So I saw this game advertised in a local convenience store yesterday for the first time and because I'm a nerd and love any excuse to put off doing what I actually should be doing with my time, I started doing some research on the game. I found it interesting that the Florida Lottery site - as well as several of the other state lottery sites I checked where the game is offered - only lists the Odds of WINNING a prize versus listing the odds/probability that each multiplier will be included as the potential prize when purchasing a ticket.
In other words, the lottery website tells me the odds of winning $5 on a $1 play is 31-1. Fact is, approximately 48% of all $1 tickets will have the $5 prize. Only 1 in every 1,000 $1 tickets includes the top $250.00 prize, but remember - if you're lucky enough to hit those long odds at the window and have a play ticket with the top prize on it, you've just begun the journey because you now need to have your number drawn (obviously at 1-15 odds representing only a 6.6% chance). Still, I guess that would make the draw all that much more exciting, but MAN it would hurt to have a worthless ticket AFTER being lucky enough to draw a ticket with the top prize at 1-1000 odds or 0.1% probability.
I also think it's interesting (though not surprising) that while the options are $1, $2, and $5, the prize payouts and odds for the $2 and $5 game are not just 2 and 5 times the payouts and odds for the $1 game. As the lottery's goal is to separate a fool from his money, the lottery employs the common tactic of providing "better" odds and better "return on investment" to those who play higher value cards with the "best" odds and ROI being playing the maximum $5.00 per ticket. NOW, for anyone not familiar with lottery (or just gambling) lingo, PLEASE understand that "better" odds means NOT AS BAD and "return on investment" means THE AMOUNT YOU EXPECT TO LOSE EVERY TIME YOU PLAY.
Anyway, for anyone interested, I've included a spreadsheet with my calculations showing the probability of receiving a given multipler on your ticket and the Expected ROI associated with each prize and each ticket price. Anyone can feel free to check my math (though I think it's pretty straightforward), but for those who are only interested in the bottom line, here it is...
Playing the $1.00 game, your expected ROI is $0.60, meaning the lottery is banking $0.40 of every dollar we spend.
Playing the $2.00 game, your expected ROI is $1.26, meaning the lottery is banking $0.74 on each ticket or $0.37 of each dollar spent on a $2.00 ticket.
Playing the $5.00 game, your expected ROI is $3.31, meaning the lottery is banking $1.69 on each ticket or $0.338 of each dollar spent on a $5.00 ticket.
Obviously, you should never play more than you can afford. That said, if you determine that you can afford to play a $1.00 ticket once a day, the better strategy would be to only play the game every fifth day and then play a $5.00 ticket. To demonstrate, if we assume a person played the game for one draw each week day, they would spend $260 on tickets (52 weeks X 5 days X $1.00) and by years end would expect to have donated just more than $100 of the stake to the State as the expected return would be $156.00 ($260 X .60). Alternatively, if a person played only once a week, but played a $5.00 ticket when they did, they would spend the same $260 on tickets, but they would expect to have $172.00 left at year's end - a $16.00 better expected outcome while playing the same amount of money.
Okay - I'm doing it again - I should be working but I'm rambling on here... Here are the tables promised above and then it's work time - for real. Well, maybe I should run to the Circle K real quick and buy a couple $5.00 tickets for the super early 8:00 AM draw - I mean after wasting this much time thinking about a game I've got to at least experience it, right? I'll report back if I hit it big - when you don't hear back from me you can rest assured that I'm much better at hitting one of the 14 numbers I didn't pick than the other way around.
For the $1.00 Tickets:
Prize |
Odds (1 in) |
Probability of Multiplier |
Expected ROI |
$5 |
31 |
0.483870968 |
$0.16 |
$7 |
75 |
0.2 |
$0.09 |
$10 |
105 |
0.142857143 |
$0.10 |
$15 |
180 |
0.083333333 |
$0.08 |
$20 |
270 |
0.055555556 |
$0.07 |
$25 |
675 |
0.022222222 |
$0.04 |
$50 |
2,625 |
0.005714286 |
$0.02 |
$100 |
5,250 |
0.002857143 |
$0.02 |
$250 |
15,000 |
0.001 |
$0.02 |
Total Expected ROI= $0.60
$2.00 Tickets:
Prize |
Odds (1 in) |
Probability of Multiplier |
Expected ROI |
$10 |
31 |
0.48387097 |
$0.32 |
$14 |
90 |
0.16666667 |
$0.16 |
$20 |
105 |
0.14285714 |
$0.19 |
$30 |
150 |
0.1 |
$0.20 |
$40 |
225 |
0.06666667 |
$0.18 |
$50 |
525 |
0.02857143 |
$0.10 |
$100 |
2,250 |
0.00666667 |
$0.04 |
$200 |
4,500 |
0.00333333 |
$0.04 |
$500 |
15,000 |
0.001 |
$0.03 |
Total Expected ROI = $1.26 per $2.00 Ticket
$5.00 Tickets
Prize |
Odds (1 in) |
Probability of Multiplier |
Expected ROI |
$25 |
30 |
0.5 |
$0.83 |
$35 |
105 |
0.142857143 |
$0.33 |
$50 |
120 |
0.125 |
$0.42 |
$75 |
150 |
0.1 |
$0.50 |
$100 |
180 |
0.083333333 |
$0.56 |
$125 |
360 |
0.041666667 |
$0.35 |
$250 |
2,100 |
0.007142857 |
$0.12 |
$500 |
4,125 |
0.003636364 |
$0.12 |
$1,250 |
15,000 |
0.001 |
$0.08 |
Total expected ROI for $5.00 ticket: $3.31