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I'm searching for an online tool a friend used in an RPG once, no more than two years ago. The tool is a dice roller that adjusted the probabilities of an otherwise fair dice roll to make it less likely to roll the same number multiple times. So, if you rolled 1d6 and got a 4, your next roll of 1d6 would be less likely to be a 4 than it would be to roll 1, 2, 3, 5, and 6.

This made for pretty interesting play, since it enforced a broader distribution of values on dice that we wouldn't otherwise have seen. We still rolled on average the same number, but the distribution was wider.

Does anyone know where I could find this tool?

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  • \$\begingroup\$ I don't actually know what the tool you're looking for is, but the same principle is used in the video game DOTA 2, where it's referred to as "Pseudo Random Distribution." That may give you a place to start. \$\endgroup\$
    – Kyle Doyle
    Jun 13, 2019 at 22:35

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I'm not sure what this site is or was, but I know what to look for. This is done by replacing the dice with cards and drawing from a deck. For a single die, you simply need cards with each value; for multiple dice you need one card for combination (so, 36 cards for 2d6).

To ensure that the results are completely fair, go through the entire deck before shuffling and repeating.

But then of course the last few draws are predictable. Adjust this (and increase the probability of getting the same thing twice in a row) by shuffling sooner.

And, the one-of-each deck means that you'll have no repeats; you can tweak that by combining identical decks (two of each value, three of each, etc.)

(And of course all of this can be implemented in software quite easily.)

In the end over a long run all of these give a fair distribution, but the deck idea arranges the values to guard against sequences of repeats or long stretchs of no-shows for a certain value.

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    \$\begingroup\$ One card of each number isn’t going to work very well, since the chance of a repeat isn’t “less,” but is rather “zero.” Of course, this is easily remedied by simply having the deck consist of some number of each value; the standard 52-card deck, for instance, has four of each. A 52-card deck with all 7s, 8s, 9s, 10s, Js, Qs, and Ks removed will make a pretty solid d6. \$\endgroup\$
    – KRyan
    Jun 13, 2019 at 23:36
  • \$\begingroup\$ @KRyan — yes, that's true... I'll edit in. I actually thought I had mentioned that already but I was writing this while on the public bus so eh. Will edit when I get a chance. \$\endgroup\$
    – mattdm
    Jun 13, 2019 at 23:46
  • \$\begingroup\$ It doesn't matter much. Over the long haul, these all result in a uniform distribution. If you draw without replacement until empty, you get a near perfect uniform distribution. If you replace every time, less so. That's all this does and in the long term it is indistinguishable from a normal die. Psychological benefit only. (Yes, I simulated multiple versions of this just now.) \$\endgroup\$
    – Novak
    Jun 13, 2019 at 23:47
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    \$\begingroup\$ @Novak For what it's worth, there's a Settlers of Catan deck that's meant to do exactly this, and without fail everyone I've played with using it hates it so much. Anecdotally, the psychological effect is strong. :) \$\endgroup\$
    – mattdm
    Jun 14, 2019 at 0:12

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