In any sort of game that involves selecting one out of many opportunities where one of those opportunities is a win, and each trial is independent and random, each trial has an equal chance of winning. For example, throwing dice, no matter how many times it has been thrown before, each digit has an equal chance of 1/6. No matter how many times a coin has been tossed before, each side has a 1/2 chance of landing.
Suppose you are throwing dice. You're trying to get 5 sixes in a row. You've thrown these dice 400 straight times. On the 401st, 402nd, 403rd, 404th, and 405th throw, they land on 6. Five straight sixes! Finally, you think. It strikes you as impressive but after all, you'd been throwing for so long. This was bound to happen.
Now imagine another scenario. This time, you've thrown dice 400 straight times. You're tying to get five straight sixes and it just doesn't happen. You decide to try something new. You open a computer and use a random number generator that generates a random number between 1 and 6. You get a 6 the first five straight times. You're bewildered at your luck. It seems too good to be true.
Almost everyone, I would wager, would have an extremely strong intuition that something surprising has just occurred. Is it reasonable for you to assume, just based on the fact that you got five sixes in a row in the random number generator, that it's a wonky program? If so, why? The chances of getting five sixes in the second scenario, assuming the generator is random, is the same as the chances of the five dice rolls after the 400th try. After all, they're independent