>>The odds of winning have absolutely ZERO to do with how many people are playing. It's all based the odds of picking the right numbers, which would be exactly the same if yours was the only ticket purchased.
>Except for the fact that sometimes more than one person picks the same winning numbers and the pot is split. The odds of that happening increases when more people play. Using your extreme example, the odds of you splitting a winning ticket when you are the only player is zero. The odds of you splitting a winning ticket increase with every increase in the number of players.
BlueMondaySkipper explained it very well. The odds of winning are not related on the number of people playing (ie, the number of tickets sold.) The odds of guessing all the numbers remain the same irrespective of the number of tickets betting. Also whatever numbers came out in prior drawing is irrelevant because lotteries are known as independent events, ie, current outcomes are not based on prior outcomes.
Absolutely. However, with more people playing, the odds are that you will split your pot which has happened in the past with very large jackpots. So although "the odds of guessing all the numbers remain the same irrespective of the number of tickets betting" the odds of you having to split your pot with another person who picked the same numbers increases with the number of players (which would decrease your winnings). The odds of you having to split your pot also increase if all the numbers are less than 31 because a lot of people choose numbers based on birthdays.