There is a common misunderstanding about how probabilities (dice, coin tossing, roulette) work. Randomness with equal probabilities does not guarantee that we will see an even distribution in a game. In the REALLY LONG run (many thousands and thousands) of trials, we would expect to see virtually even distribution, but not in the short run.
The dice have no memory. They do not know what numbers came up on the previous toss. They don't take notes and monitor the history of tosses over time so they can tell #1 to show up more. They just get what they get. You can count cards at poker, but that's because there is a fixed number (52) and the probabilities change based on what cards have been dealt and which remain in the deck. In cards, this is "sampling without replacement". In dice, it's "sampling with replacement". If you roll a 1, that doesn't change the probability of getting a 1 on the next roll. It's still 17%.
It's like you draw a king of hearts, then put it back and reshuffle. The probability of drawing a king of hearts the first time was 2% (1 out of 52). If you put the cards back in, then the chance of drawing the king of hearts remains 2%. The odds don't change.
Justin,
That's not how physical dice work. They don't guarantee 16% within any limited time period, like a turn, or a game, or ever a dozen games. 16.66667% is what we EXPECT to see over many many roles of the dice, perhaps several thousand. Dice have no memory. There is no way that the dice know that you have been rolling extra 1's during a game, much less any way they can fix that in the rest of the game.
Steve Clements
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