Official Rulebook from the Basisgruppe NAWI Physik (only available in German)

The game is played with two dice and a dice cup with a coaster. Players take turns rolling the dice. The player rolling the dice may look at the first roll secretly. The coaster, with the dice hidden by the cup, is then passed to the next player, who must announce the total of the dice. Unless the player started the round, their announced total must exceed the previously announced total. The announced total may be true or a lie. The next player has the following two options:

• they roll the dice themselves as described above and must announce a higher score
• they can doubt the announcement and look at the dice

If a player reveals the dice, either the exposed liar or the player who doubted unjustly must drink a shot. The player who was wrong then starts the next round.

Ranking

Different numbers have the lowest value. The higher number is interpreted as the tens digit, and the lower number as the ones digit. Above these are the doubles, i.e., two identical numbers. The highest is the “Mäxchen,” the combination 21. This results in the following ranking: 31, 32, 41, 42, 43, 51, 52, 53, 54, 61, 62, 63, 64, 65, 11, 22, 33, 44, 55, 66, 21. The numbers are called thirty-one, thirty-two, …, single pair (or one pair), double pair, …, Mäxchen.

Physicists' Rules

• Betting low does not count as lying—that is, declaring a triple as a single is legitimate (it can be raised and passed on without question if you trust the previous player). A triple declared too low is occasionally indicated by adding “with (plenty of) room.”
• The announced number only needs to be no higher than the one announced by the previous player if a Mäxchen has been rolled. Thus, one Mäxchen can be outbid by another Mäxchen. In principle, the round can continue until someone reveals their roll.
• If you don’t roll a higher number and don’t want to lie, you may roll again, pass the cup without looking, and simply call out a higher number.
• If you lie or reveal a Mäxchen, you must drink two shots.
• If a mistake is made during the game (e.g., moving the dice while passing the cup), the rule is: drink a shot.
• Serious mistakes (dropping the dice) are penalized with two shots.

Classic drink: rum or vodka orange juice mix. Later, tequila.

This text is largely taken from Wikipedia.

The rules for the relay race at the Vineyard Ralley:

Relay-Race Rules (only available in German)