Watch this Video Guide on Computing Powerball Odds

Hello everyone, this is Mike and in this video, we are going to explore how to determine the odds for winning in the Powerball lottery as well as the expected return on investment for a Powerball ticket.

Hi friends, I’m Mike and today, I'll show you how to work out the chances in the Powerball . Everyone on my forum Some viewers have mentioned that my videos tend to be lengthy, so I’ll aim to present the calculations more swiftly than in my past videos.

Let me go over the rules real quick:

For the lottery, five white balls will be drawn from a pool numbered one to 69, without replacement, meaning a ball can only be selected once, alongside one Powerball drawn from a separate set of balls ranging from one to 26.

Players will replicate this process and hope their selected numbers align with the ones drawn in the lottery. I've provided the payout table for the jackpot here, inputting a hypothetical amount of $100 million as a benchmark. This tutorial presumes you have a basic understanding of the COMBIN function in Excel which is the mathematical concept of choosing X items from a total of Y.

If you don\"t know how to do that..

I recommend you watch my previous tutorial discussing probabilities in five-card stud poker. which I just made yesterday.

Let’s dive right in. It’s evident that there is only a single combination to win the jackpot since you must select the exact same numbers as those drawn by the lottery, and there’s no other way to achieve that. If you correctly pick four of the five white balls along with the Powerball, you win $10,000. By the way, a ticket will set you back two dollars.

What is the total number of combinations available?

The total combinations possible are derived from 'five choose three', which indicates the various ways to select three out of the five lottery balls, along with 'sixty-four choose two', representing ways to select two of the losing balls from a group of 64. There are 20,160 ways to match three out of five in Powerball. If you match two out of five and also get the Powerball, you will win $7. The number of combinations for this scenario is 416,640.

If you correctly pick one number in the Powerball - you will receive $4, and there are approximately 3.2 million combinations that can lead to that outcome. If you fail to match any of the white balls but do get the Powerball, you will also win $4. Securing the Powerball guarantees you a win of some sort. The number of ways to select five numbers from the pool of 64 the lottery did not pick is about 7.6 million.

Now, let's examine the scenarios where you didn't pick the Powerball

In those cases, you would simply multiply the number of combinations of winning scenarios by 25, as the lottery will only select one Powerball, leaving you with 25 numbers in the pool that were not chosen. Should you fail to select the Powerball, there are 25 different ways in which this could have occurred.

We will now multiply the combinations we calculated earlier by 25. This reveals that the overall number of potential combinations adds up to 292,201,338. This figure is often cited in media discussions as the odds of winning, signifying a one in 292 million chance. In order to work out the expected return for your lottery ticket, let's calculate the likelihood of winning any specific prize, which is determined by dividing the number of winning combinations by the total combinations available.

Next, let’s analyze the anticipated returns from different prize levels, calculated as the probability of winning multiplied by the prize amount for each scenario. For a jackpot of $100 million, you might expect to gain back around 61.8 cents from a $2 ticket, meaning you recoup approximately 30.9% of your original wager. Further breaking it down, we see that the $100 million jackpot contributes about 34.2 cents towards that expected return on your ticket value. Essentially, for every $100 million in the jackpot, that translates to an expected return of about 17.1%.

Before comments arise on this topic, keep in mind that this analysis does not incorporate three key factors:

• Firstly - when you win the jackpot, it can be received either as an annuity or as a lump sum, which is generally 61% of the total jackpot amount.
• Secondly, - tax implications. Winning the jackpot brings a substantial tax burden. While I’m unsure of the current rates—especially after the recent tax cuts under Donald Trump—you should be prepared to allocate a significant portion of your winnings to federal taxes, in addition to state taxes.
• Lastly - jackpot sharing can become an issue. This might not be a concern for smaller jackpots, but once the prize grows significantly, like nearing half a billion dollars, competition increases, and there’s a high likelihood of multiple winners, meaning any prize you win may need to be split with others.

Finally, let me say:

It’s worth noting that in California, the rules differ; they don’t distribute fixed prizes but operate on a pari-mutuel basis. Ultimately, the takeaway is that lotteries like Powerball are generally poor bets, and I advise against wasting your money on them.

For additional insights regarding Powerball, I have a comprehensive section dedicated to it on my website, Wizard of Odds , where you can find information about expected ticket sales by jackpot size and how jackpot sharing influences your odds. Admittedly, I’ve gone over the intended duration for this video, so I’ll wrap it up here.

Thanks for watching.

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Written by: Michael Shackleford