mega millions math

by santoki

From the roof deck bar atop the Hotel Gansevoort Tuesday past, the Imperialist, his cronies and I entered into a pact. It was similar to that which took place across the country – we would share the Mega Millions jackpot. Mind you, when we entered into the pact, the drawing had already taken place. You see, I bought $10 worth of tickets. Since we were all unaware of the results, they took the opportunity to buy into the potentially valuable tickets. Kind of like taping the game. Until the outcome enter your reality, anything is still possible.Everyone chipped in $2.50, and we were all proud shareholders in a fortune.

We won! Well, okay. The payout was only $3. Okay, according to NY State law, 2 out of the 3 Brits were ineligible to play. That’s neither here nor there.

Here is the ha ha. An interesting thing happens when smart people gamble. They tend to toss logic off the roof deck. Seriously, you wouldn’t believe the cock and bull math swirling about. Odds of winning were halved when doing this, or quartered when doing that. Now I don’t claim to know a ding dong thing about math, but I am pretty sure that in this case, my fu is good.

Here’s what we do know:

When buying a ticket for the Mega Millions, you will pick 5 numbers from 1 through 56. Next, you will select one number from 1 through 46. At the time of the drawing, if your 5 numbers match the numbers on the white pingpongs, and your solo number matches the drawn super duper deluxe gold mega ball, you are the mega winner. Doing a little mega math, we find that the odds of winning the mega prize are 1 in 175,711,536.

equation.pngCombinatorics, baby!

So what happens when you buy 2 tickets? According to some of our lotto-drunk cohorts, the odds are cut to 1 in around 88 million. By that math, you are either cutting your odds in half with each ticket you buy, meaning you only need about 28 tickets to hit the big one, or you might as well stop after 100 tickets, as the rate of improvement with each dollar you spend will be a fraction of a percent.

Frankly, I don’t buy into any of this cockamamie hocus pocus. That is because for all of those numbers, there are 175,711,536 possible combinations. The winning outcome represents 0.000000569114597006311% of the total, a mere drop in the pool of combinations. If this was math class, we would round to zero. If you buy 2 tickets, you are selecting 2 possible combinations out of 175,711,636, or 0.00000113822919401262% of the total. Again, we would usually round to zero. And 20 tickets? Your chance of hitting the jackpot is a just over a hundred-thousandth of a percent. Say it with me, round to zero.

With all that, I say happily that girlfriend will keep buying those $1 day dreams, even though the math might say that there is zero chance of winning.

So there.