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I have noticed that some bookmakers will offer free bets but have a condition that in order for the winnings to be withdrawn they must be placed on bets with at least 1/5 odds for example.

If I have a £5 free bet and wagered it on a bet with even odds then I would expect to win half the time but only double my (free) money. If instead I placed the bet on something with odds of 5 to 1, then I would only win one in every five times but then would make a five-fold return. From the bookies perspective they would expect to pay out the same total winnings across all bets anyway.

Why do they care what odds you pick?

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It's a question of risk (variance), not expected profit (mean).

Free bets are often offered along the lines of "bet £10, get a £10 free bet". If I can run the free bet through on very short odds, then that's pretty close to a zero risk investment as the "non-free" bet is then pure profit - and at that point the professional gamblers will be on it like a hawk (at least until they trigger the bookie's alerting systems). If I have to run the free bet through at longer odds, it's a riskier investment which is less attractive to the professionals.

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