Sorry, that was imprecise. My impression is that, at least on some prediction markets, transaction fees (and maybe also inflation?) make it low-return to buy high-probability contracts. I don't bet on prediction markets myself so I may be wrong about this though!

How would the fees make it any less profitable for high probability contracts vs low probability contracts? And could you expand on the inflation theory? Appreciate the insight!

If you look at it in terms of risk-adjusted returns (Sharpe ratio), a fixed transaction fee costs more Sharpe on a low-variance bet than it does on a high-variance bet. The variance of balanced contracts is higher than the variance of unbalanced ones (p(1-p) is concave with maximum at p=0.5), so after adjusting for risk the transaction fee is more significant for the unbalanced contract.

what’s a ‘balanced’ contract?

I would be guessing that it's one where equal amounts of money are bet on each side/ there's a 50% probability of the result going either way.

A market where expected returns are 1, I. e. the implied probabilities sum to 100%

High probability contracts require you to put up a lot of capital to make a small profit. This would be fine for a bet that has a quick turn around, but prediction bets often require the bet to be placed well in advance of the event, which means the capital is locked up for a long time.... it is basically a low interest loan to the bookie.

Yep cost of capital != inflation

Opportunity costs on long term high probability events eats up significant portions of the value of winning.

Add withdrawal fees and you could easily lose money while making an accurate prediction.

Sure but cost of capital != inflation. And I understand the impact of fees but I’m wondering how they could influence high likelihood bet profitability more than low likelihood bet profitability?

Let’s suppose your paying a 10% withdrawal fee on winnings and 0% fee on principle. If your payoff is 10% and you're also losing out on 2% to opportunity cost. Net winning is (10% * 0.9 - 2%) = 7% but your withdrawal fee is effectively reducing your winnings from 8% or 7% a loss of 12.5%.

On the other if the bet paid 100% of your money you would net (100% * 0.9 - 2%) = 88% and your fee dropped you from 98% to 88% a net loss of 10.2%.

PS: These numbers get much worse if the withdrawal fee includes the principle. Then you would be have a net loss of (110% * 0.9 - 2%) = 3% on the first bet and a net gain of 78% on the second.

I don’t know how you got those numbers. In all the betting markets I participate in, the fees are charged on profit - so it isn’t related to how much of my money I bet, it’s just related to profit. Win a 3:1 bet with 10% fees? You’re losing 10% of $3 if you bet $1 (ie: 30c). Win a 30:1 bet with 10% fees? You’re losing 10% of $30 if you bet $1 (ie: $3). I’m still trying to work out how the fees are “higher” for high probability bets - they’re always the same rate.

Edit: Numbers where picked for clarity, the principle is the same with a 0.1% fee or an 80% fee.

To simplify not using money for some time period has an opportunity cost. Either because you could have paid off a loan sooner, or bought a T bill, or whatever. If the bet takes a year then at the end of that year you could either have (principle + opportunity) cost if you don’t make the bet, (principle + winnings) if you make the bet and win, or nothing if you lost. Therefore the cost of making the bet in 2010 that paid out in 2020 isn’t the money you put upfront, but the money you could have had in 2020 without making the bet.

However, the winnings are calculated based on your initial payment not the payment + opportunity cost. So let’s look at a bet that pays 1$ after fees and costs you 1$ worth of opportunity costs. In such a bet the fees reduce your winnings to zero because you could have the same amount of money without the risk of the bet.

To simplify, why bet when the winnings are tiny. There's other things you could do with that money.

Sure, but that’s a cost of capital discussion not a “fees are higher for bets with higher likelihood of winning” one.

It’s related. Your actual gains = (Fee * winnings ) - opportunity cost.

The effective withdrawal fee is 1 - (actual gains / ( winnings - opportunity cost)).

So if the actual fee is 10% your winnings are 2$ and your opportunity cost is 1$ them the effective fee is 20%. In other words a 10% withdrawal fee dropped your actual gains from 1$ to 80 cents.

However if your winnings where 1,000$ then your effective withdrawal fee is 10.01% dropping your actual gains from 999$ to 899$. In other words fees are more impactful on high probability bets than low probability bets.

Other way around. 10% profit 5% withdrawal.