Probabilities for an extended ticket lottery – revised

This paper updates the original with a section on expected winnings, a conclusion, simplified Equation 3 and a lot of rewriting through the whole thing to make it more consistent.

NOTE: This post has been imported from my old it’s learning ePortfolio readables blog.

ePolio اثنين

In my previous post I shared a few of my complaints on the ePortfolio system.

I’m not done complaining yet.

Since my last post I’ve noticed that it’s problematic (read: impossible) to upload attachments in Firefox or Opera, but somehow IE always works. Seriously, it can’t be that hard to properly implement the upload feature that it had to be made IE only.

And also a ticking time bomb of sorts: Anonymous comments = gigantic spam magnet

Footlike notes

1 اثنين is Arabic for the number 2 according to translate.google.com, and also “Jan Magne” is apparently “Magnetic” if translated to Chinese and back into English. Magnificent!

Edit: Google “fixed” the translation so now it returns “January magne” although “Magnificent” will currently return “Majestic”. I enjoy to mess with those translation services.

NOTE: This post has been imported from my old it’s learning ePortfolio blog.

Probabilities for an extended ticket lottery

This paper describes an extended ticket lottery model with an upper bound on the number of tickets and how to maximize the probability of success. The lottery works on the basis that there will always be one and possibly two winners each round even though there are more tickets in the pool than the number of tickets distributed to the participants.

It can be compared to a competition where participants guess a number and the winner is the one who made the best guess. This way the winner does not necessarily have to guess the exact number, but must be the one who guessed the closest number. If the range within where the winning number is chosen is known in advance and nobody can is allowed to pick the same number the probabilities are as described in this paper (probably).

The method of maximizing the probability of success was intended to be used for the type of ticket lotteries being run in the online game Jottonia.

The beauty (read: inherent uglyness) of these results is how Equation 3 takes care of calculating unused tickets covered by a picking the ticket in the middle of a gap. Honestly, there must be a simpler formula which does the same job.

NOTE: This post has been imported from my old it’s learning ePortfolio readables blog.