These three six-sided dice have numbers that give different distributions to die rolls.

Because these dice are a little less frequently used, each appears on only one third of the cards (the least frequent of any dice on the cards), so you may need to keep drawing a little more than normal to get a result.

The "average" die has been around in games for a long time. It is intended to represent the fact that an average person should not be expected to show huge success or failure in every day tasks. Rather than running 1-6, this die runs from 2-5, with there being two 3s and two 4s. Using this die instead of a regular d6 gives the same average result (e.g. rolling 2d6 still averages 7), but reduces the range of possibilities: on two dice you can only roll from 4-10. The average die is a greenish grey with an icon on each face showing two arrows pointing together.

The "extreme" die is the opposite of the average die. It gives results that are more extreme. You can use it for situations which are particularly high risk, or where the possible rewards are greater than normal. The extreme die runs from 1-6, but has two 1s and two 6s, with no 3s or 4s. Its average roll is the same as the regular d6, and unlike the "average die" its range is the same too. So you will average 7 on two dice, with a range from 2-12. Unfortunately, the probability distribution for rolling more than one extreme die is not a smooth hump, it has several peaks and troughs, making some intermediate values very unlikely.

The "expectation" die has six sides, but has two each of 0, 1 and 2. It has the unique property that its average value is equal to the number of dice you roll, and its range goes from zero to twice that number, with results in the middle being more likely. This makes it perfect for deciding how many of something there is. If you decide that there should be about 10, but there could be anything up to 20, then rolling ten expectation dice gives you the right distribution. The expectation die is grey, with an icon on each face showing a square with a line over it.

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