RogerBW's Blog

Multiplied Dice 24 January 2023

Here's a core game mechanic with no game wrapped round it. It might be useful for someone, or I may use it myself some day. Have fun.

The basic idea is to multiply the values of two dice to get the value of the roll. (This probably limits its popular appeal; gamers under about 40-50 may not have had multiplication tables drilled into them at school, and therefore may not find this as automatic a process as I do.)

Depending on the emphasis of the game, one die might be a skill level and the other an attribute level, or one die might go up with increasing PC competence and the other go down with increasing challenge.

A double 1 is automatically the worst possible result. Otherwise, success levels go up as powers of 2: 2, 4, 8, 16, etc. This is where I envision difficulty levels coming in, if they're needed: I have a d6 dexterity and a d10 Picking Locks skill, and the lock is quality level 16, so that's what I need to equal or exceed to pass the test. (And perhaps a 32 will let me do it particularly well, or particularly fast.) Higher levels are unachievable by small dice sizes. For opposed rolls, if one value is twice the other, that's a basic success, and so on; if they're closer than that, neither side is getting an advantage.

Using a progression of d2, d4, d6, d8, d10, d12, the probabilities of achieving each success level are:

  • d2 × d2; 2+: 75%, 4+: 25%
  • d2 × d4; 2+: 88%, 4+: 50%, 8+: 13%
  • d2 × d6; 2+: 92%, 4+: 67%, 8+: 25%
  • d2 × d8; 2+: 94%, 4+: 75%, 8+: 38%, 16+: 6%
  • d2 × d10; 2+: 95%, 4+: 80%, 8+: 50%, 16+: 15%
  • d2 × d12; 2+: 96%, 4+: 83%, 8+: 58%, 16+: 21%
  • d4 × d2; 2+: 88%, 4+: 50%, 8+: 13%
  • d4 × d4; 2+: 94%, 4+: 69%, 8+: 38%, 16+: 6%
  • d4 × d6; 2+: 96%, 4+: 79%, 8+: 50%, 16+: 17%
  • d4 × d8; 2+: 97%, 4+: 84%, 8+: 59%, 16+: 28%, 32+: 3%
  • d4 × d10; 2+: 98%, 4+: 88%, 8+: 68%, 16+: 38%, 32+: 8%
  • d4 × d12; 2+: 98%, 4+: 90%, 8+: 73%, 16+: 44%, 32+: 15%
  • d6 × d2; 2+: 92%, 4+: 67%, 8+: 25%
  • d6 × d4; 2+: 96%, 4+: 79%, 8+: 50%, 16+: 17%
  • d6 × d6; 2+: 97%, 4+: 86%, 8+: 61%, 16+: 31%, 32+: 3%
  • d6 × d8; 2+: 98%, 4+: 90%, 8+: 69%, 16+: 42%, 32+: 13%
  • d6 × d10; 2+: 98%, 4+: 92%, 8+: 75%, 16+: 50%, 32+: 20%
  • d6 × d12; 2+: 99%, 4+: 93%, 8+: 79%, 16+: 56%, 32+: 28%, 64+: 3%
  • d8 × d2; 2+: 94%, 4+: 75%, 8+: 38%, 16+: 6%
  • d8 × d4; 2+: 97%, 4+: 84%, 8+: 59%, 16+: 28%, 32+: 3%
  • d8 × d6; 2+: 98%, 4+: 90%, 8+: 69%, 16+: 42%, 32+: 13%
  • d8 × d8; 2+: 98%, 4+: 92%, 8+: 75%, 16+: 52%, 32+: 23%, 64+: 2%
  • d8 × d10; 2+: 99%, 4+: 94%, 8+: 80%, 16+: 59%, 32+: 31%, 64+: 5%
  • d8 × d12; 2+: 99%, 4+: 95%, 8+: 83%, 16+: 64%, 32+: 39%, 64+: 10%
  • d10 × d2; 2+: 95%, 4+: 80%, 8+: 50%, 16+: 15%
  • d10 × d4; 2+: 98%, 4+: 88%, 8+: 68%, 16+: 38%, 32+: 8%
  • d10 × d6; 2+: 98%, 4+: 92%, 8+: 75%, 16+: 50%, 32+: 20%
  • d10 × d8; 2+: 99%, 4+: 94%, 8+: 80%, 16+: 59%, 32+: 31%, 64+: 5%
  • d10 × d10; 2+: 99%, 4+: 95%, 8+: 84%, 16+: 65%, 32+: 39%, 64+: 11%
  • d10 × d12; 2+: 99%, 4+: 96%, 8+: 87%, 16+: 69%, 32+: 46%, 64+: 18%
  • d12 × d2; 2+: 96%, 4+: 83%, 8+: 58%, 16+: 21%
  • d12 × d4; 2+: 98%, 4+: 90%, 8+: 73%, 16+: 44%, 32+: 15%
  • d12 × d6; 2+: 99%, 4+: 93%, 8+: 79%, 16+: 56%, 32+: 28%, 64+: 3%
  • d12 × d8; 2+: 99%, 4+: 95%, 8+: 83%, 16+: 64%, 32+: 39%, 64+: 10%
  • d12 × d10; 2+: 99%, 4+: 96%, 8+: 87%, 16+: 69%, 32+: 46%, 64+: 18%
  • d12 × d12; 2+: 99%, 4+: 97%, 8+: 89%, 16+: 73%, 32+: 52%, 64+: 24%, 128+: 2%

As this is a game mechanic you can intrinsically re-use it as long as you put it in your own words. In case you want the words too and for the avoidance of doubt, I licence this as cc-by-sa 4.0. (If you want to use it in a more restrictive way, talk to me.)

Tags: rpgs

  1. Posted by J Michael Cule at 01:02pm on 24 January 2023

    I suspect you're right about the lack of appeal of this. I've had the arithmetic of the BRP d100 roll pounded into my head since 1979 but though I can do the chances of a 'special' result in my head I can't figure out whether a roll is a critical or a fumble without looking it up the way some of my players can.

    What's the advantage of this over established systems?

  2. Posted by RogerBW at 02:26pm on 24 January 2023

    Clean asymmetry, as opposed to the flat probabilities of a single die, the Gaussian approximation of multiple summed dice, or the Poisson approximation of dice pools. Going up the low levels is relatively easy; getting to the higher levels is much harder, and IMO that's where games are interesting.

  3. Posted by DrBob at 05:13pm on 24 January 2023

    The first edition of Sufficiently Advanced involved multiplication. Multiply this dice roll by this stat, and then multiply that dice roll by that stat, then compare them and do some other stuff which might change the final numbers. I ended up printing out a grid of results from the 1 times to the 13 times table, because it was doing my head in. I never actually ran the game, because the maths was such a pain.

    Simon Burley's "Code of..." RPGs involve multiplying 2 x d6 and adding to stat, which is much simpler than Sufficiently Advanced. But it made for rather a swingy game. Simon likes this style, so it is feature not a bug.

  4. Posted by John P at 10:39pm on 31 January 2023

    I always liked the Silent Death & Bladestorm dice mechanic. Roll 3 dice based on stats/skills/equipment (e.g. a d6 for lockpicking, a d10 for dexterity to use your example & a d4 for the pick) plus maybe a bonus for quantity/quality. The total of the roll had to be over the target value. But then the magnitude would be something like the sum of the lowest dice values, or the highest dice value or whatever.

  5. Posted by RogerBW at 11:27pm on 31 January 2023

    There's also the Sentinel Comics RPG, where you have a die pool of three from different places, but you then sort them numerically - most of the time what matters is the middle value, but sometimes the others get used too.

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