It's much simpler than that. Although the show appears in the beginning like it's a "magic trick" (though that is never actually claimed), in the end the audience is clearly shown how there's no trick at all. It's all simple probability and there really is no way to "beat the odds". Which IMHO is ultimately more entertaining and valuable than just some slight of hand or magic trickery.
Anyway, I apologize for my error in recollection. I sincerely remember the gist of the show being as I described. Another reminder that memory can sometimes be weirdly porous yet not be correctly 'flagged' with an appropriate sense of uncertainty.
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.
Anyway, I apologize for my error in recollection. I sincerely remember the gist of the show being as I described. Another reminder that memory can sometimes be weirdly porous yet not be correctly 'flagged' with an appropriate sense of uncertainty.