"Zero sum" means that adding the winners and subtracting the losers produces a result of zero - both winners and losers are equal.
  This is because in a zero sum market, you buy something from someone who is selling it, so if one wins, the other has to lose.
  Good examples of zero sum markets are the options and futures markets, both of which are very popular with day traders.
The stock market on the other hand, is not a zero sum market because stocks go up over the long term and it is possible for everybody to be a winner if they all wait long enough.
  In the very short term, that is far from certain however and this is where day traders play-the very short term.
  This is why, for day traders, even the stock market ends up being a zero sum game because when they close out their positions for the day they either won, causing the person on the other side of the trade to lose, or they lose, causing the person on the other side to win-adding up to a net zero between the two sides.
As you can see, it is all really a question of blind luck but it is important to understand that the winners in this zero sum game are usually the folks who have a strict discipline in place and play against those who do not.
  The winners will typically have a clear game plan, have set limits and act only on cold facts whereas the losers typically act on their emotions, mainly fear and greed.
  Also, the biggest winners are typically the ones who take the biggest risks.
  I would consider any money I set aside for day trading to be money that I will feel OK about losing completely.
  Much like I would treat the slots in Vegas.
  At least that way I have some fun with it.
  You, and many others, may take it very seriously and make it your main financial strategy.
  There is no right or wrong way to look at it as long as you know what you are doing and can manage your expectations.