This is going to drastically decrease your chances of actually winning should both you and your competitors be using a max EV strategy.
3) Should you participate in a trading competition that doesn’t offer cash prizes? No! Well, that’s the short answer, the long answer is only if the difference in the sum of our competition trade EV vs our regular trading EV is less than the arbitrary value you personally assign to the ‘bragging rights’ of winning. The marginal value of competing in a trading competition with no cash prize against other people that care about winning such that they’re willing to take trades with reduced E’s and increased R’s+Py’s is a negative number. You are losing money by participating and trying to win, proportional to the difference in EV between the two trading strategies. Game theoretically, nobody has an incentive to take higher R+Py trades in a competition with no cash payouts, so if everyone just trades normally the EV of competing is zero. It’s when someone makes inefficient trades for the sake of ‘bragging rights’, sacrificing some E for Py, that you’ll lose EV attempting to beat them.
4) How should I calculate if a trading competition is worth participating in? Determine the EV of your normal trading strategy, then the EV of a competition strategy, then the EV of the prizepool payouts. If EV(prizepool) > EV(normal trading) — EV(competitive trading), you’re making money by participating. Otherwise, you are not. Develop a strategy that gives you higher prizepool EV or higher competitive trading EV until the inequality shifts into your favor. If you can’t find one, you should not play that trading competition.
5) I am a terrible trader who is very bad at locating large E setups. I played a trading competition recently and I lost. The reason I played is I believed my understanding of my limitations as a trader and the incentives of how the competition worked actually put me in a much better position to win than even some of the actual excellent traders. My strategy wasn’t to risk 100pct of my capital per trade — which I believe is very stupid — but my risk management parameters were far more degenerate than I would choose or any sane person would recommend for regular trading. They had to be, I suck at trading and have to just rely on luck. My strategy will necessarily result in tons of losses. That’s OK, you’re supposed to lose a bunch when only 2pct of the field gets paid. The thing is, a wonderful trader making normal trades *CAN NOT WIN* a trading competition if there are enough players employing a high R/high Py strategy. The normal trader may make money almost every time, but he will *NEVER* win. The high R/high Py strategy may have a pitiful winrate, but a blind squirrel finds a nut every now and then and a broken clock is right twice a day — the winrate is not zero — and the strategy is going to occasionally make more money than you could *possibly* make using a regular trading strategy. No gamble, no future.
6) I will not be participating in future trading competitions which is why I’m willing to share these game theory insights. Good traders are catching onto what the max EV strategies in these games are more and more as these competitions become more popular. Thus, the edge of a crappy trader like me who perhaps understands the incentives a bit better is vanishing.
Shoutout to Crypto Cartel for hosting the trading competition that inspired this article. Sign up to trade on BitMEX with their ref link and get a 10pct discount on trading fees for 6 months — https://www.bitmex.com/register/N64gBc
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