As a child, I was fascinated with lottery odds. I recall that the odds of winning the Florida lottery jackpot at that time were about 1 in 14 million, and that scratch-off tickets displayed the odds of winning a prize on the back, which was usually around 1 in 4.
The above graph (drawn by me) is actually far too optimistic. The odds of overall gains are lower than 1 in 4 because a typical scratch-off or instant-win ticket counts a prize of the same amount as the purchase price as “winning,” even though this is actually breaking even. Of course, buying a $2 ticket and “winning” $2 is the second commonest outcome, behind the most common outcome of losing $2. Further, the overall odds of making money decline precipitously as additional tickets are purchased. Although the “1 in X” odds of winning X fantastic prize increase with the purchase of additional tickets, the value of the improved odds is always far below the ticket price.
These same principles apply to drawings like the Powerball and to games of chance at casinos. If you don’t want to lose money, the best number of tickets to buy or tokens to insert into the slot machine is zero. The next best number is one, followed by two, three, and so forth. Regardless of past events, the best financial decision is to stop gambling immediately. There are no hot streaks or “lucky” numbers. You are not “due” to win something after buying 10 losing tickets. If you have lost money gambling, the most reliable way to get “back to even” is to stop gambling and make money through some other means.
Scratch-off tickets can roughly be represented by the skewed curve above (courtesy of Dan Ma). The numbers on the y-axis (far left) are the number of scratch-off tickets purchased. The numbers on the x-axis (bottom) are the probabilities of losing money based on purchasing that number of scratch-off tickets. Multiply these numbers by 100 to get percentages.
Here, we see that buying one ticket gives you about a 79% chance of losing money, two tickets an 83% chance of losing money, and eight tickets a 95% chance of losing money. This is pretty close to your actual odds when buying scratch-off tickets, and this same statistical principal of probability applies to all forms of gambling. More gambling results in nearly 100% certain losses.
A better use for you money is long-term investing in the entire stock market, where putting more money in for longer times results in nearly 100% certain gains rather than losses.