Investing can be tough some times. Wouldn’t it be great if you just won the lottery? Man, that would set you for life. Seriously.

Now, we’re not suggesting you run to the closest mini-mart with your life savings. The odds of winning the Big Game (a multi-state lottery open to adults in Massachusetts, Maryland, Georgia, Illinois, Michigan, New Jersey, and Virginia) are roughly 70 Million to 1. That is only slightly better than your chances of making money going long on

So we all know playing the lottery is a suckers game, but does that mean you should avoid it entirely. The question came up for me when a group at the office I work at started a lottery pool. These are “clubs” where co-workers pool money together in order to increase their chances of winning. If the group (with about 20 members now) hits the $300 Million jackpot, they’ll split it 20 ways. Cut $300M in half for taking the cash option and split it 20 ways, and you get $7.5 Million per person. Not too shabby.

Anyway, I didn’t contribute to the pool the first few times they played since I know how unlikely it is to hit the lottery. Take this analogy from an article by Kevin Devlin entitled Lottery Mania:

Well, imagine laying standard playing cards end to end from New York to San Francisco. The underside of just one of those cards is marked. Start to drive across country, and at some point stop and pick up a card. If you’ve chosen the marked card, you win the jackpot. Chose any other card and you lose. How much would you be willing to pay to play this game? In terms of the odds, you’ve just played the Big Game.

Makes you feel good about blowing your weekend finding a good oil stock to invest in, doesn’t it? Still, even though the odds are so terrible, there is a time to play. I mean isn’t it work about $3 per week to ensure that if my entire office became millionaires I wouldn’t be left out. “Jason, we hit. We hit! Oh… you didn’t enter the pool this week? I’m so sorry. Well, good luck with the project; I’m off to Fiji.” This kind of reasoning aligns with Kevin Devlin’s suggestion for playing the lottery (emphasis mine):

However you look at it, the odds against winning the Big Game jackpot are truly staggering. Does that mean that the best strategy is not to play at all? Oddly enough, the optimal strategy is to play, but to restrict your wager to an amount of money that is truly of no value to you.

Optimal strategy #1 is to play the lottery with a sum of money “that is truly of no value to you”. $3 a week is right about at my “no-value” level; so I shouldn’t feel bad blowing it on the lottery. In addition, $3 is well worth the entertainment I get from anticipating the results and the comradeship that is created by sharing the moment with my co-workers.

So what is optimal strategy #2? While strategy #1 focuses on minimizing the impact to your finances (in perception at least), strategy #2 will focus on maximizing your odds to win. To understand this strategy, I’ll describe a very simple lottery scenario.

The PA State Lottery Association has gone crazy. They’ve setup a lottery in which the drawing is of just 1 number, ranging from 1 to 3. In any given day, the lotto number could be 1, 2, or 3. Let’s figure the odds if you played $1 (or 1 entry) per day for 3 days. This is easy to do; just multiple the chance of losing in any given day by 3 and subtract that from 1.

2/3 * 2/3 * 2/3 = ~0.3 or a 30% chance of hitting nothing over 3 days.

1.0 – 0.3 = 0.7 or a 70% chance of winning over 3 days.

What if you just played $3 on the first day? Obviously your chance of winning would be 100% since you could cover all 3 numbers. The lesson here is that playing all of your lottery budget in one drawing is going to get you better odds that playing every day or every week.

Now don’t get too excited. The difference in chance of winning using this strategy goes down the larger the possible combinations are. So you’re not going to increase your chances of winning the Big Game by 30%. Let’s do some calculations to see how much you would increase you chances by playing $156 in one drawing rather than $3 per week.

1 – [chance of losing] ^ [number of times playing]

$3 per Week:
1 – (69,999,997 / 70,000,000)^52 = 0.00000233%

$156 in One Shot:
1 – (69,999,844 / 70,000,000)^1 = 0.00000233%

What gives here! Well, turns out that my calculator (Excel) can’t even tell the difference in strategies with these huge numbers. But if you’re an astronomer (astrologers have their own strategy by the way) or used to dealing with really big numbers, you might be moved by strategy #2.

Also notice that strategy #2 goes completely against strategy #1. $156 is an amount of money that has meaning for me. So it would be hard to part with on a long-shot gamble.

Hopefully we here at InvestorGeeks and others in the blogging community can help you think of some more fruitful things to do with your money. But you also shouldn’t feel bad playing a few bucks each week as long as you won’t miss the money. Good luck.