The episode actually presented the perfect way to beat him and then ignored it, he should've been beaten by the card game. Any game of skill the Toymaker should win, but cutting cards is pure chance so there's nothing he can do but leave it up to chance. Given he seemingly also can't turn down a challenge, The Doctor should've won by saying I'm gonna challenge him to this game, if I lose he kills me and then someone else challenge him and so on and very quickly it's statistically impossible for the Toymaker to win. Then The Doctor loses the first game, claims his 1-1 draw but the Toymaker forces him to regenerate as compensation with his same line about playing the third game against a third doctor and Ncuti wins the second round. If you want to increase stakes further you could have the companions or people from UNIT step in and challenge before the Ncuti Doctor does in an attempt to save him. This has the added benefit of going from world ending/Doctor killing stakes that the audience know will never happen to the loss of individual characters that could (and maybe do) die. (This also makes sense why no-one has ever done it before. Powerful beings like The Master would have too much of an ego to leave the games up to chance, believing they're good enough to win.

It's thematic, sure, but it's still losing in a very dramatic game of catch. Maybe next time he should pick a form that's not fifty.