# How to Win More in a Lottery Pool

TR Smith is a product designer and former teacher who uses math in her work every day.

## 4 Mathematcial Strategies for Playing in Lottery Pools

Have you ever wondered why large groups of players often win the big lottery jackpot prizes? It's simply because groups buy lots of tickets, and buying more tickets is the best way to increase your chances of winning.

If you want to improve your odds of winning the lottery by playing in lottery pools (also called clubs, syndicates, or collectives) there are several tricks that will give you an edge over other lottery pools and individual players. Most lotto pools just buy a bunch of tickets using quick picks (called "lucky dips" in some countries) and don't give much consideration to which lotteries they play or how the numbers are distributed. However, with a little research and some understanding of probability math, your lottery pool can make the most of your collaboration to win more often. Here are four secret tricks used by the winners.

## Tip 1: Select Ticket Numbers Deliberately to Minimize Overlapping Combinations

What increases your probability of winning the lottery is not just buying more tickets for a particular drawing, but buying tickets with different numbers, and with as few overlapping combinations as possible. If you use quick picks, you run the risk of buying tickets where some subsets of numbers are duplicated.

For example, consider the Mega Millions Lottery offered in most parts of the US. This lottery is structured as five distinct white ball numbers chosen from 1 to 75, and one gold ball number chosen from 1 to 15. If your lottery pool decides to buy 15 tickets for this game, the strategy that will maximize your odds of winning any prize is to make sure that every single number is used exactly once for the white balls and gold balls. The following set of 15 tickets perfectly partitions the set of white and gold balls:

{1, 2, 3, 4, 5} + 1
{26, 27, 28, 29, 30} + 6
{51, 52, 53, 54, 55} +11
{6, 7, 8, 9, 10} + 2
{31, 32, 33, 34, 35} + 7
{56, 57, 58, 59, 60} + 12
{11, 12, 13, 14, 15} + 3
{36, 37, 38, 39, 40} + 8
{61, 62, 63, 64, 65} + 13
{16, 17, 18, 19, 20} + 4
{41, 42, 43, 44, 45} + 9
{66, 67, 68, 69, 70} + 14
{21, 22, 23, 24, 25} + 5
{46, 47, 48, 49, 50} + 10
{71, 72, 73, 74, 75} + 15

Since the Mega Millions Lottery awards a \$1 prize for matching only the the gold ball number, you are guaranteed to win at least \$1 if you play a set like this. With quick picks, it is very unlikely that you will get perfect non-overlapping sets.

If you buy 16 tickets for a 6/49 game, such as Canadian Lotto 6/49, the following set also has the least amount of overlap. No two numbers appear together twice, and every number is used twice, except for 48 and 49 which are only used once.

{1, 2, 3, 4, 5, 6}
{1, 9, 17, 25, 33, 41}
{7, 8, 9, 10, 11, 12}
{2, 10, 18, 26, 34, 42}
{13, 14, 15, 16, 17, 18}
{3,11, 19, 27, 35, 43}
{19, 20, 21, 22, 23, 24}
{4, 12, 20, 28, 36, 44}
{25, 26, 27, 28, 29, 30}
{5, 13, 21,29, 37, 45}
{31, 32, 33, 34, 35, 36}
{6, 14, 22, 30, 38, 46}
{37, 38, 39, 40, 41, 42}
{7, 15, 23, 31, 39, 47}
{43, 44, 45, 46, 47, 48}
{8, 16, 24, 32, 40, 49}

There are many ways to make these partitions; the examples in the tables are only to illustrate the basic principle. The more tickets you buy for a drawing, the harder it is mathematically to come up with these optimal partitions. However, you only have to do the legwork of finding good sets once, and then you can play the same combinations over and over.

## Tip 2: Don't Pay Extra for Multipliers and Bonus Numbers

Many lotteries offer multipliers and bonus numbers for an extra \$1 per ticket. For example, Florida Lottery with Xtra and Illinois Lottery with Extra Shot are two state lotteries that sell "upgrades." These add-on features increase the prize amounts if you happen to win, but they don't increase your overall odds of winning. They also don't increase the size of the jackpot if you happen to make a perfect match. For the same amount of money, you can buy more basic tickets, which is the only thing that will increase your chances of winning.

For example, with \$18 you can buy either six Powerball tickets with the Powerplay option, or nine regular Powerball tickets. For the same \$18 you can buy nine Mega Millions tickets with the Megaplier option, or 18 regular Mega Millions tickets.

## Tip 3: Don't Split the Pool Among Several Lotteries! Play a Single Game Only

Some members of lottery pools mistakenly think that dividing the pooled money among different lotteries will increase their chances of winning. In fact, the opposite is true. The more tickets you buy for a single drawing, the better your odds of winning that drawing.

Suppose your lottery club collects \$30 from its members. If you live in Texas, the best strategy would be to spend that amount on 30 Texas Two Step tickets that cost \$1 each. The worst strategy would be to buy a few Powerball tickets, several Mega Millions tickets, some Lotto Texas tickets, a couple of Texas Two-Step tickets, and some scratch cards. Spreading the money over several different games dilutes the power of group buying.

## Tip 4: Play Games with Better Odds of Winning Non-Trivial Prizes

The definition of "non-trivial" varies from person to person, but for the purpose of this article let's say a non-trivial lottery prize is greater than \$10. The probability of winning a non-trivial Powerball prize is about 0.0001358 or about 1 in 7,364. The probability of winning a Mega Millions prize greater than \$10 is about 0.001136, or about 1 in 8,801. Powerball is even worse because a basic ticket costs \$2, whereas other lotteries' basic tickets cost only \$1.

In contrast, the probability of winning a prize over \$10 in Ohio Classic Lotto is about 0.0009871, or about 1 in 1,013. In general, state lottos offer much better odds than the big national lotteries. Here are the odds of winning prizes over \$10 in other US lotteries.

As you can see from this sample, playing low-stakes lotteries increases your chances of winning a prize that's worth the effort to claim. Even though Powerball, Mega Millions, EuroMillions, and other large national lotteries around the world offer enormous jackpots, they are a bigger waste of money odds-wise than smaller games with less publicity.

## Tip 5: Don't Buy Scratchers or Scratch Offs

Scratchers or scratch off tickets are "instant win" games. Many informal studies have shown these games are rigged and are more of a sucker's bet than the regular draw lottery. Curiously, convenience store owners account for a large proportion of winners of scratch cards, which suggests they know how to identify winning tickets or tickets that are likely to win in their inventory. What they leave for the unsuspecting public to purchase are the losers or likely losers.

## Related Lottery Math Articles

To better understand how lottery probabilities work, see these related articles

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## Popular

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• canton 21 months ago

we always buy 9 lotto texas tickets at a time with the numbers

1-4-23-24-45-51

2-10-13-43-49-54

3-14-29-33-35-47

5-8-12-19-37-46

6-11-20-30-41-52

7-15-21-22-28-39

9-16-25-36-48-50

17-18-26-27-31-40

32-34-38-42-44-53

to split up the 54 numbers into 9 groups of 6 and give every number an equal chance. but sometimes two tickets could both win a lower prize in the same drawing even though they have different numbers, so what is the total probability that we win something with this set? i'm thinking it has to be less than 9 times the base probability because of the times when two tickets can both win.

• Elisabeth Meier 15 months ago

Too bad, I wish you would tell how to win the 6/49 ticket your first pictures shows. =) If this all really just follows a logic how much money have you won over the years? I think what makes it difficult is a double probability which means all numbers have the same probability in each new lottery game. But how probably is it that all numbers appear again or how probably is it that one number appears again more than twice in a row of three weeks?

So, are they any tips and tricks for 6 aus 49?