Probability of winning the lottery the more you play it? Recently I was having a conversation with a philosophy student on gambling and it intrigued me because of what the person was saying. Before I say what the person said, I remember learning in class that the probability of something occurring does not increase as you use it. For example, if I flipped a fair coin, no matter how many times I flip the coin it will always have a 50% chance of landing heads or tails. However according to the person, he said that the more times I play a lottery machine, my chances of winning will increase as well. Can someone explain to me the difference between my statement and his? 
I am thinking that my statement only refers to single events, but his refers to total probability?
 A: The outcome of any coin toss is independent of the previous result; be it heads or tails, the coin is "memory-less".
However you have a greater chance of winning the lottery if you have more goes it at.
Similarly if you only flipped a coin once you are going to see only one of either heads or tails, if you flipped it 100 times say, chances are you are going to see both. 
A: Just to elaborate a bit on what others have said.
Suppose you flip a coin 3 times and that a winning flip is heads. There are 8 different equally-probable outcomes
(H H H), (H H T), (H T H), (T H H), (H T T), (T T H), (T H T), (T T T)
The probability of never winning (which corresponds to only the outcome (T T T) ) is therefore $1/8$, which is lower than the probability of losing a single coin flip.
A: Exactly.  Try it like this:  let's say instead of drawing balls, the "lottery" would consist of a single coin flip.  If you play once, you have a 50% chance of winning.  If you play twice, your probability of winning at least once is already 75% (there are four equally likely outcomes:  First round win, second round win (WW), first round win, second round lose (WL), LW and LL).  The more you play, the smaller the percentage of "lose-only" outcomes will get.  (The exact probabilities can be derived with the binomial distribution as mentioned in a comment above.)
If you keep playing until eternity, and then look back..., you will see that you have won it about half the time... but lost in total money terms, as the price of the lottery ticket exceeds your average gain (usually drastically).
A: In the example of a coin toss, each flip is discrete, therefore you have a 50% chance of guessing correctly and a 50% chance of guessing wrongly. The result of the previous flip has no bearing on the result of the subsequent flip, therefore you still have a 50/50 chance.
The same can be said for the lottery; the balls are drawn at random, after fully mixing with each other in the machine, we are led to believe that each ball is of identical mass and size, thus no ball is more likely to be drawn than any other. The result of this, is again, a discrete game.
E.G. Let us say that the outcome of a lottery was thus: 8, 12, 42, 24, 5, 38. The probability of winning the national lottery is around 1 in 14m, thus there is a 1 in 14m chance that the next draw will yield the exact same result (order does not matter). In summary, each lottery draw is discrete, thus you have no more, or less, chance of winning each time you play. You can increase your chances by purchasing multiple tickets, but this will not make you more likely to win any subsequent lotteries.
Hope that helped :-)
