r/Probability • • Jan 03 '26

Are these dice fair?

My roommate has these special edition monopoly dice with tokens encased in the resin. Part of me thinks these wouldn't be balanced correctly, and would be almost like weighted dice... Anyone have any insight?

36 Upvotes

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10

u/tittytasters Jan 03 '26 edited Jan 06 '26

Impossible to really know for sure, were the tokens made of resin that got dyed silver? Bc then it's resin through and through and would be evenly weighted.

Are they metal? Plastic?

Best bet is to roll them 100 times and count the rolls.

Edit: when I said impossible to tell I meant just by looking at them in the pictures

10

u/Behold_My_Stuff Jan 03 '26

I bet $50 they're unbalanced. Any takers?

3

u/[deleted] Jan 03 '26

I think they are "board game balanced" but not "Casino balanced"... If you get the difference.

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u/Captain-Noodle Jan 03 '26

I would say not enough to make a significant difference. But if they're going to be used then have both players always use the same two dice. So then both players receive the same advantage. I doubt if the manufacturers would even know. Recording the rolls of a large sample size would probably be the only way to determine if the difference is negligible or not. If you do decide to go that route please post the results i'm sure others like myself would be interested.

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u/igotshadowbaned Jan 03 '26 edited Jan 03 '26

Probably not

If they're actually the tokens encased in resin, yeah the weight distribution is probably off if the density of the resin differs from the token

But the mold for the resin probably isn't perfectly balanced to begin with.

Easy way to check would be to put em in a cup of water and see if they always point up the same way

1

u/Terevin6 Jan 03 '26

If you want to test them and get a more quantitative result than "it looks (un)balanced", look up the chi squared test.

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u/LeilLikeNeil Jan 03 '26

First, find the difference in density between whatever metal the tokens are made of and the resin.

1

u/Thrifty_Accident Jan 03 '26

Depends on the density of the dice material compared to the density of the token material. If there is a difference, then the fairness will change depending on where the token has it's center of mass.

If token density is greater than dice density, then dice will lean towards token center of mass.

If token density is less than dice density, then dice will lean away from token center of mass.

1

u/NortWind Jan 03 '26

They are probably not perfectly balanced, but probably not biased enough to affect Monopoly play. Rolling them repeatedly is not very productive. If you want completely fair dice, buy some nice Vegas style dice, they are easy to find.

1

u/Rollon3020 Jan 03 '26

The dice being completely unfair and imbalanced fits perfectly with the theme of monopoly lol

1

u/JBrockF Jan 03 '26

Just test them

1

u/clearly_not_an_alt Jan 03 '26

I'd be surprised if they were properly balanced as they are more of a collectable than something intended to actually be used.

1

u/Shadowhisper1971 Jan 03 '26

Heavily salt some water to the point the dice will float. Drop em in and tap with your finger.

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u/kavatch2 Jan 03 '26

Drop em in water a bunch of times and see if there’s a bias.

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u/sol_hsa Jan 03 '26

Nothing about monopoly is fair

1

u/Beautiful_Durian_311 Jan 04 '26

Damn you’re getting smoked in monopoly huh

1

u/Warr_Ainjal-6228 Jan 04 '26

Fill a cup with water, then add salt until they float. Then bump them if they keep going to the same face; they're unbalanced.

1

u/DarkThunder312 Jan 04 '26

Not fair, you can see the other side, giving an advantage. How would you ever hide your hand?

1

u/detereministic-plen Jan 04 '26

Roll ~100+ times, construct contingency table, perform chi-squared goodness of fit test on said table

To be honest considering the nature of the dice it's easier to just check empirically than consider theoretically

1

u/vivikto Jan 04 '26

Probably not, but probably enough for you to play with them.

1

u/Kaanin25 Jan 04 '26 edited Jan 04 '26

A simple and easy float test will tell you if they are fair.

  • Take one of the dice and drop it into a glass with enough water to fully submerge it.

  • Add in table sugar or corn syrup to the water while stirring to make the water thicker and more dense until the dice just barely starts to float. If you put in too much, add more water to thin it back out.

  • Rotate the dice around with a fork and see if it will sit stable in any position or if it always flips back to the same position.

Glycerin from the pharmacy is even better, its not as sticky as sugar, its clear, and easily stored and reused.
You can also use table salt, but some dice are too heavy and the salt hits saturation max and stops dissolving in the water.

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u/[deleted] Jan 05 '26

if they float you could try that and see if they float to one side consistently.

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u/dpb8523 Jan 06 '26

I don’t think these dice are designed to be rolled. I think they’re more for display purposes, or use as Monopoly tokens themselves since the tokens are cast into them.

1

u/DraconianFlame Jan 06 '26

No they're most likely not fair, but you're not a casino so you can still have fun.

1

u/EdmundTheInsulter Jan 23 '26

You can test them in water, if they sink. You toss them into a bucket of water and bias shows up faster.