Tyson is respectful of other people’s superstitions, though he doesn’t have many of his own: beyond the innate belief that inanimate objects can be spiteful, especially at the worst possible moments.
Soldiers are a very superstitious lot, - in a high stress, dangerous environment built around structure and repetition, it’s not that surprising - and Tyson went through a lot of mental gymnastics to abide by people’s, often contradicting, superstitious rituals. Naturally, ones involving numbers - unlucky numbers, lucky numbers, Friday the 13th, et cetera - are the ones that interest Tyson the most.
He doesn’t believe in lucky charms themselves, but he does believe in the ‘power’ in people wishing for whatever the charm is supposed to give: especially when given as a gift. Tyson thinks of them in the same way he thinks of prayer. Hamsa hands hold a special place in Tyson’s heart, and he also has a great respect for Omamori; far more than lucky rabbit’s feet or horseshoes.
Tyson doesn’t believe it will have any impact, but whenever he knows someone else is superstitious, he will go out of his way to respect that: actively avoiding cracks on the pavement, avoiding walking under ladders, throwing spilt salt over his shoulder, et cetera. He isn’t as aware of ‘knock on wood’ as he is ‘touch wood’, but Tyson still tries whenever he can.
The only common superstition that it could be said Tyson actively partakes in is ‘kiss it for good luck’, most commonly with his dog-tags in his army days and prior to that with his Delaney family crest ring. However, that is more Tyson paying lip service to the tradition than actually believing it will have any impact; a way of reassuring those around him. Also, kissing is fun.
In so far as more supernatural superstitions and beliefs, Tyson’s general rule of thumb is: it might not be real, but why mess with it? He doesn’t believe that ghosts exist, but he believes that they could exist and doesn’t discredit the idea. He doesn’t believe in fairies either, but he won’t walk through a fairy circle.
Belief has power, regardless of whether or not the thing being believed in is real. If it matters to someone, it is real enough to be respected. If someone who does believe in fairies sees him walk through the circle, or sees his footprints in the ground, then that person is the one psychologically predisposed to feel unlucky: to stack the odds against themselves because they assume they will fail.
Tyson does not need to believe in fairies, pixies, ghosts, or gnomes to listen patiently and respectfully as others tell him how to catch a pixie for good luck: with a glass jar baited with honey, then covered with a cobweb to trap them. He doesn’t need to believe anything bad with happen, to give another peace of mind by leaving his breadcrumbs by the pond edge for the garden gnome.