Why "same day" and not same week or month? If it's not the same instant, then you're hypothesizing some kind of back-propagation (where alternate futures in which you die influence the likelihood of current events)[0]. Under that hypothesis, it would only matter whether some event would cause you to die sooner than you otherwise would.

[0] https://arxiv.org/abs/0707.1919

[edit] FWIW, I actually corresponded with one of the authors of this paper back in 2007, and from what I could tell, this wasn't an attempt at parody, although now it might be dismissed as one. Personally I'm not willing to declare my (non)commitment to the theory either way.