So after my post on how dumb it was to play the lottery, a reader emailed me to be more concise with what I meant by “statistically fair shot of winning.” This guy must be a smarty pants because he broke down the math for me. He provided the specific odds of winning the 6/49 lottery. I haz the best readerz on the internetz!
Who is this reader? His name is Eytan. And how does Eytan claim to know all this? He’s an engineer for SkyPro and he, along with his team, created and developed this golfing product that they sell all over North America. I’m going to go out on a limb and guess that he is really, really good at math and knows what he is talking about.
This might be a bit of a snooze fest for those of you not interested in the details of the probability of winning a 1 in 13,983,816 game of chance, so I would suggest you go peruse 15 beautiful pictures instead. Or if you feel like exerting a modicum of brain power, go browse these 10 essential blogging tips for getting more out of your blog.
If you don’t follow my advice, you might risk going all ZzzzZZZZz at work over there. Yes, I know you’re
wasting spending time here instead of working! I promise I won’t tell your boss.
However, IF you are interested in how the detailed probability of playing the 6/49 works, read on!
I’m just going to copy and paste the email Eytan sent in so as not to
fuck up mess up any of the equations he so succinctly laid out. He even put it up on his personal website here. Take it away Eytan!
I love the articles. I’ve started reading them. One article I recommend you touch up is the lottery article. The math doesn’t quite add and might lead to readers losing confidence.
Remember the official odds? 1 in 13,983,816. Statistically speaking, you need to play 13,983,816 times to have a statistically fair shot at winning.
I found this statement a bit vague; what does a statistically fair shot at winning mean? I took it to mean you need to play 13,983,816 times to have a 50% chance of winning. If this is what you meant, lets take a closer look at the math and see what we can figure out about the odds of winning Canada’s 6/49.
Lets start by defining some notation. Specifically, we’ll say that p(n) is the odds of winning the lottery at least once after n plays. The odds of winning the lottery for one game is p(1) = 1/13,983,816.
If we played the lottery once, there are only two possible outcomes: win or lose. If you played the lottery twice, there would be four possible outcomes: lose.lose, lose.win, win.lose, and win.win. If we play 10 times, there are 1024 possible outcomes. If wanted to calculate the odds of winning, we’d have to add every single one of those up.
Lets examine the case when we play the lotery twice. As previously mentioned, we have four outcomes and they each having the following odds:
The odds of winning after n plays, p(n) is thus given byAs we play more and more games, the different combinations in which we can win increases, but there remains only a single way to lose. Since the sum of all probabilities is equal to one, we can subtract the odds of losing from one to leave us with the odds of winning.
Now, we are in a position to find out how many times you’d have to play in order to have a 50% chance of winning. We substitute 0.5 for p(n) in the above equation and solve for n.
Wow, that’s a lot of plays. With that in mind, we can clarify the sentence by saying:
Remember the official odds? 1 in 13,983,816. Statistically speaking, you need to play 9,692,843 times to have a 50% of winning at least once.
Well, looks like Eytan is about to put me out of the personal finance blogging business. I should just give him the keys to Kapitalust and pack it up. At this pace, it looks like he could out-math anyone in this blogging niche. It’s a good thing he’s not interested in that (or if he is I choose to ignore him).
All jokes aside, I am amazed that a reader would take the time to break down the probability like this and email me about it. I think it’s incredible. And I had to share it with all of you (who stuck around rather than moving on to look at pretty pictures).
The lesson I have learned: be less vague with my statements with readers like Eytan around.
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