East Columbus Rotary Club - RotoLotto
A year or so ago I put a couple of comments together about the fun of the weekly drawing vs. the odds of winning. There were a couple of positive comments (we like those) with few complaining that I had taken the mystery out of the process.
I have been recently asked to re-publish the comments about the odds of winning the weekly Rotary lottery. The facts might be interesting if you missed the first version.
In games of chance, there are rigid rules of probability which one must follow in order to be ‘ahead of the odds’ just a little. First, a recap of the way the game is played. A standard deck (52 cards) starts the fun. A card is removed each week until some person draws the ace of spades. For the purposes of selecting who gets to draw the next card out of the deck, a preliminary drawing is held to see who will have that honor.
In order to visualize the mathematics of the situation, let’s consider a situation like the following. Suppose 36 tickets are sold for $1.00 each for a chance to draw a card from the deck. If you have one of those tickets, you have 1 in 36 chances of being selected to draw a card. While the odds are not great, you are compensated 1/3 of the ticket sales ($12.00) for having your ticket selected. Depending on the number of cards in the deck at the time your winning ticket is selected, you could have 1 in 1 through 1 in 52 chances of pulling the ace of spades.
If you pull the ace of spades, you will win the “big” pot. This amount is not fixed, but steadily grows by 1/3 of all of the ticket sales of the previous week. If the pot starts with $100 and 12 tickets are sold, the pot would grow $4.00 to $104 if the ace of spades wasn’t selected.
Let’s look at this from the mathematical point of view. Your odds of winning the big pot are determined by the number of tickets sold that week and the number of cards in the deck. Suppose you purchase only one ticket. The probability of you winning is determined by the arithmetic below:
1 1
Probability = ------ x ------
T C
Where T represents the number of tickets sold and C represents the number of cards in the deck.
What happens to your chances of winning if you purchase multiple tickets? The tables below show the comparison of your odds in purchasing one ticket vs. two tickets. As you would suspect, you double your chances with the purchase of a second ticket.
| Tickets | Cards |
Chances | Tickets | Cards |
Chances | |
| 24 | 50 | 0.0833% | 24 | 50 | 0.1667% | |
| 38 | 36 | 0.0731% | 38 | 36 | 0.1462% | |
| 45 | 15 | 0.1481% | 45 | 15 | 0.2963% | |
| 60 | 12 | 0.1389% | 60 | 12 | 0.2778% |
As probabilities go, you might think that the best 'strategy' of winning the big pot would be to wait until there were just a few cards in the deck and then purchase several tickets. This would dramatically increase your chances of winning the chance to draw from the small deck of cards. Unfortunately, your fellow Rotarians are equally smart in recognizing this strategy. Over the years of watching this Rotary purchasing ticket strategy, I have observed that the number of tickets sold is inversely proportional to the number of cards left in the deck. That is, many, many tickets are sold when the deck of cards is small. Few are sold when the deck is large.
What does this do to your odds? Well, it doesn't get better.
| Tickets | Cards | Chances |
| 24 | 50 | 0.0833% |
| 38 | 36 | 0.0731% |
| 45 | 15 | 0.1481% |
| 60 | 12 | 0.1389% |
| 100 | 12 | 0.0833% |
| 150 | 12 | 0.0556% |
Just so there is no confusion over your chances, the percent figures suggest that if you were to play the game every week, you should expect to win
approximately once every two years!
If the big pot was $100 or more when you drew the Ace of Spaces, you would 'cover' your costs of tickets for two years, but would you win anything? The answer seems to lie with what is called a "fair" return on your "investment".
Consider the situation where you can buy a raffle ticket for $100. Suppose there will be 100 tickets sold. Your chances of winning are 1 in 100 or 1/100. How much should the prize be worth? The ticket sales would bring in $10,000 (100 tickets at $100 each). Ideally, the prize should be worth $10,000 but this would not be worth the effort of the raffle organizers (no profit). Suppose the prize was worth only $500. Would you invest $100 to win $500 if your chances were 1 in 100 to win? Probably not...unless the profit was for a good cause you supported.
This brings us back to the North Columbus Rotary Club's lottery pick. The total ticket sales are split into thirds - 1/3 goes toward the lucky ticket, 1/3 goes to build the big pot even larger, and the final third goes toward club projects - something we can all support! That is, we have a fund raising project that is enjoyed throughout the entire year. We hope you will contribute to the fun of our club by participating in the ticket sales. If not, we hope you will consider making a contribution to the club to be used for club projects. Personally, I had rather make my project contribution in a fun way.
My record of having my ticket selected is dismal to say the least. I won a couple of years ago, when I left early, I asked Susan Curry to watch my ticket. My ticket won, but that was because I wasn't there. My son has visited me for a Rotary lunch three times. I bought him a ticket each time. He won twice. I have adopted a "game-within-a-game" I play. I declare myself a "winner" if the winning ticket number is +10 or -10 of my number. With this additional edge in winning, I think I have "won" twice in five years! It is probably not a good idea to sit next to me at lunch if my luck is contagious. Enjoy the excitement of the chance of winning a big pot or enjoy knowing that you contribute to the club's projects. You can't win unless you purchase a ticket. Enjoy your Rotary experience!