Pick Your Power Mafia 2! - Page 5

On September 07 2010 11:06 SiNiquity wrote:


Problem
Your system is not designed with a player's goal in mind. Your justification for keeping the 2 number system is that it's easier to pick 2 unique numbers instead of 1 unique number. But that's not the player's goal. The goal is to optimize one's position in the list, which hinges on picking the highest unique number. There is little strategy involved with choosing the second number, and it is not justified in the additional complexity.

Proof
Here's the strategy for choosing the second number. For N > 0, suppose you anticipate overlapping with N players. Then you should choose a number between N (safest, assuming minimal overlap, RNG with the last guy for 2nd to last place) and (N+1)/2 rounded up (riskiest, assuming maximal overlap). This holds both in the current system and in the proposed uniqueness-first system (except the safest bet is N+1 instead of N for N > 1).

In the case of N = 1 (arguably the most common case), the optimal answer is always 1 (giving you a 50% chance at the top spot, compared to a 0% chance for any other number choice). Furthermore, the penalty for overlapping in the second column is negligible when compared to overlapping in the first column, and as a result you'll see riskier play here. This mostly explains the distribution of the second column: 35% (7) of the players chose [*][1] and 15% chose [*][2], and those that chose various numbers such as 9, 20, etc. just didn't take the time to analyze the problem (or perhaps misunderstood it).

Solution
However, since you seem interested in keeping the second column, then I suggest the following: all overlappers are thrown into a single pool, completely disregarding their initial choice, and ordered entirely based on their second number. Overlaps here would follow the current system (edit: with the addition of uniqueness taking priority), with overlaps being bumped to the bottom and RNG'ing within their subgroup for order.

In the current system, your first number choice is shooting either for a low number and hope it's not overlapping (e.g. BrownBear's 20), or for a high number but running under the assumption it will probably overlap (e.g. 75% of players choosing numbers 10 or less).

In the new system, your first number choice is first and foremost a unique number, as its rank is meaningless if it's not unique. The second number then will play much like the current first number, albeit on a slightly smaller scale (as the pool size will be smaller, yet just how much smaller will not be known from the outset - an interesting twist IMO). This gets you closer to your stated goal: players choosing 2 unique numbers.

Hope you take this into consideration Ace.