I’ve seen semi-regular mentions of arbitrage opportunities on the political prediction market PredictIt. .These arbitrage opportunities are almost entirely illusory due to PredictIt’s fee structure but I haven’t seen a clear explanation of why. I’d like to lay that out here: a general explanation and two clarifying examples.

By arbitrage, I mean markets where the total probabilities of all the options are greater than 100%. For example, imagine a market with four candidates, each one having a 27% chance of winning on PredictIt. These odds total 108%, you should be able to bet against all of them occurring and make a free 8% return.

Such arbitrage opportunities don’t exist because PredictIt takes 10% of your profits on any winning bet and does not allow you to deduct your losses from other bets. This means if you attempt arbitrage, the fee comes out of the winning bet without regard to your losses in other markets, which means you need to win significantly more. In our above example, you don’t pay the 10% fee on you 8% gain, you pay it on each of the gains in the three winning markets.

Let’s start with a simple example. Imagine a market with two candidates, Candidate X and Candidate Y. Each candidate has a 52% chance of winning on PredictIt. You spot an easy arbitrage opportunity and bet $48 that Candidate X will lose and $48 that Candidate Y will lose. At these odds, $48 buys 100 shares which cash out for $100 when that candidate loses. One candidate will lose and therefore you must win $100 at a cost of $96. You’ll make $4 profit, so you expect to pay 10%, or $0.40 in fees, leaving $3.60 in free money for you.

What actually happens is you pay the 10% fee on the $52 profit you made. Imagine Candidate X loses. The money you gambled on Candidate Y winning is gone. From PredictIt’s perspective, however, you made a $52 profit in the Candidate X market (You paid $48 to win $100) and they take their 10% fee out of the $52. That fee amounts to $5.20. You therefore receive $94.80 in total, which is the $48 you initially put in, plus the winnings of $52, minus the fee of $5.20. Since you put in $96 and only got $94.80 out, you’ve lost $1.20. The odds indicate that there is a real arbitrage opportunity, because there can’t be 104% odds of something happening, but it’s illusory because off this fee structure.

This gets significantly worse with multiple linked markets. Consider a primary election with 11 candidates, each with a 10% chance of winning, not too far off from the 2016 Republican primary market. Total odds of 110%, so there’s a clear arbitrage opportunity. For simplicity, you bet $90 dollars against every single candidate, winning $100 for each candidate that doesn’t win. At the end, you’ve invested $990 dollars ($90×11 candidates) and won $1,000 ($100×10 losing candidates). Already much less impressive than you would have predicted but remember, as far as PredictIt is concerned, you made a $10 profit in each of the 10 markets where the candidate lost, meaning you pay a $1 profit fee for each market or $10 total, meaning you receive $990 after fees, exactly the amount you put in.

This is how arbitrage illusions work: the initial odds look crazy but experienced investors understand the fee structure and allow these imbalances to exist because they can’t make a profit correcting them.