BX Advanced Rules: Multiple Success Rolls and Probability

BX Advanced Playtest 0.1 Cover CoverIn the “GM Advice” section of the BX Advanced rules, I’m trying to tackle a problem I see quite a bit of in play: Gamemasters not truly understanding that requiring multiple successful rolls to complete a simple task will reduce the final chance of success. Even those Gamemasters who realize this often do not seem to realize just how much requiring even a single extra roll will reduce the chance of success. The theory seems to be that players enjoy rolling dice and that having to roll dice increases tension, so breaking a task down into smaller steps that each require a success roll is a good thing. Don’t get me wrong, it can be a good thing if used carefully, but most of the GMs I know don’t understand how probability works when dealing with multiple independent events like die rolls. To find the probability of success you have to multiply the probabilities involved which means the final result is likely to be lower that one might expect. For example, if you require two rolls to successfully complete a task and the character has a 60% chance of success with the first roll and a 45% chance with the second roll, the character’s actual chance of successfully completely the task is only 27% (.60 x .45 = .27) — which is likely less than the average GM assumes it will be.

I’ve added a few paragraphs on this to the GM Advice section of the BX Advanced rules. I’m trying to explain the situation clearly while not going into a lot of math/probability theory detail and will not taking up a lot of space in the room book (as I expect most peoples’ eyes will glance over if I explain the math in detail or if the section is “too long”. Here is my current draft. I would really like comments on it. Is it clear enough? If not what needs to be clearer? Does it take the right tone (i.e. I’m not trying to say never require multiple rolls, just that if one wants to require them one needs to understand their effect on the game)? Is it too long? Too short?

Note that the quoted text below is Open Game Content under the OGL and any suggestions for improvement that you make and I use will be released as Open Game Content under the OGL.

Multiple Success Rolls and Probability
Many Gamemasters like to break tasks like climbing a cliff into a number of success rolls, as players tend to enjoy rolling dice and Gamemasters often believe that rolling dice adds tension to the game. There is nothing wrong with doing this provided you understand and accept the effects requiring multiple successes have on the chance of failure.

For example, let’s take climbing a cliff. You have decided that the party needs to roll 15 or less on a D20 (a 75% chance of success) to successfully climb the cliff face and that each attempt will take about an hour. This is one roll and the characters have a 75% chance of successfully climbing you gave them, so the characters will find themselves at the top of that cliff in an hour 3 out of 4 times (i.e, 75% of the time just as you would expect from their success chance). However, if you decide that the cliff is high enough that two rolls are required, one to reach the midway point of the climb and another to reach the top of the cliff from the midpoint, then the characters will only find themselves at the top of the cliff about 12 times in 20 attempts – their chance of success dropped from 75% to about 56% (75% x 75%). If you require three rolls, the characters will only find themselves at the top of the cliff about 21 times out of every 50 attempts – the chance of success dropped to just over 42% (75% x 75% x 75%). Requiring 4 rolls drops the chance of reaching the top to just under 32% (75% x 75% x 75% x 75%). Requiring 5 rolls drops that chance to about 24% (75% x 75% x 75% x 75% x 75%).

While multiple die rolls for success can fun and can increase tension, multiple rolls should probably be used sparing due to the reduction in the chance of success caused by requiring multiple successful rolls to complete the task. When you choose to require multiple rolls you should generally ensure that the result of failing any one roll does not result in a disaster. For example, if you are going to require three rolls to climb a cliff, the result of failing a roll should be something like time lost to having to try another route up the cliff instead characters injuring themselves or worse, falling to their doom.

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3 Responses

  1. Clear and understandable. Your intention to offer advice not lay down the law is also clear. Thanks for explaining. I will be more careful with multiple dice rolls. BTW I think you mean "glaze over" instead of "glance over."

  2. Vb Wyrde says:

    Reads well to me. And good advice.

  3. Unknown says:

    As a trained mathematician with a lot of background in probability, I found it very clear. Well done.