# Dice Probability - Exploding dice

##### New Member
Hi everyone, my apologies in advance for not being the best at math.

I am trying to work out the probabilities of a dice system for a game I am working on.

I am rolling six sided dice (D6), and scoring a success on a 1, 2, or 3. If I roll a '1', my dice explodes - allowing me to roll a 4 sided dice (again scoring a success on a 1, 2, or 3). My D4 will not explode if I roll additional '1s'.

My working out has been: I have a 50% chance of scoring a success on the D6, and a 16.7% (rounding up) chance of that dice exploding. If it explodes I have a 75% chance of scoring a success. 16.7% of 75 = 12.525.

So the probability of rolling a success on my original D6 would be 50% + 12.5% - or 62.5% (or an average of 0.63 successes per dice, rounding up).

Is this correct? I know I have rounded up in places, but am I working this out in a way that gets me to the correct answer?

Thanks in advance for any help!

#### Dason

To clarify - if you roll a 1 on the D6 we need to roll the D4 first to see if we have a success or not? If so I wouldn't count rolling a 1 as a success on the D6 roll but the rest of the logic seemed right so the only change would be the probability of success of success on the original D6 would drop to 1/3 or 33.3%

##### New Member
To clarify - if you roll a 1 on the D6 we need to roll the D4 first to see if we have a success or not? If so I wouldn't count rolling a 1 as a success on the D6 roll but the rest of the logic seemed right so the only change would be the probability of success of success on the original D6 would drop to 1/3 or 33.3%

If I roll a 1 on the D6 I score 1 success, and I get to roll a D4 to see if get further successes (so the 1, 2, 3 on the D6 scores 1 success, but the 1 also allows me to roll a D4, which has a 75% chance of netting me another success).

#### Dason

Then I guess you need to better clarify what you're looking for. If it's probability of at least one success then that's just 50%.

It seems like you're trying to do something else though.

##### New Member
Then I guess you need to better clarify what you're looking for. If it's probability of at least one success then that's just 50%.

It seems like you're trying to do something else though.
It is the probability of one success. But I can roll multiple D6s, so...

I get a success on a 1, 2, or 3, when rolling 1D6. A 50% chance.

But, if I roll a 1, I get 1 success, and I also roll a D4, getting a success on 1, 2, or 3. A 75% chance.

I have a 50% chance of getting 1 success. And, I have a 16.7% chance of rolling a D4, which has a 75% chance of getting me a second success.

My question is whether this amounts to a 62.5% average for every D6 I roll.

Can/should I regard the probability of each D6 as being 0.625 successes?

#### Dason

I think the idea you're looking for is "expected value".

#### katxt

##### Well-Known Member
I think the idea you're looking for is "expected value".
Dason is right, and so are you. An average (not "probability") of 0.625 successes each turn of the game.

##### New Member
Awesome - thanks very much! Sorry - I am not au fait with the terminology - I appreciate the advice!