I'm going to take one more shot at clarifying the math. I know it's moot considering the update is out but for others who are interested. Your assumptions that the probabilities add is a fallacy somewhat similar to the idea of having a 100% chance of winning a prize by buying 5 raffle tickets with a 1 in 5 chance to win. I could give a break down of the actual odds of that if you're interested and give a breakdown of the different macrostates (never winning, winning once, winning twice, etc). Sorry, this is the physicist in me talking.

For this scenario, let's do a break down of what could happen and the statistics that follow.

Day 1: day 1 = 0.75, day 2 = 0.15, day 3 = 0.1

I'm in decimal form because it's easier to understand the math in my opinion. Covering all the options means everything should add up to 1 or 100%. At the end of day 1, there are 2 possibilities, the update happens (reality) or it doesn't happen (fantasy, thank God!). In scenario 1 (reality), the game is over. It 100% came out on day 1, so there's a 0% chance updates BEGIN on day 2 or 3. This scenario had a 0.75 chance of happening.

Scenario 1: day 1 = 1.00, day 2 = 0, day 3 = 0 (0.75 chance to happen)

Scenario 2: day 1 = 0, day 2 = 0.60, day 3 = 0.40 (0.25 chance to happen) (Notice that the ratio of day 2:day 3 remains constant)

The probabilities of both these scenarios are normalized to a particular outcome. If we multiply both scenarios by their respective probabilities we should return the original day 1 probability

day 1 = 1.00x0.75 + 0x0.25 = 0.75

day 2 = 0x0.75 + 0.60x0.25 = 0.15

day 3 = 0x0.75 + 0.40x0.25 = 0.1

One final point of clarification, one reason why this doesn't seem intuitive is that these are based on a certain condition. In this case the 1/4 chance they missed the Monday update. There's the classic stats problem (referenced in the movie 21) that's a good example. I'll modify it to make the point clearer. Imagine you're playing a modified version of deal or no deal. There are 100 briefcases, 1 has $1M the rest have a penny. The host of the show knows what briefcase is the winner. You pick a random briefcase. The host then opens 98 briefcases all revealed to be empty. The host then gives you a choice to stick with your briefcase or trade with the remaining briefcase. What would you do? The correct answer is swap briefcases. When you first picked a case there was a 99% chance you picked the wrong one. There was however, no way the host was going to reveal the winner, so there is now a 99% the case you didn't pick is a winner but still a 1% chance you got insanely lucky.

Why did I do this long rant? I'm still waiting for the OTA to reach me

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