0

Do you stand more, less, or the same chance of winning a lottery jackpot by playing 100 tickets for one draw once a month? Or by buying one ticket every day for 30 days?

My initial assumption is that by playing 100 tickets once a month, you have moved the decimal point over two positions and thus stand a better chance with 100 tickets once a month. However, with one ticket every day for 30 days, you face the same astronomical odds each day. Is my assumption correct that playing 100 tickets once a month gives a slightly better chance of winning than buying one ticket every day for 30 days (the same game throughout, of course, in both instances)?

Tom Cullem
  • 9
  • The easy thing is that by buying $100$ instead of $30$ tickets your chances will be about $\frac {10}3$ times higher because you bought more tickets. Buying multiple tickets to one game gives you a slightly higher chance than buying single tickets to multiple games. The expected number of wins is the same, but buying single tickets to multiple games gives the chance of winning more than once, so less chance of at least one win. – Ross Millikan Jun 30 '20 at 00:41
  • Thank you, Ross. My assumption was that while you get yourself more chances to win by buying one ticket every day, this is offset by the fact that you're betting daily against a new draw; while you are gaining more chances to win, they're at the smallest chances possible each time. The 100 tickets 1x month gives better chances at 1 set of numbers. I wouldn't bet my life on those reduced odds, by the way, but if you're running a Lotto pool where the gains are maximized (not guaranteed, mind) and the losses spread around, it seems to make more sense. I could be wrong? Tom C. – Tom Cullem Jun 30 '20 at 12:39
  • 1
    The difference in the number of tickets swamps everything. If you ask about buying $30$ tickets one day vs one per day for a month, the only difference is the small chance of more than one win. Otherwise the chances are the same. Buying them all on the same game lets you make sure the numbers are different and at most one ticket wins. – Ross Millikan Jun 30 '20 at 13:21
  • Does this answer your question? If I play the lottery with a specific amount of money, should I put it all on one game or distribute it among several games –  Apr 05 '23 at 00:41

2 Answers2

2

Well, in one case, you're buying $100$ tickets for a single lottery, once a month, while in the other case, you're buying about $30$ tickets a month, so your chances are more than three times as good in the former case.

But imagine that you compare buying $30$ tickets for a single lottery, once a month, against buying one ticket a day, each for a single lottery, for the thirty days in a month. Then it's more of an apples-to-apples comparison.

Suppose that the lottery is a lotto: Each ticket has a one-in-$N$ chance of winning. We'll also assume that you're buying $30$ distinct tickets in the former case. Then the odds of being a winner in the former case is $\frac{30}{N}$, while in the latter case, the odds of being a winner are $1-\left(1-\frac1N\right)^{30}$, which is ever so slightly less than $\frac{30}{N}$. The difference is made up for by the fact that you have an even more microscopic chance of being a multiple winner, which you obviously can't do in the former case.

On the other hand, suppose that each day, there's exactly one winner, and $M$ other players. So in the former case, on the day that you play, you have a $\frac{30}{M+30}$ chance of winning.

In the latter case, you have a $\frac{1}{M+1}$ chance of winning each day you play, but you play $30$ times, so your overall chances of winning are $1-\left(1-\frac{1}{M+1}\right)^{30}$, which is this time slightly higher than in the first case (for large values of $M$)—with the difference being accounted for by the fact that you're not buying a bunch of tickets with diminishing returns.

Brian Tung
  • 35,584
  • The particular game I'm addressing is played every day. On rare occasions, there have been a couple of winners in one day, but for the most part, the odds being 21 million:1 (on one bet, of course), usually two months can go by with no jackpot winners. This is the Cash4Life game. 100 tickets reduced the chances of winning from 21+ million:1 to 218,460:1. Again, I wouldn't bet my life on those odds, but it does seem that 30 consecutive days at 21 million:1 makes less sense than 218,460:1 once a month, especially with a Lotto pool. No? Tom C. – Tom Cullem Jun 30 '20 at 12:57
  • @TomCullem: Yes, but you can't just look at the $21$ million and say, well, obviously. If you divide $21$ million by $30$ you get about $700$ thousand, and that's well above $218$ thousand. If you played at $21$ million-to-$1$ odds for over $100$ days, then that's approximately when the switchover happens to favoring that option. – Brian Tung Jun 30 '20 at 16:38
0

yes -- odds are the same per ticket, no matter when you buy them (provided it's the same lottery). So buying 1 ticket per draw over the course of 100 draws gives (technically) the same odds of winning as buying 100 tickets of the same draw HOWEVER, if you skillfully selected different numbers in all of those 100 tickets that you bought to play on just one draw, then that would give you better odds than if you were to buy 1 ticket in each of 100 different draws. IN both cases, buying only 30 tickets gives lower odds of winning.

Rene
  • 33