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doppelgreener
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I'm not sure what the real question is. I'm thinking at least part of it is "Help me understand the mechanics of exploding dice" so I'll start there.

Where N is the size of the die.

Average # of rolls = N/(N - 1)\$\dfrac N {N - 1} \$

Average result of an exploding die = N*(N+1) / (2 * (N-1))\$ \dfrac {N (N+1)} {2(N-1)} \$


Die    Average        Average
        Rolls          Value
d4    1.3333334      3.3333333
d6    1.2            4.2
d8    1.1428572      5.142857
d10   1.1111112      6.111111
d12   1.0909091      7.090909
d20   1.0526316     11.052631

\begin{array}{l|ll} \text{Die} & \text{Average rolls} & \text{Average value} \\ \hline \text{d4} & 1.3333334 & 3.3333333 \\ \text{d6} & 1.2 & 4.2 \\ \text{d8} & 1.1428572 & 5.142857 \\ \text{d10} & 1.1111112 & 6.111111 \\ \text{d12} & 1.0909091 & 7.090909 \\ \text{d20} & 1.0526316 & 11.052631 \end{array}

Once you know the averages, or the formulas, you can better eyeball your odds of any particular result at the table.

Gory math details are here

I'm not sure what the real question is. I'm thinking at least part of it is "Help me understand the mechanics of exploding dice" so I'll start there.

Where N is the size of the die.

Average # of rolls = N/(N - 1)

Average result of an exploding die = N*(N+1) / (2 * (N-1))


Die    Average        Average
        Rolls          Value
d4    1.3333334      3.3333333
d6    1.2            4.2
d8    1.1428572      5.142857
d10   1.1111112      6.111111
d12   1.0909091      7.090909
d20   1.0526316     11.052631

Once you know the averages, or the formulas, you can better eyeball your odds of any particular result at the table.

Gory math details are here

I'm not sure what the real question is. I'm thinking at least part of it is "Help me understand the mechanics of exploding dice" so I'll start there.

Where N is the size of the die.

Average # of rolls = \$\dfrac N {N - 1} \$

Average result of an exploding die = \$ \dfrac {N (N+1)} {2(N-1)} \$

\begin{array}{l|ll} \text{Die} & \text{Average rolls} & \text{Average value} \\ \hline \text{d4} & 1.3333334 & 3.3333333 \\ \text{d6} & 1.2 & 4.2 \\ \text{d8} & 1.1428572 & 5.142857 \\ \text{d10} & 1.1111112 & 6.111111 \\ \text{d12} & 1.0909091 & 7.090909 \\ \text{d20} & 1.0526316 & 11.052631 \end{array}

Once you know the averages, or the formulas, you can better eyeball your odds of any particular result at the table.

Gory math details are here

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Pat Ludwig
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I'm not sure what the real question is. I'm thinking at least part of it is "Help me understand the mechanics of exploding dice" so I'll start there.

Where N is the size of the die.

Average # of rolls = N/(N - 1)

Average result of an exploding die = N*(N+1) / (2 * (N-1))

Die    Average        Average
        Rolls          Value
d4    1.3333334      3.3333333
d6    1.2            4.2
d8    1.1428572      5.142857
d10   1.1111112      6.111111
d12   1.0909091      7.090909
d20   1.0526316     11.052631

Once you know the averages, or the formulas, you can better eyeball your odds of any particular result at the table.

Gory math details are here