「大富翁快骰版」骰數的概率分析 (Probability analysis of the "Speed dice Monopoly" dice rolling)

「大富翁快骰版」骰數的概率分析

Probability Analysis of the "Speed Dice Monopoly" dice rolling

—方潤 (推廣弈棋委員會)

by Fong Fu Yun (FCC)

(2009/09/12)

規則簡介 / Basic Rules

快骰版大富翁除了原有的兩粒白骰外，另加上一粒「快骰」。玩家用兩粒白骰開步，第一次繞過起點後便可以啟用快骰。

A "Speed dice" is added besides two white dices in traditional version. Players start their game with white dices, and roll the Speed dice together after their first time passing Go.

快骰的六面分別是「一」、「二」、「三」、「巴士」和兩面「大富翁」。

The faces of Speed dice includes "1", "2", "3", "Bus" and two faces of "Mr. Monopoly".

擲到數字骰面，就把數字加到原有兩粒白骰的點數之中。(但計算「孖骰」和公用事業路費時不計算在內)

如果三面骰點相同，就可以選擇前往圖板上任何一格。(亦可留在原格，當繞了一圈)

When you roll a number, then add up to the roll of white dices. (Speed dice is not count for "rolling doubles" and the rent of utlities)

However, if you rolls "triples" (three dices with same faces up), you may go to anywhere on the board. (You may also choose passing Go and back to the same place.)

擲到「巴士」，可以選擇只依照其中一粒白骰的點數行走，亦可以選擇按兩粒白骰的總和行走。

When you roll a "Bus", you may choose to use the total from one die or both dice to move.

擲到「大富翁」，先走完原有的點數，然後﹕

—如果當時還有地段未售出，則直接前往最近未售出的地段。

—如果所有地段已售出，就前往最近需要交租的地段。

When you roll "Mr. Monopoly", after you move according to the white dice:

- if there are unowned property, move to the next unowned property.

- if all property are owned, move to the next property on which you would owe money.

快骰的出現令大富翁原有的概率分佈有所變化，為簡便計，本文僅探討快骰對擲骰點數的影響。

The use of Speed dice alters the probability distribution of Monopoly. For easy discussion, this article only faces on the roll of dice.

骰面分佈 / Faces of Dice

傳統大富翁的點數分佈 / Roll of dices distribution in traditional Monopoly﹕

快骰版大富翁的點數分佈 / Roll of dices distribution in Speed dice Monopoly﹕

概率分佈圖 / Graph showing probability distribution﹕