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The Numbers In Lottery Games

There are many lottery games to choose from. The games vary in themes, the number of matches or picks that are made, the pay out methods and how the winning number are selected. All lottery games have some common elements to them. The first and most significant common element is that the lottery is a game of chance. How much of a chance is determined by the second common theme to all lottery games. You pick a certain number of items, usually numbers, that you believe will be selected during the drawing. If the items you selected match the items chosen during the drawing you win. If more than one person matches the winning drawing then you share the jack pot.

The odds of winning are determined by the number of things you have to pick and match to. If you are playing lottery games that you have to match 2 numbers in a range of 20 possible numbers then the odds are calculated in the following manner.

The first number you have to pick correctly has 20 possibilities so you have a chance of 1/20 or 1 in 20. That is 0.05.

The second number you have to pick correctly has one less possible outcome (the number picked above) so you have 1/19 or 1 in 19. That is 0.0526.

When we multiply the two odds together we get 1/20 X 1/19 = 1/380 but wait, we are not done yet. Since the order of the numbers does not matter we can win with two sets of numbers. The first way we can win is with our first number matching the drawing's first number and the second way is with our first number matching the drawing's second number so we could win one of two ways. That changes our odds to 2 in 380 or 1 in 190. Not too bad but most lottery games have odds that are much higher than this!. Change the number of picks we have to match to something more inline with a real lottery and we get something else all together.

The math for a lottery with 5 numbers and 50 numbers looks like:

First pick is: 1/50 or 0.02
Second pick is: 1/49 or 0.020408
Third pick is: 1/48 or 0.020833
Fourth pick is: 1/47 or 0.021277
Fifth pick is: 1/46 or 0.021739

or 1/50 x 1/49 x 1/48 1/47 x 1/46 = 1/254251200

and since we have to pick 5 numbers and order does not matter we use 5! (5 factorial) whichis 120 so we get: 120/254251200 or 1 in2.19 million.

So you can see that the odds go up quickly with the number of items you have to pick and the number of items you pick from. Organizers of lottery games know this and do everything they can to keep the odds high so the jack pots continue to climb making more people want to play. Lottery games are number games and no matter what you wind up picking or what they call it, the odds are calculated in the same manner.