10-sided die with chance of bonus die
May 13th, 2015 at 11:28:47 PM
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Needing some Math help!
I'm working out part of a system for a game I'm working on, and I need to know if I need to tweak some things, so I'm checking to see if it all adds up (no pun intended).
defender has a base of 1, 3, 5, 7, or 11 for the target successes that the attacker has to roll; if the attacker achieves the # of successes required the attacker wins the roll, otherwise the defender wins.
the attacker rolls 1-5 10-sided dice based on his/her increasing skill, however only 8-10 count as a success, and each 9-10 granting an additional die to add to the pool. That means, there is a 3/10 chance of at least one success, and 1/5 chance to add another die, to increase the chance for the attacker to hit the defender's number.
I feel like this should be really easy, but I can't figure out how to get started...
What is the chance (expressed as a ratio please...) for the attacker to win the roll against a defender with a target of 1? a target of 3, 5, 7, 11?
I'm working out part of a system for a game I'm working on, and I need to know if I need to tweak some things, so I'm checking to see if it all adds up (no pun intended).
defender has a base of 1, 3, 5, 7, or 11 for the target successes that the attacker has to roll; if the attacker achieves the # of successes required the attacker wins the roll, otherwise the defender wins.
the attacker rolls 1-5 10-sided dice based on his/her increasing skill, however only 8-10 count as a success, and each 9-10 granting an additional die to add to the pool. That means, there is a 3/10 chance of at least one success, and 1/5 chance to add another die, to increase the chance for the attacker to hit the defender's number.
I feel like this should be really easy, but I can't figure out how to get started...
What is the chance (expressed as a ratio please...) for the attacker to win the roll against a defender with a target of 1? a target of 3, 5, 7, 11?
May 15th, 2015 at 10:28:14 AM
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The far left column is the number of dice that the attacker has and the top column is the defender target number. The probabilities are how likely the attacker will win.
The bolded probabilities are exact (as these were easy to compute). I computed the 2 dice and 3 target probability, but then I realized the problem became much more complicated with multiple dice and targets. So I simulated the rest of the probabilities (100 million times).
The bolded probabilities are exact (as these were easy to compute). I computed the 2 dice and 3 target probability, but then I realized the problem became much more complicated with multiple dice and targets. So I simulated the rest of the probabilities (100 million times).
| 1 | 3 | 5 | 7 | 11 | |
|---|---|---|---|---|---|
| 1 | 0.3 | 0.012 | 0.00048 | 0.0000192 | 3.072e-08 |
| 2 | 0.51 | 0.0492 | 0.0031238 | 0.0001724 | 1e-07 |
| 3 | 0.657 | 0.11264 | 0.010769 | 0.000795 | 3.2e-06 |
| 4 | 0.7599 | 0.19544 | 0.026272 | 0.002554 | 1.45e-05 |
| 5 | 0.83193 | 0.28779 | 0.05175 | 0.00647 | 0.00005 |
