Great question! With just the few updates I've given you're probably right that it would affect things significantly. However, the more data you have the less

Great question! With just the few updates I've given you're probably right that it would affect things significantly. However, the more data you have the less the prior matters. This is known as swamping the priors. In this case a uniform prior isn't incorrect, but you could definitely say its suboptimal and that I could make my examples much more accurate by choosing a prior that most represents my initial beliefs (like the one head one tail histogram for example.