A Scientific Way to Compare Risk vs. Reward in Games of Chance

Calculate Your Risk to Reward Ratio Before Playing the Lottery

Dice Rolling. Will They Land in Your Favor?

If you are playing games of chance like sweepstakes and lotteries, it's smart to concentrate your efforts where you have the biggest potential reward for the smallest amount of risk. Here's how to calculate the ratio of risk to reward for various games of chance to ensure you get the best possible outcome.

There are a few ways to determine the best sweepstakes and lotteries to enter. For example, you could use the odds of winning a giveaway or lottery to decide which games to spend your time entering. However, odds give you an incomplete answer because they don't take the size of the prize into consideration.

While you might be more likely to win a $10 gift card than a million-dollar Dream Home or a billion-dollar Powerball jackpot, winning the second two prizes would change your life while the gift card would only be a nice bonus.

On the other hand, when the odds are 100 million to one against you, the chances of winning are so low that you risk falling prey to sweepstakes burnout before you win a prize.

When you are talking about games where you pay to participate, like the lottery, relying on the odds alone to determine whether or not you should buy a ticket gets even chancier. Before you spend your hard-earned cash, you should be sure you know how high your risk is going to be. And that's where the risk to reward ratio comes in handy.

What a Risk to Reward Ratio Is

A risk to reward ratio is a simple but scientific way to evaluate whether taking a risk is likely to pay off for you. The concept comes from the investment world, but it can be adapted to evaluate various games of chance to see which make the most sense for you to play.

The most basic risk to reward calculation is to divide the reward, or the value of the potential prize, by the cost of playing. The lower the resulting fraction is, the lower the risk. Many investors find that the risk is not worthwhile until the ratio reaches 2:1. If the fraction comes out to be larger than one, your risk is higher than the profit you could potentially make from playing.

When it comes to games of chance, this simple risk to reward ratio usually looks great. For example, let's say that you are considering whether or not to enter a raffle at your local school. The tickets cost $2 apiece and the prize is a $100 Visa gift card. Your risk to reward ratio would be two divided by 100 or 0.02, nice and low.

A lottery has an even more impressive risk to reward ratio. If you pay $2 per ticket and the jackpot is $100 million, you have a risk to reward ratio of .00000002.

This method of evaluating risk has limited usefulness for people who are entering sweepstakes and lotteries since it doesn't consider probability. While the risk to reward ratio looks great for entering the lottery, the odds of winning approach zero.

So another way of applying the basic risk to reward ratio to lottery purchases is to consider the reward to be zero, at which point it becomes clear that, mathematically, buying tickets is a waste of money. But that way of thinking doesn't help much if you have decided you want to play the lottery but you want to know which games have the best potential of winning.

One case for using a basic risk to reward ratio when entering sweepstakes is to compare the risk of using paid versus unpaid entry methods. For example, if you are considering using the HGTV Dream Home "loophole" of sending unlimited entries per mail, you can see how paying for stamps and envelopes affects your risk.

How to Factor in Probability When Calculating Your Risk and Reward

If you want to get a better grasp on which games of chance to play, you need to be able to include both the prize value and the probability of winning in your risk and reward calculations. You do this by factoring the odds into your potential profit to get a value for an estimated reward. 

The formula you'll need to follow to do this calculation is:

Estimated Reward = (odds of winning expressed as a decimal) x (prize value)
Modified Risk to Reward Calculation = (cost of playing) / (estimated reward)

Let's use the Powerball Lottery as an example since the odds of winning Powerball are fixed and do not depend on the number of entries. For this example, we'll assume that the jackpot is worth $100,000,000.

The odds of winning that jackpot, according to the Powerball website, are one in 292,201,338. With some rounding, that means you have a 0.00000342 percent chance of being a winner. Multiply the hundred-million dollar jackpot payout by that percentage and you get a reasonable value for your estimated reward: .342. 

When you apply your risk to reward ratio and divide the cost of a ticket ($2) by the estimated reward value ($.342) you get a risk to reward ratio of 5.8:1. Since that number is (quite a bit) greater than one, you can see that you've crossed the threshold where the estimated payout is more than your investment in tickets.

Of course, the risk versus the reward of playing Powerball is actually more complicated than this, since the lottery has many more payouts than just the jackpot, and each potential payout has its own odds. Matching the Powerball alone has odds of approximately 38 to one and a $4 payout. 

To do the math here, you need to divide one by 38 to get approximately 0.026. Multiply the $4 payout by 0.026 and you get .104 as your estimated reward. Then divide .104 by the cost of a Powerball ticket ($2) to get 0.052:1 and you have your risk to reward ratio. The risk is still high, but better than those of winning the jackpot.

For another example, let's say you are trying to determine whether or not to send entries to the HGTV Dream Home Sweepstakes by mail. We'll use an example where the HGTV Dream Home is worth $1,000,000, the cost of a mail-in entry (including stamps, the envelope, etc.) is $0.75, and the giveaway gets 100 million entries.

If you've already taken advantage of your two free online entries, a single mail-in entry will bring your odds of winning down to 3 in 100 million or .00000003. Multiply those odds by the million dollar prize value to get an estimated reward of 0.03. Divide the cost of mailing in an entry ($0.75) by the estimated reward to get a risk of 25. With those odds, you might be better off sticking to your free entries.

How to Use Your Modified Risk to Reward Ratio

It should be no surprise that the risk to reward calculation for playing the Powerball lottery isn't in your favor. The same holds true for many games of chance such as roulette or blackjack. There's a good reason for the old saying, "The house always wins."

There's no reason not to throw a couple of bucks toward lottery tickets, as long as you have the money to spare and you realize that the most likely outcome is that you are going to lose your cash. Sometimes it's worth a couple of bucks to dream about striking it rich.

However, these calculations can help you decide where your time and money are best spent. If you are considering which lottery to play or which paid entry method to use to enter sweepstakes, calculating the risk and reward gives you a scientific way to compare them.

Note that these calculations only deal with financial risk. When you enter online sweepstakes for free, you have a different type of risk because your time and energy have value as well. It's a good idea to create a sweepstakes strategy that balances sweepstakes with big prizes but low chances of winning with giveaways with better odds so that you win often enough to feel your time is well-spent.