# Cluemeister's Corner

### Results for March

For his final conundrum, the Cluemeister took a walk on the Boardwalk--and, being of a fundamentally lazy character, chose to ask just how short that perambulation could be. The March question was:**Alan, Bob, and Charlotte are playing Monopoly. What is the shortest possible number of player turns in...**

1) A complete game?

2) A complete game with no trades?

3) A complete game with no trades or auctions?

4) A complete game with no trades, auctions or mortgaging?

1) A complete game?

2) A complete game with no trades?

3) A complete game with no trades or auctions?

4) A complete game with no trades, auctions or mortgaging?

The following are the Cluemeister's answers...

**1)**Alan, being an unbelievably good negotiator, convinces the other players to give him all their money. (Technically, the rules of Monopoly don't allow players to give away money, even for promises, but we can imagine that he starts by rolling doubles and buying a property, and then trades it in turn to each other player for all their money, buying it back from each for a dollar apiece.) He then lands on Community Chest and draws the "Collect $50 from every player" card. Voila! The game is won in a single turn.

**2)**We may imagine that Alan rolls doubles twice, picking up two properties and then landing on Community Chest. This time he declines to buy either property, but drives up the prices in the ensuing auctions so much that Bob and Charlotte each end up spending all their money on a property apiece. Then he draws the same Community Chest card as before. However, this doesn't end the game, because the players can mortgage their newly acquired properties! No property but the two dark purples mortgages for less than $50, and they can't be acquired from the starting position by a roll of doubles. So while the starting player can drive his foes to the brink of bankruptcy, he can't quite finish them off on his first turn without trades taking place.

Can it be finished in two turns? Certainly. Alan auctions off two properties as above, buying one while the other goes to Bob. Neither is left with any money. With his third roll he lands on Chance or Community Chest and gets an unfortunate draw--let's say the school tax for $150. Goodbye, Alan! Bob then suffers a similar fate on his own turn, leaving Charlotte as the winner.

**3)**This one is tricky. Without reckless auctions, the players have no simple, quick way to impoverish themselves. They still have a quick way, however, if not a simple one!

Consider this possibility. Alan rolls double threes and buys Oriental Avenue. He chooses to repeatedly mortgage and unmortgage it, paying a $10 interest penalty each time, until he has only a mortgaged property and $50 left. Why does he do it? Chutzpah! He then rolls an eleven, lands on Community Chest, and pays a doctor's fee of $50, leaving him with nothing. Bob then rolls double fours and picks up Vermont Avenue. He does the very same thing, leaving him with $50. He rolls boxcars, landing on Chance, and draws the card that says, "You have been elected Chairman of the Board. Pay each player $50."

What happens now? He can afford to pay one player, but not both. Does he get to choose who to pay off first? Is his money split equally? What happens to his property? The rules of Monopoly offer no clarification on how exactly this card works, and the Cluemeister can find no clarification on the network of colorful tubes known as the internet. In his estimation, the best way for it to work is for the player who draws the card to choose which debt to honor first. In this case, Bob may choose to give his $50 to Charlotte and then default to Alan. Because Bob owes money he cannot pay to Alan, he goes bankrupt and Alan collects his property. Since Vermont Avenue is mortgaged, Alan must pay an immediate 10% interest penalty (look it up, it's in the rules!) As Alan is flat broke, he is unable to pay the $5 penalty and goes bankrupt as well, leaving Charlotte as the winner. Strange, yes, and a little sad.

But does the Chairman card really work this way? The Cluemeister doubts that anyone can really say. Fortunately, there is another, less elegant way for the game to end in two turns. Alan proceeds as above. Bob opens with snake eyes and lands on Community Chest. He draws the "Collect $50 from every player" card, thus bankrupting Alan (and pays the $5 penalty on Oriental Avenue). He then either lands on a property and uses the same trick to impoverish himself, or simply uses Oriental Avenue to do the trick. In either case, he rolls another pair of doubles. For his third roll he lands on the second Community Chest space, upon which he draws an unfortunate card and is knocked out, leaving Charlotte victorious.

**4)**Without trades, auctions or mortgages, it's much harder for players to go bankrupt. It is possible for Alan to acquire various monopolies (such as the dark blues or, with the help of the "Go back 3 spaces" card, the oranges) on his second turn and build them up sufficiently for Bob and Charlotte to go bankrupt paying rent for them on their own turns. A six-turn game is thus possible. But can we do better?

Without the above tricks, no combination of prices, rents, taxes and fees can come close to draining anyone's initial funds of $1500 until someone has a monopoly. Without trades or bankruptcies, it's impossible for anyone to get a monopoly on their first turn, even with lucky rolls and draws. Therefore, no one will go bankrupt on their first turn. Alan can go bankrupt on his second turn, but if he defaults to the bank, his properties will be auctioned, which violates the conditions of the problem. Bob can default to the bank because the game will end before an auction can take place, but we must find some way for Alan to default to another player--without requiring him to mortgage his properties.

It's not easy, but it can be done. Suppose that Alan, on his first turn, rolls double fives, double sixes, and a 9, landing him on Just Visiting, Chance and Community Chest respectively. Chance gives him a dividend of $50, while Community Chest gives him $45 from sale of stock. He now has $1595.

Bob, on his first turn, rolls double threes and buys Oriental Avenue. He then rolls a 3 and buys Connecticut Avenue.

Charlotte begins with boxcars and picks up the Electric Company. She then gets a 10, putting her on Chance, and draws the card that lets her advance to the nearest utility, which gives her the Water Works as well.

On Alan's second turn, he rolls double fours, passes Go, and buys Mediterranean Avenue. He follows up with snake eyes and buys Baltic Avenue. This leaves him with $1675. Now that he has the dark purple monopoly, he can buy and sell houses as much as he likes, and since houses are sold at half cost, he loses $25 each time he buys and sells one. He goes as far as he can go with it, finishing his spending frenzy with just $25 and no houses. Why does he do such a thing? Sun spots. For his final roll, he gets a 9, which puts him on the Electric Company. He now owes $90 to Charlotte. As mortgaging his properties would earn him only $60, for a total of $85, he cannot pay the debt and goes bankrupt. (No actual mortgaging takes place.)

Bob rolls double fours and lands on Community Chest, drawing the "Advance to Go" card. He rolls double fours again and lands on Vermont Avenue. He buys it, thus completing his light blue monopoly. He buys and sells and buys houses maniacally until he has only $5 left, with four houses on each property. Now he rolls a nine and lands on Community Chest again. He happens to draw the card that reads, "You are assessed for street repairs. $40 per house; $115 per hotel".

With 12 houses, his fee is $480. He sells all his houses (ironically) and reaps $300. If he were to mortgage all his properties, he would reach a total of $465, but that isn't quite enough to fix those streets. Bob therefore goes bankrupt and Charlotte wins.

SO, TO SUM UP, the answers are:

**1) 1 turn**

2) 2 turns

3) 2 turns

4) 5 turns

2) 2 turns

3) 2 turns

4) 5 turns

Only two readers, both Andys, sent in answers to this question. For Part 1, both hit upon using the Grand Opera House card to finish the game in 1 turn. For Part 2, one entrant found a 4-turn solution which he later revised to 3 turns, but apparently overlooked the possibility of rolling doubles to produce more complicated turns. The other, Andy H., improved slightly on the elegance of the Cluemeister's solution as follows:

*This depends on suicidally mortgaging and unmortaging a property as many times as possible in quick succession. It leaves the player with a mortgaged property and less than (1/2 + 1/20) the face value of the property - if the player had more money than that, he'd unmortgage and remortgage the property again. I'm calling this action "mortgage looping."*

Alan rolls a three, buys Baltic Avenue, and mortgage loops it. He now has a mortgaged Baltic and between $30 and $32, and ends his turn. Bob rolls double ones, lands on community chest, and draws "Grand opera Night." He tries to collect $50 from Alan who goes bankrupt and gives him Baltic and his cash. Bob runs the mortgage loop and ends up with Baltic and $30-$32. Bob rolls a five, lands on Chance, and draws "You are elected chairman of the board - pay each player $50." He can't afford it and goes bankrupt. Charlotte wins without ever having moved.

Alan rolls a three, buys Baltic Avenue, and mortgage loops it. He now has a mortgaged Baltic and between $30 and $32, and ends his turn. Bob rolls double ones, lands on community chest, and draws "Grand opera Night." He tries to collect $50 from Alan who goes bankrupt and gives him Baltic and his cash. Bob runs the mortgage loop and ends up with Baltic and $30-$32. Bob rolls a five, lands on Chance, and draws "You are elected chairman of the board - pay each player $50." He can't afford it and goes bankrupt. Charlotte wins without ever having moved.

This solution also works for Part 3. For part 4, Andy H. provided a six-turn solution with the aesthetic merit that it "could actually be played. No one is trying to lose, and everyone makes rational decisions based on the circumstances. This one also works for any number of players." The solution is also impressive in that it utilizes a monopoly on the light purple properties (which the Cluemeister barely even considered)--but still, it is six turns, not five.

Even so, Andy H. wins a prize to be collected from the Medallion Hunt Office (located conveniently so as to occupy exactly the same space as the Bozo Bus Tribune office) at Minicon 46...which is later this month!

Watch this space for one final message from the Cluemeister's Corner before Minicon, including a list of winners and information regarding the Medallion Hunt. In the meantime, as always, feel free to write to

*thorin (dot) tatge (at) pobox (dot) com*with your post-mortems and remarks.