2023 UPDATE: Full analysis in this spreadsheet has been updated to reflect the latest products offered by California Lottery.
I’ve always been fascinated by how the lottery works. From a mathematical point of view spending money on lottery tickets is a complete waste of time and money. There are a few exceptions – when a lottery is poorly designed, it is possible to game the system and actually earn money – here’s a famous example of how MIT Students Won $8 Million in the Massachusetts Lottery.
The North American lottery system is a $70 billion-a-year business, an industry bigger than movie tickets, music, and porn combined. So general public seems to ignore the probability theory and continues to spend money in pursuit of the elusive multi-million grand prizes of the numerous lotteries.
I decided to take a closer look at California State Lottery and came across a very nice analysis done by the Wizard of Odds. I do wholeheartedly agree with the advice given by the Wizard: “Don’t play in the first place. Every state lottery offers terrible odds. With few exceptions, it is the worst bet you can make.”
But I was intrigued by the following passage in the article: “The California Lottery is nice enough to indicate how many tickets for each win have already been cashed. If there is a game that is almost sold out, as evidenced by the small wins, with a high ratio of large wins still unclaimed, then it may mean the remaining unsold tickets are rich in big winners. The same principle as card counting in blackjack.”
I decided to take a close look at the odds of winning and the average return for each of the scratch card games CA Lottery offers and see if there are substantial changes in probability of winning and return on investment with the additional data provided by state lottery.
Here is a summary of my findings:
- More expensive scratchers have higher odds of winning and higher return:
Scratch Card Average Returns Bet Average Return $1 52.49% $2 56.06% $3 57.57% $5 62.37% $10 67.75% $20 69.02% $30 72.63%
- There is indeed a potential advantage play in scratch card games, as with the information about the number of claimed prizes that CA Lottery publishes it is possible to calculate updated winning odds and returns – see the spreadsheet for details.
- Over time changes in the odds of winning and expected return can go up or down ~20%, so if you gamble, it definitely makes sense to run the numbers first
- As of February 10, 2018 Set For Life scratchers have the highest estimated return of 75.65%
- As of February 10, 2018 $10 Million Dazzler scratchers have the highest estimated chance of winning of 36.5%
- In the unlikely event you win a grand prize – be aware of the fine print – the lottery is not going to pay it to you straight away. You’ll have a chance of taking home ~1/2 of it before taxes immediately or getting it paid out as installments over 25 years or so.
My full analysis is in this spreadsheet – it automatically downloads the latest stats on claimed prizes and winning odds from calottery.com, so results you see there might differ from the examples I provided above.
And as a closing note – my general advice is “do not gamble”. If you do, then California Lottery is a good choice – its mission is to maximize supplemental funding for the state’s public schools, which is very similar to what we have as a mission for Veikkaus – the Finnish national betting agency. At least the money you lose will go to a good cause.
13 thoughts on “2023 UPDATE: California Lottery – Scratchers – picking the winning tickets using math”
Your analysis here seems to assume that tickets are claimed at an equal rate. Small prizes (which can be claimed at any lottery retailer) can be claimed in a shorter amount of time than large prizes (which have to be mailed in). So your data will make it seem like there are a higher proportion of large prizes available than is true in reality.
It’s a f****** jip joint.
I’m not sure when, but as of current, the CA Lottery website changed dramatically. The details it gives on prizes claimed and unclaimed are superficial at best now.
this world we live in is outrageous high to survive these days you would think lottery instead having one winner of 200 million why couldn’t be 500 people or even 200 split pot that way wealth gets spread out more
I agree with David Tolbert 100%
This analyses is useless. Winning tickets are NOT distributed evenly or proportionally to all the counties, cities, stores, gas stations, etc.
ValS i completely agree!!
What David d Tolbert said is something I’ve thought about for such a long time. Does one person really need 200 million? If you split that spread it out so that 500 people could receive a share of that would make everyone happy. But! This is America and everyone has to be greedy.
California lottery hides important information from the customer. I don’t see the total number of dollars spent on each game or the complete odds per game level. They will print the overall odds like 1-2.97 but not the odds of winning the big prize and others where the odds could be 1-2000000 or higher. What a rip off.
I’m not sure with the percentage of return that is shown above. Is there any article or study that can support the data? It’s somewhat out of reality.
Ca lotto scratcher odds are totally BOGUS!!! Such a rip! Their odds are sooo off its not even funny but an actual RIP!! I have over 8,000 yes 8,000 loser tickets since 2017 and most ive ever won was $500 just a few times!! As far as 2nd chance goes…. IT DOESN’T!!! Biggest joke of all jus to hold on to disappointed memories and keep ur trash instead of gettin angry n tossin em carelessly into tha street!
Best advise is still …best advise, don’t gamble. You win EVERYTIME !
That being said, I think we all want to take a shot at the big enchilada at least once.
Might as well go big. Two items on your list of things to do will be checked.
Throwing caution to the wind and burning money. ….but, the possibilities. Good luck !
There is no need to trick consumers by offering tickets that all 10 prizes can be won so if you have a 5 dollar ticket and you happen to win all 10 prizes then how much is the minimum amount you will win?
Lets see, If the back of card reads PRIZES RANGE FROM A FREE TICKET TO 30,000 DOLLARS then it appears you could win 10 free tickets at a minimum.worth $50. Hell no! they lie and make each prize $ 1.00 so really it should read PRIZES RANGE FROM $ 1.00 TO 30,000 DOLLARS. there is no need to trick us ! So they brag how many tickets they produce with 10 prize winners on one ticket and really its all a scam to get more to pay the lottery top employees vacatiopns