I know that entering the lottery ( which has a stated probability of 1 in 14 million of winning the jackpot) every week for 20 years dose not significantly increas your chances of winning it, over some on who enters just once.
How ever if you do enter 1X52X20 times how do you calculate how much more likely you are to win?
 Conversly 
If you enter 1040 times on the one draw how much more likely are you to win than the dedicated weekly player?
 Is it simply 1040 divided by 14 million ( ie 1 in 14,000) or
is it calculated using a sequence like (1 / (14,000,000))   (1 / (14,000,000 - 1)) (1/13,999,998)etc.
if so is there a quick way of evaluating the sequence?