You might be misremembering (it's my fav DB show btw...)

It's not really revealed how he does the last trick. In the last bet she believes she loses because the horse he tips doesn't win - and during the race he reveals there is no system.

However, he places the final bet - not her - and after the race ends she opens the ticket to find it's placed on the winner, not the tipped horse.

Almost certainly it's slight of hand (which he is excellent at) but that is never revealed.