I’ve been seeing commercials about the Mountain Dew “Every 2 Minutes” thing for Xbox One, so I looked at how it works today. If I understand correctly, the “Every 2 Minutes” refers to auctions where you can win by bidding points that you get by entering codes you get from Mountain Dew and Doritos. There’s also a daily sweepstakes that you can enter with entries that you earn from those same codes. It looks like there are fifteen or so sweepstakes left at this point.
I’ve already got my Xbox One preordered, and I’ve mostly stopped drinking Mountain Dew, so the contest itself isn’t that interesting to me, but I was interested in how one might maximize the chances of winning. This is what I do during my lunch hour… statistics. That’s why I’m cool.
Let’s say that there’s only one other entry in each sweepstakes, and that I have fifteen tickets to put into whichever sweepstakes I want. If I put them all in one sweepstakes, I have a 15/16 shot of winning, or 93.75%. If I spread them out so that I put one in each entry, I have a 1/2 (50%) chance of winning in each sweepstakes.
From that, it sounds like I’m better off putting all my eggs in one basket, so to speak, but I don’t think that’s the case. I have a 50% chance of losing each sweepstakes, but there are 15 sweepstakes. The chance that I lose every sweepstakes is 50%^15, or 0.00305%, which means that spreading my entries out gives me a 99.997% chance of winning… at least once (see the image above). There’s also a chance that I could win multiple times, which means that spreading my entries out gives me a better shot at winning and gives me a shot at getting more than one Xbox One.
The benefit of entering in multiple sweepstakes seems to hold true when more people are entering, as well, though the benefit is somewhat lessened in this situation (0.14978% vs 0.14988% at 10,000 entries – see image). I’m still assuming that there’s an equal number of entries in each sweepstakes, but I honestly have no way of knowing if that’s true.
The takeaway from all this is that
statistics are fun the old proverb is right, and you shouldn’t put all your eggs into one basket.