The basic rule is that if you don’t have a chance of winning your bet, then it is void, and your stake money is returned to you. Typically this happens when your horse is declared a “non-runner” and takes no part in the race.
With football betting, a first goal scorer bet is void if your nominated player comes on after the first goal has been scored. If he is substituted before the first goal is scored however, the bet stands because he has had the opportunity to score the first goal.
An exception to “the non-runner is a void bet” rule is with ante-post betting. Bookmakers offer ante-post markets on major horse races (such as the Derby) long before the race is run. In such markets, non-runner stakes are not returned. These markets will change to normal non-runner rules a week or two before the race (but with a respective odds shortening.) Check the rules clearly before you place your bet.
The converse to having your stake returned on a non-runner is that if another horse in the race is declared a “non-runner” then the chances of your horse winning have improved. If it wins, then the price paid to you is reduced to reflect this, which is known as a “”Rule 4” deduction.
Rule 4’s are quoted in pence in the pound reductions. The full stake is returned, and the win element calculated on the original odds, then reduced by the Rule 4. For example, a £10 win bet at Evens would normally return £20 (based on the £10 stake returned, and £10 won.) With a 10p Rule 4, the win would be reduced by 10p in the pound, giving £9, and the return on the bet would be £19. With a 20p Rule 4, the return would be £18. The Rule 4 deduction is determined by the price of the withdrawn horse, and the shorter that price, the higher deduction. For example, a withdrawn horse priced at between Evens and 6/5 is a 45p deduction, and one between 9/2 and 11/2 is a 15p deduction. Withdrawn horses at over 14/1 do not trigger a rule 4.
A final note to betting shop punters. Bookmakers make millions of pounds every year on bets that are voided by non-runners but where the punter never collects his returned stake. This happens with bets when the punter just glances at the race winner and throws his slip away in disgust, without checking if his selection ran. It also happens where a non-runner in a multiple bets, generates a slip with a minor return. The punter either can’t be bothered going to collect it or feels embarrassed to do so. Don’t, it’s your money.