In this thread we will discuss how to calculate your odds of winning a draw game if you buy more than one ticket.
Any lottery's website gives you the odds, but that is for one ticket.
When you buy more than one ticket, you can calculate your odds of winning simply by dividing the stated odds by the number of tickets you hold.
Let's take, for example, a Pick 2 game. Even if your state's lottery doesn't operate a Pick 2, if they operate a Pick 3 and let you bet on the front pair or back pair, that is a Pick 2.
In the Pick 2 game, there are 100 possible winning combinations that range from 00 to 99. All 100 possible combinations are equally likely. Each one has a 1 in 100 (or 0.01, or 1%, they're all the same) chance of winning.
Let's say you buy one ticket, and you choose to bet on 37. 37 has a 1 in 100 chance of being the winner.
Now let's say you decide to buy a second ticket. While you could buy another ticket betting on 37, your odds of winning will not change but you'll double your winnings because you've doubled your bet. So let's say you buy another ticket with a different number. How about 65.
If you hold two tickets for Pick 2, betting on 37 as well as 65, your odds of winning are 1 in 50. The calculation is 2 [number of distinct bets you have made] divided by 100 [number of possible outcomes]. 2 divided by 100 is 1/50. 2/100=1/50=0.02=2%.
You could also buy a third ticket (betting on a different number) and then your odds of winning improve to 1 in 33.3333. And so on.
If you continue with this and buy all 100 possible numbers, you now have a 100% chance of winning. It's guaranteed. You'll lose money, though, unless the lottery is doing a great promotion (like the Mississippi triple pay promotion) because the lottery pays you less than what that ticket is really worth. In a perfect world, one ticket in Pick 2 should pay $100 on a $1 bet, but they will pay you only $50, with the other $50 used to pay for retailer commissions, ticket paper, advertising, etc., and of course, profit.
This very easy way to calculate your odds of winning apply only if you buy multiple tickets with different numbers on them. If you buy QP, then things will start to change. With the second QP ticket, you have a 1 in 100 chance of the QP generator picking the same number as your first ticket.
If you were to buy 30 QP tickets, your chances of all 30 tickets being different are quite low -- only 0.78%. In other words, with 30 QP Pick 2 tickets, you have a 99.22% chance of having at least one duplicate.
For draw games with really long odds, like Powerball or Megamillions or even your state's in-state draw game, the chances of getting duplicate QP is really low. With PB/MM and its 1 in 300 million jackpot odds, if you buy 100 QP tickets, your chances of one duplicate is only about 1 in 60,000. So for those games, if you buy multiple tickets using QP, it's okay to estimate your odds of winning by taking the stated odds of a single ticket winning and divide by the number of tickets you bought.
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