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Is it possible to roll a fair, n-sided die with a controlled throw such that a particular face is landed on with a probability higher than 1/n? The golden touch craps claims that he can teach you dice control.

EDIT: Is there a statistical proof that someone can manipulate the dice? (even only without a cup, without hitting the wall etc...)

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    If backgammon is played for money the dice are always rolled out of a cup with an interior lip. For tournaments see [bwcmc.com/rules.pdf], 3.2. and 4. The lip allows shaking the cup without the dice falling out, even if the hands don't cover the cup (which would leave room for manipulation). Experienced players can manually roll the dice such that more double rolls occur, even though the dice appear to roll freely. (Backgammon is played with a pair of dice. The cheater inconspicuously aligns the dice when picking them up, resulting in more double rolls.)
    – Peter - Reinstate Monica
    Jul 7, 2020 at 23:01
  • bwcmc.com/rules.pdf
    – Cohensius
    Jul 20, 2020 at 14:14
  • Any particular reason you repeat the link I mentioned?
    – Peter - Reinstate Monica
    Jul 20, 2020 at 15:10
  • your link takes me to 404.php page not found
    – Cohensius
    Jul 20, 2020 at 18:50
  • Ah. I see, a square bracket slipped into the link, an editing error. Thanks for the proper link.
    – Peter - Reinstate Monica
    Jul 20, 2020 at 23:23

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In theory, yes (the macro nature of the dice and the table overcoming any quantum-level randomness, leaving you with classical physics). In practice, the bulk of the evidence says no, that the chaos in the system is greater than human skill can overcome, but some people claim such a special skill.

See the short wiki article for (the scant) details.

In response to the addition to your question: "is there statistical proof"? The answer is (in 2018, at least): "no", according to this article in the UNLV Gaming Research & Review Journal

We do not assert whether dice control is possible or not (there is a lack of published evidence).

This assumes that you throw them in a standard way. If you "throw" a die in an obviously forced way (pick it up and drop it from a small height with no shake and no bounce), then obviously the side that was on top in your hand has a greater likelihood of staying on top. Any throw of a die with the usual features of a throw (shake and roll, true roll) will be too chaotic to control.

Exception: for n=2 in the particular expression of a coin, it is possible to "not flip" the coin but instead make it wobble in the air, fooling most people and yet resulting in significant deviation from fair. Again, this deviates from a true "roll" of the die, but unlike other faux rolls, this one can be mistaken for a true roll.

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