Set aside the regular six-sided dice and try these replacements for dice.
Instead of playing monopoly with a regular set of dice, what if instead you played with just one coin? It would totally change the dynamic of the game. Heads would be one, tails is two. Each player could only move one or two spots at a time. It sounds like it would really slow up the game, but instead, it would speed up the game. Almost every property would be bought in the first round of the game. How would people build? Would someone end up bankrupt after just two rounds on the board?
Try a die with 50 sides. A Monopoly board has 40 squares, so using a D50 die would enable you to go around the entire board with just one roll! To make counting the number of squares easier, you could mark a number on each square on the board. The numbers would go up sequentially. If you are on Baltic Avenue (#3), and you roll a 31 on the die—that means you go to property #34: Pennsylvania Avenue!
Deck of squares
Now if the math from the 50-sided die is too much for you, then why not just make a deck of cards where each card represents a square. So every turn a player draw a card from the deck to see where that player will end up. It’s completely random–but not quite. Because once a card has been drawn from the deck, you know it won’t be used again until all the cards are used. Therefore the properties would be bought so much faster.
It would be more fun if there were two copies of every square in the deck. That way when you buy something, there’s still a chance that someone might land on your property on the very next turn. Plus, it adds an element of memory and strategy to the game where you have to keep track of what cards have been drawn already.