[Retric]

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.

[admax88q]

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

[nstj]

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

[Retric]

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.