How I Earn Money By Playing the Lottery
A new investing app called Yotta Savings has made headlines recently for their unconventional form of earning interest for their customers. Yotta offers a 0.2% annual return when keeping your money with them, which isn’t the best option compared to some of the other top savings accounts right now, but Yotta does offer a unique feature that these other banks don’t.
Each week, Yotta hold a lottery that offers prizes ranging from $0.10, all the way to their $10,000,000 grand prize. They even offer the chance to win your own Tesla.
For every $25 that you have saved in your account, you’ll earn 1 ticket into these weekly lotteries, so if you have $1,000 in your account, you’ll earn 25 tickets into each week’s lottery.
Each lottery drawing consists of seven numbers. Six of these are regular numbers which range anywhere from 1 to 73 and are shown in yellow on the chart above. There is one number drawn per night from Monday to Saturday. One Sunday night, the final ball is drawn, known as the Yotta Ball. This is the red ball shown in the prize chart above and can be any number between 1 and 63. We can see in the chart that any ticket that matches the Yotta Ball automatically wins a prize.
Here’s the question. After factoring in the additional interest from these lottery prizes, what is your total annual return when keeping your money with Yotta Savings? That is what we will be covering in this article.
Disclaimer: This article is not sponsored by Yotta or anyone else and is meant for educational purposes only.
Alright so here’s what we’re going to have to find out. We need to calculate the probability of a given ticket matching each possible combination of lottery numbers that are shown in the prize chart above.
Drawing values from a range of numbers without replacement can be modeled by what’s known as a hypergeometric distribution with the following probability density function, where M is the amount of numbers to choose from, N is the amount of numbers we are drawing, n is the amount of numbers that we have on our ticket, and x is the amount of our numbers that matched the drawn numbers.
For example, let’s calculate the probability of winning the $7 prize shown above. We can see that in order to win this prize, we will need to match three of the regular numbers, as well as matching the Yotta Ball. To obtain this probability, we’ll first find the probability of matching the regular numbers, and then multiply by the probability of matching the Yotta ball.
Using our hypergeometric equation above, we can find the probability of matching three of the six regular numbers by setting M=70, N=6, n=6, and x=3. We can use scipy.stats’s hypergeom function to help us find that the answer is about .64%.
from scipy.stats import hypergeom
hypergeom(M=70, n=6, N=6).pmf(3)>>> 0.006355289173932535
Now all we need to do is multiply this probability by the probability of matching the Yotta Ball, which is 1/63, so our final probability comes out to be about .01% or more exactly, 1 in 9,913.
hypergeom(M=70, n=6, N=6).pmf(3) * (1/63)>>> 0.00010087760593543706
When we check with Yotta’s official rules, we can see that this number seems to match.
So now that we know the probabilities of winning each prize, we should be good to calculate the total expected value of a ticket by multiplying each prize by the probability of winning that prize, but we have a small problem when we look at the additional rules.
It states that any prize greater than $1,000 will be equally split among everyone else that won that prize for the week. We are also told that the $10,000,000 prize is actually only $5,800,000. And lastly, instead of taking the Tesla, you are allowed to take your share of $37,990 instead, so we’ll use this value to make our calculations easier.
To find the new expected value of the prizes after learning that they are split if there are multiple winners, we will have to find out the number of total tickets in each drawing, but this number is not given to us. Fortunately there is a way that we can estimate the total number of tickets.
Yotta displays the people who have won a prize greater than $10 for each week as shown below. On the week of October 11, we can see that there were 29 people who won $51.72 each.
When we multiply 29 x $51.72, we get almost exactly $1,500, so I’m assuming that this means there were 29 people who split the $1,500 prize.
The $1,500 prize has a 1 in 346,955 chance of being won, so if it was won 29 times, our best estimate of total tickets becomes 10,061,695. Normally, there a much less than 29 winners who split the $1,500 prize, so I calculated the estimated number of tickets using the number of winners from the past 2 weeks to get a more accurate number. Our final estimate of total tickets in each week’s drawing becomes 6,450,169.
Now there are other possibly ways to earn tickets, such as referring friends or depositing money into your account for the first time, but if we ignore these and assume that all tickets come from the $25 that you have saved in your account, we’d estimate Yotta’s total user deposits to be around $161,254,225.
So, now that we have our estimate of total tickets in each week’s drawing, we can find the distribution of the number of winners splitting a given prize, and then can calculate the expected value of the portion of the prize you would get if you won it.
Here are our final estimates of true prize values given that we won the prize:
We can see that winning the $1,500 prize only has an expected value of $85.32, whereas the expected value of the $5,800,000 prize remains very close to its original value, just because the chances of two tickets matching all seven numbers in a given week is so low.
After multiplying each possible prize by the probability of winning it, we arrive at our final expected value of a given ticket for a single week’s drawing: $0.00856.
Now this does not seem like that large of a number, but remember that this is for each $25 in your account, and you receive these tickets weekly. Multiplying by 52.143 weeks in a year, we should see that over the course of a year, each ticket’s expected value becomes $0.4464, and when we divide by the $25 we had to deposit in our account for this amount, we arrive at a 1.786% return.
But remember, Yotta also pays out a .2% return on top of this, bringing the final estimate of the yearly return to 1.986%, which is much better than the returns of those other accounts we saw at the beginning.
Now this number will most likely fluctuate, as Yotta is still very new and is attempting to acquire new users, so I will try to update this article if I am aware of any changes that occur to the total ticket count, or to the prize structure.
Thanks for reading, and if you decide to sign up for Yotta, feel free to use my referral code: MTD. Please contact me if you have any questions that you’d still like to have answered, and also be sure to check out some of the other topics that I cover on my YouTube channel!
