Greed Dice Game Probability

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Greed Dice Game Probability. In each round, players roll a dice (taking turns is fine) and both receive the number of points shown. The length of this path is $l=\sqrt 2 r$

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You have to continue doing this until all the dice show the number. In each round, players roll a dice (taking turns is fine) and both receive the number of points shown. You may choose to stop at any time.

Roll all of your dice at once and identify the number you want to achieve for all the dice.

Farkle, or farkel, is a dice game has also been called or is similar to 1000/5000/10000, cosmic wimpout, greed, hot dice, squelch, zilch, or zonk. Throw the dice to make winning combinations but beware, you have to learn to stop before raw greed overtakes you because the first time you don’t add to your score you lose. This is a game that is won by getting the higher total after five rounds. Furthermore, i believe that the spirit of the problem is indeed about relative final value: