The Truth About 20-Sided Dice:
There are a limited number of “twenties” in any given d20. That is, no matter how many times you roll a d20, you cannot roll another twenty once the supply has run out. These twenties can only be replenished by rolling a corresponding one with the same die. Thus every gamer is duty-bound to protect their supply of good rolls. If a friend rolls a twenty using your die, not only have they stolen your good roll, but they have doomed you to the extra one required to replenish the twenty.
Some players get excited when they roll several twenties in a row, concluding the dice are “hot”. Don’t make this blunder! This is like driving your car for 400 miles without gassing up, and then concluding that your car is a perpetual motion machine. After a few good rolls, pass the die off to an unwitting companion and let them charge it up for you.
Statisticians have known about this behavior for years. They call it “the probability seesaw”. Unlike the bell-shaped curve, in the seesaw system the odds of rolling high or low is directly proportional to what has been rolled in the past. They usually pretend this isn’t true. If a statistician hands you a die insisting that “any given roll has the same odds of rolling a one or a twenty”, it means he’s handing you a depleted die in the hopes of taking advantage of you. Don’t fall for it!
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