Design “Riddle”
Posted by Rob Herman at August 29th, 2007
How do you split a cookie between two people? One person cuts, the other one chooses. Great.
OK, Solomon, help me out with this one. I wish to assign starting positions on, essentially, a map board. Assume that the map board has no particular symmetry and, in particular, no rotational symmetry. Resources may be unevenly distributed. Furthermore, I would like to adhere as closely as possible to the following parameters:
- From 3-5 players will be choosing locations. Each player will choose basically one location.
- It’s OK if the locations are not quite equal, but no position should be hopelessly bad. In particular, it is not OK to have every player choose one location and then randomize who gets what location.
- Two players should not be able to collude to give one of them an excellent location.
(Likewise, there should be no frustration that an inexperienced player has inadvertently handed out a gift.) - It should not take too long–nothing very mathematical. The Settlers of Catan initial settlement placement is the outside limit for how long this should take.
- Since this will take place before a new player gets to see the game, it should be possible for experienced players to offer meaningful advice to a new player without having to worry about who among them will be helped or hindered by the placement.
If you can’t guess, I’m fishing for ideas to see if this basic layout can be made to work. I think it would be a lot more flavorful than a clever board with rotational symmetry for 3, 4, or 5 people; yet I still want the basic balance I’ve come to expect from Euros.
There’s always the trusty auction. Players could bid victory points, or starting capitol. To keep it quick, have players choose locations in reverse drop out order.
You could go the Amun-Re route for bidding.
Or, the start player assigns bonuses to each of the areas. So a less desirable areas comes with 5 gold (or whatever), while the best area starts with no extra gold. Players than choose starting locations, starting with the player to the left of the start player. This way the player that assigned the bonuses gets the last choice. This could get dicey if the start player doesn’t know what they’re doing though.
Iterated Pie Rule!
This is formulated for n starting position cards. Player 1 takes the pile, and divides it in half. Each other player then chooses a pile, and finally player 1 chooses one of the piles as well. If the number of players that voted for a pile is equal to the number of cards in that pile, shuffle the cards and deal one randomly to each player. If a player is alone in voting for a pile, he gets his choice of card. Otherwise, repeat this process recursively on both sub-piles until each player has been assigned a card, with only the people that voted for that pile eligible. In each case, resolve the pile the divider didn’t vote on first. Pass the privilege of dividing the piles to the next eligible player to the left of the last person who divided.
Players may not vote for a pile if there are already a number of players voting on it equal to the number of cards.
Example:
5 players, 15 cards
Player 1 puts 6 cards in pile 1, 9 cards in pile 2.
Player 2 votes for the pile of 9
Player 3 votes for the pile of 6
Player 4 votes for the pile of 9
Player 5 votes for the pile of 6
Finally, Player 1 votes for the pile of 9.
We now resolve the pile of 6 (because Player 1 didn’t vote on it).
Player 3 divides, cause he’s next on the left of Player 1.
Player 3 divides the cards into two piles of three.
Player 5 votes for one of the two piles, then Player 3 for the other. They’re now alone in their respective piles, so they choose a card and are done.
In the pile of 9, Player 2 divides into a pile of 4 and a pile of 5. Player 4 votes for the pile of 4, Player 1 then Player 2 vote for the pile of 5. Player 4 is alone, he chooses his card, and is done.
Player 1 then splits the last pile by the pie rule, and he and Player 2 choose a one of the cards they end up with.
There is the possibility of collusion in that player 1 could leave a pile of 1 card for player 2 to snatch up, for example. A possible modification that would alleviate this to some degree is to require the players to put equal numbers of cards in each pile. This can still arise in later rounds, but I think it’s less of a problem, since a player would have to walk into it - ie, if a pile contains two cards of interest amidst junk, and two people have already voted for it, it’s clear that if anyone else jumps in, they’re risking getting screwed. Since the divider chooses last, it’s in his best interest that both piles are equally valuable so that he isn’t left in that unenviable situation.
Mark: I like your idea, in particular the option to let the players compensate locations with extra resources. A novice-friendly alteration would be to allow one person to place more than their share of the settlements, al long as the picking is fair.
Fu Leng: That’s pretty neat. I like it. The only disadvantage I can see is that the value of positions may change depending on which are chosen. For instance, a position may be very strong unless it it “boxed in” by others, in which case it is poor. This happens in Settlers pretty often.
I saw another technique for dividing resources that, unfortunately, is completely unsuited for this challenge. It works better for an abstract pie or pile of resources. It works like this: one player carves out a share of the resource, and is the “owner” of that share. Any other player has a chance to reduce the size of the share, putting whatever’s removed back in the common area; this transfers “ownership” to that person. When nobody wants to reduce the share any more, the “owner” takes the share and drops out of the distribution scheme.
Rob, I do agree that the ‘boxed-in’ factor is an issue; to minimize that partially, this is why the procedure is to do the first split, then all the second splits, then all the third splits, and so on, so that players have some idea of what the other likely starting positions are going to be. Another way of dividing the spoils that may reduce this factor would be when a player ends up alone voting for a pile, he picks up the entire pile. Therefore, a strong position that is isolated would be voted lower, while weaker positions that work well together would be valued higher when in the same pile. This also allows for greater variance in the quality of each card, since players could end up with differing numbers of cards.
This probably doesn’t work but I think it is a neat system and I wanted to see what people thought.
Players are numbered 1 to N. Each player secretly selects a location. When everyone has selected a location everyone reveals which location they picked. Then every player starting with player 1 in ascending order will be assigned a position in the following way
If your selection matches someone elses selection then each of the players who made a selection that matches yours gets to vote on what location you get and you can break a tie if needed. Then anyone who matched your selection and anyone who selected the spot you ended up with get to secretly pick an available location which has not been selected already and then reveal them once everyone has picked.
If no one matches your selection then you get what you selected.
Like I said I doubt that this meets the requirements but I am curious what dynamic and selection strategies it would generate. What are peoples thoughts on this?
Edit to the last comment
When a match is resolved instead of voting which would land you in the worst spot instead you get to choose from any spot that has not been selected already. Then everyone who matched you makes a new selection that has not already been selected. This way you still don’t wnat to match anyone but still have a chance of wining if you do. Also with a distinct ranking of locations and sufficently savvy players: player 1 gets the 2nd best spot 2 gets the 4th best and so on … which is probably not ideal
I’m a fan of the auction mechanic, but with one caveat… Initial placements should be made by the players, using grey pieces. Ownership of those placements could then be the auctioned commodity. Variant: make all placements, then bid on each with a pool of starting points, converted to some resource at a later stage. This takes out the fuckanewb problem and the backfire-surround issue. I don’t know if I prefer limited auction-points at startup or unlimited bids with big spender =zero resource bonus and everyone else making the difference.