Dungeon Crawl Classics uses a combination of weird dice, d5, d7, etc up to d30. Now they’re mostly traditional polyhedral or other common numbers with the sides doubled, but the probability still holds. Might be interesting for a class too.
Oh, and I don’t know of any game that uses them (aside from rigged betting games), but there’s also nontransitive dice. They’re numbered in a nonstandard way, and come in sets of three. You offer your markcustomer his choice of the three dice, so he can get the best one, and then you have to settle for one of the other two. You each roll the die you chose, and whoever gets the higher number wins.
Specifically, the dice are marked:
A: 3, 4, 7, 8, 17, 18
B: 1, 2, 11, 12, 15, 16
C: 5, 6, 9, 10, 13, 14
See, they’re all marked with different numbers, because that way, we can never get a tie, right? Nobody wants a tie.
So, which die do you want?
Other ideas could be “What’s better on average, rolling 2d6 or a d12?” or maybe “How does the distribution shift if you get to add a d4 to your 2d6 rolls?”
I suppose teaching the kids to shoot craps and why they should take max odds while avoiding the horn is probably not going to go over well.
It’s got to be B, right? 4/6 of the faces beat 4/6 of the other two dies.
You take B, I take A.
I win 20 out of 36 rolls.
3,4,7,8 each win against 2 rolls on B.
17 and 18 each win against all 6 rolls of B.
4 * 2 + 2 * 6 = 20.
The trick is each die is week against one and strong against the other. Picking a die first is a sucker’s bet.
In other words it’s playing paper-rock-scissors except without the part where you make your choices simultaneously.
Eh, I’ve placed bets with far worse odds than that.
You could try exploring the likelihood of getting (or not getting) at least one 6 in a certain number of rolls. They can learn how a 1-in-6 chance of getting a 6 doesn’t mean a 2-in-6 chance with two rolls, and by extension how you aren’t guaranteed to get a 6 if you roll six times.
Or you could look at the odds, when rolling n dice, of all the dice showing the same result.
7th Sea uses a mechanic where you roll a certain number of d10s, and keep the highest results. If I remember right, the typical skill check has you roll (stat plus skill level) dice, and keep (stat) of them.
The d10s typically explode, though there are situations where they don’t.
Legend of the Five Rings has the same mechanic but that’s no surprise because they’re both from Alderac Entertainment Group.
Fun fact, AEG was formed by Jolly Blackburn, best known for the Knights of the Dinner Table comic.
There’s a popular carnival game called Chuck-a-Luck, that’s based on this. A player puts a dollar down on one of six numbers. The operator rolls three six-sided dice (usually oversized, so everyone can see them), and if your number comes up on any of them, you walk away with two dollars. It “feels” fair, because 3/6 is 50%, but it’s actually quite good house odds. The easiest way to see this is to imagine six players playing at once, each betting on a different number (which is in fact a fairly common setup): If all three dice are different, then the three losers pay the three winners, and the house gets nothing. But if any two (or three) dice are the same, then there are only two (or one) winners, and the rest losers, and so the house pockets the difference.
As-is, this already gives the house a fairly large take. But lately, I’ve seen it played with a wheel instead of actual dice: Each spot on the wheel has three dice-faces shown on it. And if you count them up, those wheel-spots show significantly more doubles and triples than real dice should.
(Before you use this as an example, check to see if your school ever uses this game in a fundraiser)
d6d6 is a weird distribution. If I’ve done my simulation right, you get increasing probabilities out to 6, then a sharp drop at 7, and a sudden change in slope at 13, too.
1 occurs with odds of 1/36
2 with odds of 7/216
6 with odds of 13/216
7 with odds of about 9/216
36 with odds of 1/(6^7)
My best friends and I love playing Two-Dice Pig, but we modify the rules a tad. If you get doubles, you must roll again; if your turn score is a double (11, 22, 33, etc.), you must roll again, if your game tally including the current turn tally is a double, you must roll again; if you end up with potential game tally of 97, you lose the current turn’s tally; if you end up with the potential game tally of 98, you lose all your points and start the game again at 0; and you must hit 100 exactly to win–if your current turn tally takes the game score over 100, you lose the current turn tally.
How would that rule set change the game strategy and the roll distribution from the regular rules for Two-Dice Pig?
I’m not going to try to answer that, but check out this video about solving the easier problem of (One die) Pig and you’ll get an idea of possible approaches and why it’s pretty much out of the scope of an SDMB post.
The current version of L5R, from Fantasy Flight Games, uses a sort of hybrid between AEG’s “roll & keep” system and FFG’s Genesys system. I played in a weekly campaign for the better part of a year, and I don’t think I could explain it at this point without the book in front of me. Even then, it seemed like literally every week one of us would discover some new wrinkle we hadn’t been aware of or that we had been doing something wrong the whole time.
Rolling extra dice and dropping the lowest is not too far out imo—it seems to be a relatively simple way of making the distribution negatively skewed.
Here is my question: you have 2d12 which are unmatched; one has a blank side, meaning that you can theoretically roll the lowest number (1) on the other; they are marked in such a way that they cover the largest possible continuous range of numbers (you can roll every possible number between one and the max combo), but there is no constraint about duplicates (there may be multiple combinations of one or more numbers in the range); what is the widest possible range with for unmatched 2d12?
(I do not have the answer for this. I am not that smart, or maybe just lazy.)
Are you sure those numbers are exact?
| odds of | |
|---|---|
| 1 | 1/36 |
| 2 | 7/216 |
| 6 | 16807/279936 |
| 7 | 493/11664 |
is what I get
I did a simulation, so everything is approximate - but the situations for 1 and 2 and 36 are simple enough that I know they’re exact; clearly 6 and 7 are not quite right.
What do you mean? 2 12-sided dice can only give 12x12=144 different outcomes, so 1–144
you could label the “unmatched” die 0, 12, 24, … and add that to the other roll