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### First gear

First gear die is a four sided die labeled 1, 1, 2, 2.

It can be handled like a d2 so we can use the following expression:

1d2

### Second gear

Is a regular cubic die labeled 2, 3, 3, 4, 4, 4.

This is a little tricky to handle, but not impossible. The expression used is:

MIN(RDN(1d6/2),2)+2

That is:

Roll a d6 and divide by two (0.5, 1, 1.5, 2, 2.5, 3)

Round down (0, 1, 1, 2, 2, 3)

Take the lower value between the one obtained and 2 (0, 1, 1, 2, 2, 2)

Add two (2, 3, 3, 4, 4, 4)

### Third gear

This is an eight sided die labeled 4, 5, 6, 6, 7, 7, 8, 8.

This is the Formula Dé's most complex die to reproduce. The formula used is:

MAX(RDN((1.3*1d4)+3.4),1d2+3)

We start with a d4 multiplied by 1.3 (1.3, 2.6, 3.9, 5.2)

Add 3.4 to this value (4.7, 6, 7.3, 8.6)

Round down (4, 6, 7, 8)

Take the larger value between the one just computed and 1d2+3 (4,5). This mean that if the computed value is 6, 7 o 8, it does not change. If the first outcome is 4, it can become 4 or 5.

So we have 1 chance out of 8 to obtain 4 or 5, and 1 chance out of 4 to obtain 6, 7 or 8, as required by the third gear die.

### Fourth gear

Is a twelve sided die labeled from 7 to 12 twice. It can be achieved with this simple expression:

1d6+6

### Fifth gear

Is a twentieth sided die labeled from 11 to 20 twice, that mean is equal to a d10 and can be achieved with the expression:

1d10+10

### Sixth gear

This is a large thirtieth sided die labeled from 21 to 30 three times and like the Fifth gear die can be achieved with a simple d10:

1d10+20

### Damage

Well, this is a simple d20 and no further explaination is needed...

Thursday, October 03, 2013
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Formula D
Formula Dé
Lanceur de dés rapide
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