To go a bit off-topic for background story: the original discussion on the other Vbulletin forum (MMO-Champion) handled about a specific way of distributing the items (mostly weapons and armor) that are the rewards for completing certain challenges inside the game of World of Warcraft (like killing a certain enemy, or reaching a certain place in a certain time). This distribution is usually handled by a system of randomized numbers as described in my earlier posts. Often times, in a group of, say, 25 players, there might be 5 players who desire a certain piece of armor or weaponry that is rewarded. For example, a staff that increases the power of your spells might be usable by 7 to 10 group members out of all 25 members of the group, while a certain shield might only be desired by 1 or 2 players.
When an item is being distributed, it usually happens as follows: the leader of the group states that players may "roll" for it, after which each member in the group that desires the item orders the game to generate a random number between 1 and 100. These numbers are displayed to the entire group. The player that generates the highest number is awarded the item. In the case of 2 or more players rolling the highest number, the leader asks for a "reroll", in which event the players generate another random number as mentioned above.
The earlier used numbers of 10 or even 25 random numbers being rolled rarely happens. If the entire group would like it (usually some really rare item like a dragon to ride) and everyone has equal benefits from it, the distribution of the item is done by another way. In this case, the group leader generates a numbered list of group members, followed by a random number between 1 and X (X being the amount of group members). The raid member that has the number corresponding to the rolled number is awarded the item.
But to return to the original discussion: depending on what group you are in, the group might choose to make the members generate a number between 1 and 100, or a number between 1 and 1,000, or even both depending on certain criteria which are hard to explain to a non-gaming audience. Someone made an offhand (and seemingly correct) remark that some groups choose to use the wider range because that allows for less chance of there being an aforementioned tie (i.e. 2 players generating the same number with noone generating a higher number).
Now, to return on-topic: the questions 4 and 8, concerning how many rolls it would on average take before you get a tie, also has a more well-known brother, the birthday paradox (
http://en.wikipedia.org/wiki/Birthday_problem). However, the problem I state is a more specific version that can be translated to the following: "Given n random integers drawn from a discrete uniform distribution with range [1,d], how high should n be before the probability p(n;d) that the highest number is drawn twice reaches 50%? Solve for d=100 and d=1,000."
I doubt it's the same way to solve this as it would be for the normal birthday problem, or even for the "same birthday as you" problem, because it isn't just 2 times the same number drawn we need, but that number needs to be the highest of all the numbers generated as well.
If there are any more questions that are needed to clarify the , please ask them and I will do my best to answer them.
Just to repeat the generalized question:
"Given n random integers drawn from a discrete uniform distribution with range [1,d], how high should n be before the probability p(n;d) that the highest number is drawn twice reaches 50%? Solve for d=100 and d=1,000."
Note that this is not homework or something. This is just something I've been wondering since I read that offhand remark.
