When Should You Play the Lottery?

A lot of people play the lottery dreaming of things they could do and buy with the winnings. The problem is they are putting their hope into something so insurmountably stacked against them that they don’t see their awful misuse of their hard earned money. So, when should you play the lottery? The short answer is almost never.

The Long Answer

Mathematically speaking, you are very very very unlikely to ever win the lottery. The chances of drawing a winning powerball lottery ticket are approximately 1 in 292 million. To put that another way, if you were to purchase 292 million lottery tickets covering every single possible combination of numbers you would have 1 matching ticket. Congratulations, you’re a lottery winner!

But wait, that is entirely unrealistic. Unless you are secretly The Flash I doubt you will ever have the time or physical capacity to collect all of those tickets. Oh and did I mention it costs nearly $600 million dollars to buy all those tickets? There’s more still, you have to pay taxes on any winnings you received which also has a chance to be split among multiple winners! You would only see a fraction of that $700 million dollar jackpot and you are actually guaranteed to lose money overall.

Okay, let’s look at something more reasonable. You’ve gone ahead and bought your lotto ticket and are hanging onto that thought, “There’s still a chance it could be me!”

vending machine

DANGEROUS!!

Let’s take a look at some things that are more likely to happen than winning the lottery. For instance, the odds of getting struck by lightning at any point in your life are approximately 1 in 12,000. That is way more likely than hitting the powerball. Even still, getting hit by lightning twice in your lifetime has more likelihood at 1 in 144 million. Hmm, looks like it is still half as likely to win the powerball than getting struck twice!

How about this. The probability of getting killed by a vending machine is still more likely than winning the lottery at 1 in 251 million. I can’t even imagine a situation that would create the necessary chain of cause and effect that leads you to being killed by a vending machine.

When You Can Play the Lottery

Now, there actually is a time when it can be a good idea to play the lottery. In poker, it’s called pot odds and it applies perfectly to your lotto ticket.

Pot Odds Explained

When a poker player is presented with a situation where he needs to call, that means to match his opponent’s bet, he will consider how much he stands to win (the pot) versus how much he must put in. Then he analyzes that ratio (pot odds) against the probability of his hand being better than the opponent’s.

Here’s an example: If the pot size is $20 and the amount the poker player needs to call is $5 then he has 5 to 20 pot odds which can be simplified down to 1 to 4. For every $1 he puts in he stands to make $4.

We don’t know if this is good or bad until we compare to his probability of winning. Now, if he sees his hand having a 1 in 5 chance of winning he might consider forfeiting the hand because he has poor pot odds. What makes them poor pot odds is the fact that his chances of winning are worse than the bet to pot ratio. If he had a 1 in 4 chance or greater it would be considered good pot odds since his chances of winning are now better than the bet to pot ratio.

poker hand

Pot Odds Applied to the Lottery

In the case of the Powerball, we know the probability of our ‘hand’ winning. We also know how much we stand to win. Finally, we know how much it costs us for a ticket. Two of these factors do not change, or very rarely change. A ticket is always $2 and you always have a 1 in 292 million probability of winning. What does change is the pot size or the total possible winnings. In order to get good pot odds on our ticket the prize needs to produce a ratio smaller than the probability of winning.

If our ticket only cost $1 then we need to have a prize pool of at least $292 million to match the probability of winning. However, our ticket costs double that. So the prize pool has to double as well. Now, the prize pool needs to be at least $688 million to match the same odds.

The Reality

Hey, the lotto claims to have that size prize pool a lot! I guess I should play it a lot too! Wrong. Keep in mind you will only get at most 70% of those winnings after federal and state taxes. And if you happen to share your winnings with another person you can halve that number as well.

With perfect circumstances where you are the only winner and the government only takes 30%, the jackpot must be at least $990 million. Again, that’s under perfect circumstances. The only time I’ve ever played the lottery was when the jackpot was at a record setting $1.3 billion (later went on to $1.6 billion) which looking back probably still wasn’t enough given the amount of people playing I would wind up splitting amongst other winners.

Now, this is only a justification to play the lottery for the fun of it with only 1 ticket, any more is not recommended. In the end you are still more likely to die trying to get that stuck snickers bar in the vending machine.

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