I think this is better posed as two random-drawn sets of numbers for the first drawing of an as-of-yet un-played lottery. Then, there's no value in considering

I think this is better posed as two random-drawn sets of numbers for the first drawing of an as-of-yet un-played lottery. Then, there's no value in considering extraneous data such as the mass of the envelopes, looking through them or other potential evidence. Instead, you're left with two identical chances. Since there is no data to suggest that either has an advantage over the other, you have a probability of exactly 0.5 that you have the better chance of winning. On the question of the switch, it's important to consider that you have no new data about the one you picked, so the odds are _exactly the same_ as they were at the beginning: there is no conditionality, nothing has changed since you picking it. The probability then of the winning ticket is still 0.5. This is where the infinite probability problem kicks in. I don't think this is an actual problem needing to be solved, unless we can find a way to mathematically express the probability modifiers of our gut feeling, which is impossible, as it comes into our own personal experiences. Still, Gladwell might have something to say about it :)