HOW TO WIN THE LOTTERY!!
Buying lottery tickets is easy. Anybody can do it, but since state-run lotteries in the USA typically pay out only half of their revenue to the winners, it's one of the worst investments one can make. That's a house edge of about 50 percent - for comparison, most casino table games have house edges under 10 percent. This is frequently combined with misleading advertising (jackpots advertised as the nominal value of a 30-year annuity, while tickets must be paid for in today's dollars) and unfavorable tax rules.
Overcoming these disadvantages will not be easy. This article is not about playing the lottery - it's about winning the lottery. That means doing a lot of math and, except in very rare and exceptional situations, deciding not to play.Steps
- 1Learn the math behind the lotteries. There are many different games being sold, each with their separate rules, but the basic tools for analyzing them are the same. At minimum, you must understand permutations, combinations, probabilities, odds, and expected value.
- 2Skip scratch-off tickets and any games whose rules you don't understand or whose odds depend on information you don't have access to. Some scratch-off games can be beaten as well, but this is more likely due to exploiting non-randomness in the distribution of winning tickets or the printing process. There is no generally effective process for discovering such exploits. (If there was, the lottery commissions would have already used it to discover and close the vulnerability.) The basic probability theory described here only applies to games that are truly random.
- 3Find the expected value of every lottery game you are considering. This is the fair value of the ticket if the game was set up so that the revenue from losing tickets would exactly pay for the winners' profits. Expected value is calculated by multiplying the probability of each type of win by the payout for that win and summing that over all winning combinations. You should be able to do this for Pick 6 or any other ball drawing game.
- 4Account for any non-cash prizes by taking their cash value to you. Convert annuities to their present values, free tickets to their expected values, etc.
- 5Look for any special circumstances that may increase the expected value. These will need to be significant in order to overcome the house edge computed above. A promotion that adds 10 percent to the prize pool will help you lose more slowly, but won't be enough to let you win. You need something that doubles the value of a ticket.
- One example of this was the Missouri Lottery's promotion in the daily Pick 3. Normally a player has a 1/1000 chance of winning a $600 prize, making a $1 ticket worth only $0.60. The promotion was to draw a second winning combination on one randomly selected day of the week. Originally, the drawing to determine whether the bonus would occur that day held six white balls and one orange, but on the last day of the week, all six white balls had been removed, leaving only the orange ball and ensuring a double drawing on the last day. This doubled the value of tickets for that drawing and converted them from an expected 40 percent loss to a 20 percent gain. See table 1 below for how the expected value varied that week.
- One example of this was the Missouri Lottery's promotion in the daily Pick 3. Normally a player has a 1/1000 chance of winning a $600 prize, making a $1 ticket worth only $0.60. The promotion was to draw a second winning combination on one randomly selected day of the week. Originally, the drawing to determine whether the bonus would occur that day held six white balls and one orange, but on the last day of the week, all six white balls had been removed, leaving only the orange ball and ensuring a double drawing on the last day. This doubled the value of tickets for that drawing and converted them from an expected 40 percent loss to a 20 percent gain. See table 1 below for how the expected value varied that week.
- 6Look for progressive jackpots. Larger jackpots increase the payouts and therefore the value of a ticket. The value of a large progressive jackpot is very sensitive to the exact rules of the game, so be sure to understand them.
- The Massachusetts lottery imposed purchase limits after it was discovered that their Cash Winfall game had a positive expected value after a jackpot was rolled down to increase the payouts for lower level prizes.
- In the Mega Millions multi-state lottery, jackpots are split equally among all winners who match all numbers. If a player could ensure that he wouldn't have to split the jackpot, Mega Millions becomes a smart bet whenever the jackpot exceeds about $420 million, but this calculation doesn't account for the possibility of a split jackpot. It has been theorized that the ticket buying frenzies as the jackpot rises increases the likelihood of multiple winners sufficiently that the jackpot can never get large enough to give a ticket a positive expected value.
- The Massachusetts lottery imposed purchase limits after it was discovered that their Cash Winfall game had a positive expected value after a jackpot was rolled down to increase the payouts for lower level prizes.
- 7Treat the lottery as a donation; play for entertainment value if you have money you want to lose, stay away if you don't.
- 8Be sure to consider the tax implications. In the United States, gambling winnings are taxable, but gambling losses are only deductible to offset winnings. This legal asymmetry may affect the math in certain situations. As shown in table 2 below, the double draw promotion that resulted in a 20 percent player advantage before tax considerations is only profitable after taxes provided the player can purchase the hundreds or tickets required to cover a significant fraction of the 1000 outcomes.
Tables
| Day | White Balls | Orange Balls | Probability of second drawing | Expected profit/loss per ticket |
|---|---|---|---|---|
| Normal | N/A | N/A | 0 | -$0.40 |
| 1 | 6 | 1 | 0.143 | -$0.31 |
| 2 | 5 | 1 | 0.167 | -$0.30 |
| 3 | 4 | 1 | 0.200 | -$0.28 |
| 4 | 3 | 1 | 0.250 | -$0.25 |
| 5 | 2 | 1 | 0.333 | -$0.20 |
| 6 | 1 | 1 | 0.500 | -$0.10 |
| 7 | 0 | 1 | 1.000 | +$0.20 |
| Number of tickets | Cost $ | Lose both drawings | Win one drawing | Win both drawings | Post-tax expected value | Post-tax percentage profit | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| prob | pretax$ | post-tax $ | prob | pretax$ | post-tax $ | prob | pretax$ | post-tax $ | |||||
| 1 | 1 | 0.998001 | -1 | -1 | 0.001998 | 599 | 419.30 | 10-6 | 1,199 | 839.30 | -$0.16 | -15.94% | |
| 10 | 10 | 0.980100 | -10 | -10 | 0.019800 | 590 | 413.00 | 0.0001 | 1,190 | 833.00 | -$1.54 | -15.40% | |
| 100 | 100 | 0.810000 | -100 | -100 | 0.180000 | 500 | 350.00 | 0.0100 | 1,100 | 770.00 | -$10.30 | -10.30% | |
| 250 | 250 | 0.562500 | -250 | -250 | 0.375000 | 350 | 245.00 | 0.0625 | 950 | 665.00 | -$7.19 | -2.88% | |
| 500 | 500 | 0.250000 | -500 | -500 | 0.500000 | 100 | 70.00 | 0.2500 | 700 | 490.00 | $32.50 | 6.50% | |
| 750 | 750 | 0.062500 | -750 | -750 | 0.375000 | -150 | -150.00 | 0.5625 | 450 | 315.00 | $74.06 | 9.88% | |
| 1000 | 1000 | 0 | -1,000 | -1,000 | 0 | -400 | -400.00 | 1 | 200 | 140.00 | $140.00 | 14.00% | |
