Chances Of Winning The Lottery
The chances of choosing a magic combination of numbers to win a draw really are quite small. For instance, to play the Powerball using your own choice of numbers and win the jackpot, your chance of winning is about one in over 292 million – so is there anything you can do? Updated November 04, 2020 More than a third of Americans believe winning the lottery is the only way they will ever retire comfortably. But the odds of winning either the Powerball or Mega Millions are roughly 1 in 292.2 million and 1 in 302.5 million, respectively.
- Chances Of Winning The Lottery Compared To Other Things
- Chances Of Winning The Lottery In The Philippines
- Chances Of Winning The Lottery Percentage
- How To Play The Lotto
- Chances Of Winning The Lottery
How do you choose your lottery numbers? Have you used the same combination or sequence for years and see no reason to change – or are too scared to now in case your winning lines come up? Perhaps you’re one of those players who does prefer to leave everything to chance and play a quick pick or lucky dip every week in the hope that a more random choice will mean you win big.
There is often quite a lot of debate amongst players on how best to go about choosing how you play. So, lottery quick picks or choosing your own numbers – which is best?
Methods of Choosing Lottery Numbers
Many who choose their own numbers will do so based on whether a number is significant to them or not. For instance, you might choose a birthday, wedding anniversary or house number. Some people, however, will choose their own set of numbers but still keep it very random. There are always statisticians who will be able to come up with reasons why choosing one way to play a game is better than another way, but with the lottery being such a big game of chance – is there really just one concrete answer?
Here’s an example of a win that happened when someone chose very special and significant dates
A Lucky Winner Who Used the Same Numbers…
A 79-year-old man from Gaithersburg won a huge jackpot after a clerical error at the time of his birth meant he seemingly had two birthdates. The man’s “official” birthday was recorded as being 23rd April, however, it was an error and the real date of birth was 21st April.
The player felt that these two numbers were extremely significant for him and played them both on a few different lottery games. He dropped very lucky on the Maryland Multi-Match Draw, when six of the numbers he’d chosen, including his two birthdays, came up, netting him a $1.9 million win!
Speaking after the win he said: “I was scanning the newspaper and flipped to the lottery section first, and when I saw the numbers my eyes just grew bigger and bigger. When I told my wife how much we had won, at first she didn’t believe me!”, he revealed.
After taxes, the couple will take home $1.45 million and are considering their options before they spend any money.
Choosing Your Own Numbers
Of course, this is only one story of good luck, and one story doesn’t mean that it will work in the same way for everyone who chooses to play the lottery in that way. Let’s examine which method could be the right one to choose.
The chances of choosing a magic combination of numbers to win a draw really are quite small. For instance, to play the Powerball using your own choice of numbers and win the jackpot, your chance of winning is about one in over 292 million – so is there anything you can do?
If you play a game like Powerball, statistics show that about seventy percent of the winners who have got a jackpot or some other large sum, have won it through a Quick Pick game, rather than opting to choose their own private set of numbers which might have a significant or special meaning to them.
If you’re just starting to play the lottery and want to up your chances, this might be the best way in – for an initial period at least. But, long term – what are the chances of making playing this way a success?
Well, the answer is, it’s not always that simple. According to how long you’ve been playing lottery games the rules change!
Frequent players increase their chances of winning if they choose the same numbers each time and buy a lot of different tickets. This will generally increase your chances of winning money anyway.
Played like this, it shows that the most frequently played (and won) numbers are 32 and 41. According to stats, these show up around seven percent of the time – so trying to add these into your other combinations might improve your chances slightly.
Bearing that in mind, the odds are still not in your favor to win a big jackpot and they’ll still stand at 292.2 million to 1, so it might not work out for you, no matter how hard you try.
Sometimes choosing your own numbers proves to be the wrong option. One cautionary tale shows this
When Choosing Your Own Numbers Goes Wrong
UK National Lottery player Martyn Tott, missed out on a £3 million UK Lotto jackpot and the reason for this was because he’d failed to store his ticket safely and check his numbers after every draw.
It took six months before his partner noticed that their numbers had come up and that they were the same numbers they use in every draw when an appeal was put out on a local news channel to find the winner.
Despite knowing they’d won, they couldn’t find the ticket anywhere and UK Lottery organizers did indeed confirm that Mr. Tott had owned the winning ticket. They couldn’t pay his prize as he no longer owned it as proof of purchase.
Sometimes changes to lottery rules mean that people who have played the same numbers for years can be affected. Recently, the Mega Millions draw pool has changed from 1 to 46 to 1 to 15, which has confused and upset many players – especially those who had numbers higher up in the draw.
One player from Washington found he would have to replace the number 33 that he has used in every draw for the past three years. There are many players who are now considering defecting to Powerball to ensure they can continue to play the numbers they are so fond of.
The moral of the story here is, if you choose the same numbers all the time – keep your ticket safe and make sure you adhere to lottery rules.
Quick Pick Luck
Using a Quick Pick is still the most popular way of playing the lottery in the USA. So, therefore, it stands to reason that the majority of winners come from buying these tickets. This includes the last three huge Powerball wins and the most recent Mega Millions jackpot.
Their popularity stems from the fact that the numbers are generated totally randomly and the player has a better chance of covering number options. When players opt to choose their own numbers that may or may not have a specific significance to them, they often come from a smaller date range (think about how the calendar works – from 1-31) and often don’t include the higher numbers.
Playing a Quick Pick game means you’re less likely to have to share a prize with anyone, but there is also no reason for any of the numbers to be unique and they might end up being chosen for other players playing the same game too.
In fact, this did actually happen some five years ago in 2013, when the $448 million Powerball jackpot was shared between three ticket holders, two of these had opted for Quick Picks.
Another popular reason for buying a Quick Pick is that it will generate totally different numbers for each draw. This can help build excitement and anticipation for players. Those who play the same numbers every week can often become fatigued, making them less likely to be careful when storing their tickets – as we saw in the strange case of Martin Tott.
It’s true to say then that the odds are split fairly evenly between the two different methods of playing the lottery and it’s pretty much all down to personal choice. The odds say that it’s the same no matter which combination of numbers is picked.
The only proviso should be that if you do decide to choose your own numbers, always keep your ticket in a safe place – preferably the same one, each week, to avoid any danger of losing it should there be a big win.
In Conclusion
The lottery is a game of chance and at the end of the day whether you choose your numbers through your own method, or decide to opt for a randomized choice such as a Quick Pick game, ultimately it is all down to the luck of the draw at that particular moment, on that particular day. It could be argued that there is slightly more advantage in using a randomized choice, but it really is negligible and at the end of the day down to whether the game is in your favor or not.
If you felt so inclined you could try and conduct your own challenge by playing two lots of tickets a week – take one Quick Pick lottery game and one with your own numbers, which never change. Play the games for a set period of time, perhaps 12 weeks or so, and see which numbers and games work best for you. Long term you can then decide whether to continue playing one way or another.
On This Page
Introduction
The California Lottery opened for business on October 3, 1985. Revenues from the lottery are directed towards education. The percentage directed towards prizes ranges from 48.5% to 79.7%, so you need to play the right game. Administrative expenses are supposed to be less than 13%. The time limit to cash a winning ticket is 180 days.
A unique feature of the California Lottery is that all games must be player against player and the state cannot have an interest in the outcome. For this reason, games based on random ball draws are all pari-mutual, which means the California Lottery takes a cut for schools and education and returns the rest to the winners. This is unlike other states that pay fixed prizes for some games.
The rest of this page contains my analysis of the several ways to play the California Lottery. However, for those who just want the executive summary, here is my advice:
- Don't play in the first place. Every state lottery offers terrible odds. With few exceptions, it is the worst bet you can make.
- If you must play, the best odds for bets under $5 is on the Hot Spot game, which claims to return 63.5% of money bet, which is better than the usual 50%.
- For bets of $5 or more, scratch cards offer the best value, with returns ranging from 67% to 80%, depending on the bet size.
- For games with the Second Chance option, don't forget to take it, which will give you about an additional 1.5% in return.
- For any game involving choosing numbers, I suggest the Quick Pick option. Players that pick their own numbers are at greater risk to get short changed on a jackpot by having to share it with many other players who picked the same numbers for the same reasons you did.
- If you play the Daily 3 or Daily 4, make Straight bets, as opposed to Box bets.
What follows is my analysis of each game.
Daily 3
The Daily 3 is a $1, twice daily game in which the player and lottery each pick three numbers from 0 to 9, with replacement.
Prizes are pari-mutual style, where the lottery takes a 50% cut (source: California Lottery Regulations, pages 21,22) of the total ticket sales and returns the rest to the winners.
The way each prize is determined is to take the dot product of the number of each type of win and the number of shares according to the table below. Then divide total prize money (48.5% of ticket sales) by the number of winning shares to determine the win per share. Prizes are rounded down to the nearest dollar with the breakage added to the Prize Reserve.
The following table shows the actual shares for each win as well as the mathematically fair number of shares, based on a box 1-2-3 ticket being 1 share. A 1-2-3 box ticket means one with three distinct numbers. A 1-1-2 box ticket means one with a pair of one digit, for example 8-5-8.
Daily 3 Shares
| Catch | Actual Shares | Fair Shares |
|---|---|---|
| Straight | 12.5 | 12 |
| Box (1-2-3) | 2 | 2 |
| Box (1-1-2) | 4 | 4 |
| Straight & box (1-2-3) win box only | 1 | 1 |
| Straight & box (1-1-2) win box only | 2 | 2 |
| Straight & box (1-2-3) win both | 7.25 | 7.25 |
| Straight & box (1-1-2) win both | 8.25 | 8.25 |
With both the Daily 3 and Daily 4, the shares given to straight bet players is disproportionately high. This means that box players are subsidizing straight players. Thus, my advice for Daily 3 players is to make straight bets only, if you must play.
The following table shows the probability of winning each prize, the average win, and return, based on an overall 50% return and assuming players bet equally between straight and box bets.
Daily 3 Return Table
| Bet | Probability | Average Win | Return |
|---|---|---|---|
| Straight | 0.001 | $510.20 | 51.02% |
| Box (1-1-2) | 0.003 | $163.27 | 48.98% |
| Box (1-2-3) | 0.006 | $81.63 | 48.98% |
Daily 4
The Daily 4 is a $1, daily game in which the player and lottery each pick four numbers from 0 to 9, with replacement. So, repeat numbers are possible.
Prizes are pari-mutual in nature, where the lottery returns approximately 48.5% of total money bet (source:California Lottery Regulations, page 17) of the total ticket sales. There is not a fixed pay table but how much you win will depend on how many other winners you will have to share with.
The way each prize is determined is to take the dot product of the number of each type of win and the number of shares according to the table below. Then divide total prize money (48.5% of ticket sales) by the number of winnings shares to determine the win per share. Prizes are rounded down to the nearest dollar with the breakage being added to the Prize Reserve.
The following table shows the actual shares for each win as well as the mathematically fair number of shares, based on a box 1-2-3-4 ticket being 0.5 shares. The numbers in parenthesis show an example of that type of box ticket. For example, 1-1-2-2 would have two each of two different digits, like 5-7-5-7.
Daily 4 Shares
| Catch | Actual Shares | Fair Shares |
|---|---|---|
| Straight | 12.5 | 12 |
| Box (1-2-3-4) | 0.5 | 0.5 |
| Box (1-1-2-3) | 1 | 1 |
| Box (1-1-2-2) | 2 | 2 |
| Box (1-1-1-2) | 3 | 3 |
| Straight & box (1-2-3-4) win box only | 0.25 | 0.25 |
| Straight & box (1-1-2-3) win box only | 0.5 | 0.5 |
| Straight & box (1-1-2-2) win box only | 1 | 1 |
| Straight & box (1-1-1-2) win box only | 1.5 | 1.5 |
| Straight & box (1-2-3-4) win both | 6.5 | 6.5 |
| Straight & box (1-1-2-3) win both | 6.75 | 6.75 |
| Straight & box (1-1-2-2) win both | 7.25 | 7.25 |
| Straight & box (1-1-1-2) win both | 7.75 | 7.75 |
The table above shows that a straight ticket pays 12.5 shares when a fair number of shares would be 12. This means that players betting box tickets are subsidizing straight ticket players. Thus, my advice for Daily 4 bettors is to make straight bets only.
The following table shows the probability of winning each prize, the average win, and return, based on an overall 50% return and assuming players bet equally between straight and box bets.
Daily 4 Return Table
| Bet | Probability | Average Win | Return |
|---|---|---|---|
| Straight | 0.0001 | $5,102.04 | 51.02% |
| Box (1-1-1-2) | 0.0004 | $1,224.49 | 48.98% |
| Box (1-1-2-2) | 0.0006 | $816.33 | 48.98% |
| Box (1-1-2-3) | 0.0012 | $408.16 | 48.98% |
| Box (1-2-3-4) | 0.0024 | $204.08 | 48.98% |
Fantasy 5
Fantasy 5 is a simple, $1 daily game where the player and lottery each pick 5 numbers from a range of 1 to 39. If the player matches at least three, then he wins instantly. Catching two wins a free game. If the player buys at least five tickets at once, then he will be entered into a 'second chance' game.
Chances Of Winning The Lottery Compared To Other Things
The percentage of ticket sales returned to winning players is 50% (source: California Lottery Regulations, page 25). That 50% is divided as follows:
- Match 5: 40%
- Match 4: 25%
- Match 3: 31%
- Match 2: Free play
- Reserve: 4%
This does not mean the odds are the same every game. Roughly 36% of the time nobody will match all five numbers, which will result in a larger prize pool in the following drawing. Naturally, large prize pools for matching all five numbers induces more competition from other players. Remember, much like poker and bingo, when it comes to the California Lottery, you're not playing against the lottery, but against the other players.
The following table shows the probability and contribution to the return for all possible outcomes, based on the 50% return percentage, the various prize shares, and the probability of each outcome. The wins shown are averages. I assume the 4% directed to the reserve goes to the other three cash prizes on a pro-rata basis. I also assume that if the player matches two numbers, for a free play, he will keep playing until he either wins something or loses. In other words, this table is on a 'bet resolved' basis.
Fantasy 5 Return Table
| Catch | Average Win | Combinations | Probability | Return |
|---|---|---|---|---|
| 5 | $107,482.71 | 1 | 0.000002 | 0.208333 |
| 4 | $395.16 | 170 | 0.000330 | 0.130208 |
| 3 | $14.85 | 5,610 | 0.010874 | 0.161458 |
| 0 to 1 | $0.00 | 510,136 | 0.988795 | 0.000000 |
| Total | 515,917 | 1.000000 | 0.500000 |
The probability of any win, assuming free plays are re-bet until resolved, is 1.12%.
SuperLotto Plus
This is a $1 game that generates the largest jackpots and is exclusive to California. It follows a format of choosing 5 'white' balls from 1 to 47 and one Mega Ball from 1 to 27. The jackpot is paid as a graduated annuity, meaning payments start out small and get larger, if the lump sum is not chosen.
The percentage of ticket sales returned to winning players is 50% (source: California Lottery Regulations, page 48). That 50% is divided as follows:
SuperLotto Plus — Prize Allocation
| Catch | Mega Ball | Probability |
|---|---|---|
| 5 | Yes | 60.50% |
| 5 | No | 3.00% |
| 4 | Yes | 1.50% |
| 4 | No | 2.50% |
| 3 | Yes | 2.25% |
| 3 | No | 11.00% |
| 2 | Yes | 6.00% |
| 1 | Yes | 5.75% |
| 0 | Yes | 4.50% |
| Reserve | 3.00% | |
| Total | 100.00% |
Based on a 50% return, the prize allocation above (assuming the reserve is spread on a pro-rata basis to the other prizes), and the probability of each prize, I show the following theoretical average wins for each prize.
SuperLotto Plus — Return Table
| Catch | Mega Ball | Average Win | Combinations | Probability | Return |
|---|---|---|---|---|---|
| 5 | Yes | $12,915,925 | 1 | 0.000000024 | 0.311856 |
| 5 | No | $24,633 | 26 | 0.000000628 | 0.015464 |
| 4 | Yes | $1,525 | 210 | 0.000005070 | 0.007732 |
| 4 | No | $97.75 | 5,460 | 0.000131832 | 0.012887 |
| 3 | Yes | $55.79 | 8,610 | 0.000207889 | 0.011598 |
| 3 | No | $10.49 | 223,860 | 0.005405111 | 0.056701 |
| 2 | Yes | $11.16 | 114,800 | 0.002771852 | 0.030928 |
| 1 | Yes | $2.19 | 559,650 | 0.013512778 | 0.029639 |
| 0 | Yes | $1.13 | 850,668 | 0.020539423 | 0.023196 |
| 0 to 2 | No | $0.00 | 39,653,068 | 0.957425392 | 0.000000 |
| Total | 41,416,353 | 1.000000000 | 0.500000 |
The probability of any win is 4.26%.
You can calculate the return for any given prizes with my SuperLotto Plus calculator.
Daily Derby
The Daily Derby is a $2, daily game in which the player chooses, in order, three numbers from 1 to 12, without replacement. In other words, the same way the player would bet a trifecta in a 12-horse race at the racetrack. In addition, the player must also pick three numbers from 0 to 9, with replacement, to represent the last three digits in the starting time of the race, which starts sometime between 1:40.00 and 1:49.00 PM. After betting closes, the Lottery will randomly choose the same things. If the player gets at least the winning horse or the race time, he will win something.
Before going further, let me review some horse racing terminology:
- Trifecta: Choosing the first three finishing horses, in order.
- Exacta: Choosing the first two finishing horses, in order.
- Win: Choosing the winning horse.
Prizes are pari-mutual style, where the lottery returns approximately 50% of total money bet (source: California Lottery Regulations, page 12) of the total ticket sales. Because it is pari-mutual, there is not a fixed pay table but how much you win will depend on how many other winners you will have to share with.
The following table shows how much of the prize pool is directed towards each type of win.
Daily Derby
| Win | Share of Prize Pool |
|---|---|
| Trifecta and time | 14% |
| Trifecta only | 36% |
| Exacta only | 16% |
| Win only | 25% |
| Time only | 5% |
| Reserve | 4% |
If the player wins for both the win or exacta and the time, then he shall be paid for both. For example, on the April 5, 2016 drawing a win for the winning horse only paid $3 and the race time only paid $56. So, a win for both paid $59.
The next table shows the probability, average win, and contribution to the return for each type of win. I assume the 4% directed towards the reserve is distributed on a pro-rata basis to the other wins, according to win share. The return column is the product of the average win, probability, and 0.5. The reason for dividing by 2 is the ticket cost is $2, and I'm trying to show the return per dollar bet.
Daily Derby Return Table
| Event | Average Win | Combinations | Probability | Return |
|---|---|---|---|---|
| Trifecta & time | $192,500.00 | 1 | 0.00000076 | 0.072917 |
| Exacta & time | $80.80 | 9 | 0.00000682 | 0.000275 |
| Win & time | $59.90 | 100 | 0.00007576 | 0.002269 |
| Time only | $56.48 | 1,210 | 0.00091667 | 0.025887 |
| Trifecta | $492.54 | 999 | 0.00075682 | 0.186383 |
| Exacta | $24.32 | 8,991 | 0.00681136 | 0.082837 |
| Win only | $3.42 | 99,900 | 0.07568182 | 0.129433 |
| Loser | $0.00 | 1,208,790 | 0.91575000 | 0.000000 |
| Total | 1,320,000 | 1.00000000 | 0.500000 |
Hot Spot
This is a keno game played every four minutes from 6 AM to 2 AM every day. The player may bet $1 to $20 per game. As in conventional keno, the player picks 1 to 10 numbers from a range of 1 to 80. The Lottery selects 20 numbers from the same range. The more numbers the player picked that match the Lottery draw, the more he will win.
Prizes are pari-mutual style, where the lottery returns 63% of total money bet to winners (source: California Lottery Regulations, page 28) of the total ticket sales. In other words, there is not a fixed pay table but how much you win will depend on how many other winners you will have to share with. Often, there are no winners for long-shot wins. The rules are rather complicated, but basically prize pools carry over to the next game for any given type of win if there were no winners.
The following table shows the probability of any given win according to the number of picks and the number that match the Lottery draw.
Hot Spot ProbabilitiesExpand
| Catch | Pick 1 | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 in 11.3 | 1 in 15.7 | 1 in 21.8 | |||||||
| 1 | 1 in 4 | |||||||||
| 2 | 1 in 16.6 | 1 in 7.2 | 1 in 4.7 | |||||||
| 3 | 1 in 72.1 | 1 in 23.1 | 1 in 11.9 | 1 in 7.7 | 1 in 5.7 | |||||
| 4 | 1 in 326 | 1 in 82.7 | 1 in 35 | 1 in 19.2 | ||||||
| 5 | 1 in 1551 | 1 in 323 | 1 in 116 | 1 in 54.6 | 1 in 30.7 | 1 in 19.4 | ||||
| 6 | 1 in 7753 | 1 in 1366 | 1 in 423 | 1 in 175 | 1 in 87.1 | |||||
| 7 | 1 in 40979 | 1 in 6232 | 1 in 1690 | 1 in 621 | ||||||
| 8 | 1 in 230115 | 1 in 30682 | 1 in 7384 | |||||||
| 9 | 1 in 1380688 | 1 in 163381 | ||||||||
| 10 | 1 in 8911711 |
There is another keno-based game called the Bulls Eye. In this game, the first number drawn by the Lottery must match one of the player's picks. If it does, the player will automatically win something, depending on the number of other balls in the draw that match his other picks. If not, he is an automatic loser.
The player may not play the Bulls Eye alone but may play it on a 50/50 basis with the Hot Spot game, if he wishes. The California Lottery web site does not indicate the return percentage of the Bulls Eye game, so you're on your own with that one.
The following table shows the probability of each possible win in the Bulls Eye game. The 'Catch' column refers to the number of picks the player matches to the Lottery draw, not including the first ball.
Bulls Eye ProbabilitiesExpand
| Catch | Pick 1 | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 in 80 | 1 in 52.7 | 1 in 46.4 | 1 in 46.2 | 1 in 49.3 | 1 in 55 | 1 in 63.5 | 1 in 75.1 | 1 in 90.6 | 1 in 111 |
| 1 | 1 in 166 | 1 in 72.1 | 1 in 47 | 1 in 37 | 1 in 32.4 | 1 in 30.6 | 1 in 30.5 | 1 in 31.6 | 1 in 33.9 | |
| 2 | 1 in 480 | 1 in 154 | 1 in 79.4 | 1 in 51.4 | 1 in 38.1 | 1 in 31 | 1 in 27.1 | 1 in 24.9 | ||
| 3 | 1 in 1632 | 1 in 413 | 1 in 175 | 1 in 95.8 | 1 in 61.3 | 1 in 43.8 | 1 in 33.9 | |||
| 4 | 1 in 6202 | 1 in 1292 | 1 in 463 | 1 in 219 | 1 in 123 | 1 in 77.8 | ||||
| 5 | 1 in 25843 | 1 in 4553 | 1 in 1408 | 1 in 583 | 1 in 290 | |||||
| 6 | 1 in 117084 | 1 in 17806 | 1 in 4829 | 1 in 1773 | ||||||
| 7 | 1 in 575287 | 1 in 76705 | 1 in 18461 | |||||||
| 8 | 1 in 3068195 | 1 in 363070 | ||||||||
| 9 | 1 in 17823422 |
The regulations for Hot Spot are confusing when it comes to how the prizes are determined. However, they do kindly indicate 'Typical Prize Amounts' for the Hot Spot game on page 29 of the Regulations, as follows:
Hot Spot Typical Prize AmountsExpand
| Catch | Pick 1 | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | $0 | $0 | $0 | $0 | $0 | $0 | $0 | $1 | $1 | $3 |
| 1 | $2 | $0 | $0 | $0 | $0 | $0 | $0 | $0 | $0 | $0 |
| 2 | $9 | $2 | $1 | $0 | $0 | $0 | $0 | $0 | $0 | |
| 3 | $26 | $5 | $2 | $1 | $1 | $0 | $0 | $0 | ||
| 4 | $75 | $16 | $5 | $3 | $0 | $0 | $0 | |||
| 5 | $450 | $60 | $10 | $10 | $5 | $2 | ||||
| 6 | $900 | $150 | $75 | $25 | $15 | |||||
| 7 | $2000 | $575 | $125 | $40 | ||||||
| 8 | $10000 | $2750 | $575 | |||||||
| 9 | $30000 | $5000 | ||||||||
| 10 | $100000 |
When these typical prize amounts are applied to the probability of winning, it results in returns of less than the 63% claimed in the Regulations. What does the Lottery do with the extra money? The Regulations say, 'The Director will prevent the Wagered Prize Fund from exceeding $2.9 million through augmentation of Prizes and implementation of Promotions, including the issuance of free Hot Spot tickets, from time to time.' -- Section 3.5.4.B(2), page 29.
The Regulations also state 'Typical Prize Amounts' for the Bulls Eye game (section 3.5.6.C(1)), as follows:
Bulls Eye Typical Prize AmountsExpand
| Catch* | Pick 1 | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | $44 | $12 | $6 | $4 | $3 | $4 | $4 | $4 | $4 | $4 |
| 1 | $55 | $15 | $10 | $6 | $2 | $2 | $2 | $2 | $2 | |
| 2 | $125 | $30 | $12 | $5 | $2 | $2 | $2 | $2 | ||
| 3 | $200 | $60 | $30 | $15 | $5 | $5 | $2 | |||
| 4 | $500 | $150 | $50 | $35 | $10 | $5 | ||||
| 5 | $1000 | $350 | $100 | $50 | $35 | |||||
| 6 | $6000 | $675 | $275 | $100 | ||||||
| 7 | $18500 | $3000 | $750 | |||||||
| 8 | $35000 | $10000 | ||||||||
| 9 | $200000 |
*: The Catch column does not include the Bulls Eye ball.
The final table on this game shows the return of both the Hot Spot and Bulls Eye bets according to the number of picks, based on the Typical Prize Amounts in the Regulations and the probability of winning. I know these fall short of the 63.5% return claimed, but the Regulations don't give me enough information to analyze this one properly.
Hot Spot and Bulls Eye Returns
| Pick | Hot Spot | Bulls Eye |
|---|---|---|
| 1 | 50.00% | 55.00% |
| 2 | 54.11% | 55.85% |
| 3 | 63.83% | 59.76% |
| 4 | 65.86% | 61.63% |
| 5 | 65.16% | 59.99% |
| 6 | 57.43% | 55.77% |
| 7 | 57.66% | 57.35% |
| 8 | 58.45% | 56.61% |
| 9 | 55.51% | 57.01% |
| 10 | 59.66% | 55.47% |
Scratchers
Scratch card games are simple games on a card. The player scratches to reveal his prize. At the time of this writing, scratch cards were available at costs of $1, $2, $5, $10, $20, and $30.
The Lottery doesn't implicitly state the percentage of money returned to the player. However, they kindly indicate the number of tickets printed and the odds of winning, which is enough to calculate the return percentage. Let's look at the Year of the Monkey $1 game, as an example. They tell us everything we need to know, except the numbers of losing tickets. We can get at the total number of all tickets printed by multiplying the number printed for any given win by the inverse of the probability of winning. For example, there were 38 $800 tickets printed. The probability of winning is 1/487263. So, the total tickets printed is 38*487,263 = 18,515,994.
Next, let's subtract out the 'ticket' winners, under the assumption the player will keep playing until he either wins some money or loses. They tell us the number of ticket wins is 1,555,344. So, the sum of monetary wins and losses is 18,515,994 - 1,555,344 = 16,960,650. The total monetary wins is 2,319,026. That leaves 16,960,650 - 2,319,026 = 14,641,624 losers.
We can now set up a return table for the game, as follows:
Year of the Monkey
Chances Of Winning The Lottery In The Philippines
| Win | Tickets | Probability | Return |
|---|---|---|---|
| 800 | 38 | 0.000002 | 0.001792 |
| 100 | 495 | 0.000029 | 0.002919 |
| 40 | 7,684 | 0.000453 | 0.018122 |
| 20 | 44,439 | 0.002620 | 0.052402 |
| 10 | 162,950 | 0.009608 | 0.096075 |
| 5 | 399,916 | 0.023579 | 0.117895 |
| 4 | 592,502 | 0.034934 | 0.139736 |
| 2 | 1,111,002 | 0.065505 | 0.131009 |
| Loser | 14,641,624 | 0.863270 | 0.000000 |
| Total | 18,515,994 | 1.000000 | 0.559951 |
The lower right cell shows the Year of the Monkey game has a return of 56.00%. The probability of any win is 100% - 86.33% = 13.67%.
However, not all games have the same return. As a rule of thumb, for any given denomination, returns are in a tight range. As you pay for more a ticket, the return percentage goes up. Here is the average return of some games I sampled, by denomination:
Scratch Card Average Returns
| Bet | Average Return |
|---|---|
| $1 | 56.75% |
| $2 | 61.95% |
| $5 | 66.97% |
| $10 | 72.95% |
| $20 | 76.22% |
| $30 | 79.72% |
I'm sure some people will not appreciate my mentioning this, but there is a potential advantage play in scratch card games. 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'll leave the details to the reader (don't you hate it when I say that?).
Multi-State Games
California participates in part of both multi-state lotteries, the Powerball and Mega Millions.
According to Lottery regulations, approximately 50% of money bet is returned to winning players source: California Lottery Regulations, page 36, 42). Unlike other states that participate in these games, all prizes in California are on a pari-mutual basis. However, the big jackpot will be the same as it is in the other states, at any given time.
Please see my Powerball page for more information on that game. A Mega Millions page is coming soon.
Second Chance
Losing Scratchers, Fantasy 5, and SuperLotto Plus tickets are eligible to enter a weekly second chance drawing. To enter the drawing, the bettor must open an account through the California Lottery web site and submit the losing ticket numbers. In the unlikely chance the player wins anything in the weekly drawing, he will be alerted by Email.
Based on a randomly-chosen week, I estimate players bet $2,561,530 on Fantasy 5 tickets. The second chance drawing for that game pays out $42,000, for an additional return to the player of 1.64%.
By similar math, for the SuperLotto Plus, I show $5,044,584 in ticket sales and $75,000 in prizes for an additional 1.49% of money bet returned to the player.
I do not know the return paid to Scratchers players, but assume it to be about the same.
Of course, to have a chance at a Second Chance, you have to enter. The expected return will be greater than the figures above according to how many other losers don't bother to enter the Second Chance drawing, as you are competing against only players that enter.
Internal Links
Chances Of Winning The Lottery Percentage
How To Play The Lotto
External Links
- California Lottery — Official web site.
- California Lottery Regulations — The fine print of the game rules.
- Wikipedia — Page on the California Lottery
Chances Of Winning The Lottery
Written by:Michael Shackleford