nontransitive dice (set of 4)

Description

You Choose, You Lose! – a set of 4 non-transitive dice

Also known as Efron Dice. These dice have the peculiar property that no matter which of the four is chosen, at least one of the remaining three has a strong statistical advantage over it.
Invite your victim to examine the dice and point out that the numbering is non-standard, one even has some blank faces, and that in fact the total number of spots on each dice varies. Ask them to choose any one of the four dice (they’ll probably choose the one with the most spots, but it doesn’t matter), then you select one of the remaining three. You both throw your dice at the same time and the highest number wins. If you do this, say ten times, you will almost certainly win more often than your opponent.

The reason is that these dice are what mathematicians call “non transitive dice.” They illustrate a probability paradox, or in other words they defy common sense! Imagine a game of scissors-paper-rock where your opponent chooses first. If they choose rock, you choose paper, if they choose paper, you choose scissors. You would always have the advantage. These dice work in a similar way.

Whichever of the four dice is chosen, you can choose one of the remaining three that will beat it 2 times out of 3.
[6,6,2,2,2,2] will beat [5,5,5,1,1,1] which will beat [4,4,4,4,0,0] which will beat [3,3,3,3,3,3] which will beat [6,6,2,2,2,2] !!!

Or to put it another way, black beats green beats blue beats yellow beats black.
The more times you throw the dice, the more likely it is that your total number of wins will be more than that of your opponent. Swindle your friends and family with the power of mathematics !!

These dice are 16mm (5/8inch), rounded corners, colours : blue, black green, yellow.

You may also like …. other Nontransitive Dice options available further down this page:
Nontransitive Dice (set of 3)
Nontransitive Dice – Double Whammy

Size : 16mm (5/8inch)
Shape : rounded edges and corners
Colour : white with black spots.
Materials : injection-moulded plastic.
Other features : The blank dice are made in England from injection-moulded plastic. I use a precision jig system to machine the pip indents into exact position then colour them with a mica infused acrylic paint which is extremely hard-wearing.
Shipping Cost : 3.50 within UK, Royal Mail (untracked, 1st class). Flat rate of 10.00 GBP to the rest of the world (tracked airmail).
Shipping Times : 95% of orders are shipped within 2 working days. If a delay is expected, you will be informed.
Custom-made options : The entire range is also available made-to-order in 36mm (1 and 1/2inch), red with white spots, rounded edges and corners, shipping time 1 – 2 weeks. Some other sizes and colour combinations are possible. Please contact me for availability and prices.