## Thursday, June 7, 2012

### Somer Blink: Utility Calculations

Disclaimer: In this post I'm going to use **MATH.** I don't mean to scare anyone away, but its something I wanted to delve into. Also, please correct me if I'm wrong on anything here.

At this point, most people have heard of Somer Blink. If not, its a lottery system using all in-game isk and it is run by a third party website. I've been intrigued by it for a while, and despite not being much of a gambler, I decided to give it a shot today. I threw in 250M isk to start, and figured if I lose it all, no big deal. I decided I wanted to calculate how many tickets I should buy. I started working on the math and then promptly got caught up in just blinking as much as possible. Out of the 250M I used to start, I got as low as 1.5M isk remaining. Then I won a few big ticket ships and got right back in the game. I'm currently sitting at 493M isk. At that point, I knew I was getting pretty lucky, so I wanted to actually run down the numbers for this lottery. The results surprised me.

To me, this looks like a classic problem in Expected Utility, which is a concept out of Economics and Game Theory. To be honest, I studied engineering, not economics, so forgive me if I've botched something along the way. Based on what I saw though, this is the formula for utility:

L = pA + (1-p)B

where L is the lottery's utility, p is the probability of option A, and 1-p is the probability of option B. To translate this to Somer Blink terms, the probability, p, is the number of tickets purchased divided by the number of tickets available. A is represented by the value of the ship minus the cost of the tickets purchased, and B is simply zero, since losing costs nothing (outside of ticket cost, which is already accounted for). So, our formula for Somer Blink is as follows:

L = (n/n_max)*A - n*bid

By changing values of n (number of tickets bought) up to n_max (total tickets available for specific lottery), you can see the utility of each possible number bought. If we rearrange this equation, we get a very useful form for the utility.

L = n * (A/n_max  - bid)

Very clearly, the utility is proportional to the number of bids. The question is whether or not the other quantity is positive or negative. As is almost certainly by design, I have yet to find a blink that has a positive quantity for the (A/n_max  - bid)  term. This means that utility is decreasing for every bid you place on an item. It also means that utility is negative for all n, indicating that there is no rational reason for you to bid ever
Taking a step back, this all kind of makes sense. If the lottery were set up so that you pay one eighth of the price of the ship, and there are eight slots, you have perfect odds. You should make your money back exactly (and by exactly, I mean statistically over time). Since this is a system where the bids are more than the respective share of the ship, you're supposed to lose over time. That's how Somer Blink makes isk.

There's one last important thing to note. You can buy enough tickets so that you automatically lose isk. Divide A by the bid price and round down to the nearest whole number. Don't be a dummy bidding to automatically lose money.

What does this all mean? Probably not a lot at the end of the day. If you buy multiple tickets, you'll earn less when you win, but you stand a better chance at winning each individual blink. Like almost all lotteries, its not really what you'd call a good investment. On the other hand, someone still has to win, right? If you get lucky, then good for you and enjoy the ride. I've doubled my money already, why can't you? Best of luck.

#### 1 comment:

1. Fun analysis - glad you're enjoying the site :)