What is the probability that the stock market closes higher on any given day?

The punch line: The probability that the stock market closes higher on any given day is (only) 53.7%. That's it. Better than flipping a coin, but not by much. The rest of the time it finishes lower (45.2% of the time) or unchanged (1.1%). Yet, because of compounding, this is all that it takes to produce a trend -- and a strong uptrend -- over time.*

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On any given day will the stock market rise or fall? I used daily adjusted closing price data from Yahoo! Finance for SPY, the S&P 500 ETF to find out. The data span 01/29/1993 to 12/11/2014. Here is a bar chart with results grouped by year:

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The bar chart is not zeroed on the y-axis and is scaled to make the differences apparent. The probability of up days spans a range of 47.4% (in 2002) to 59.2% (in 2014). On any given day, the stock market will rise 53.7% of the time (and fall or remain even 46.3% of the time). Your odds of making money are roughly 27:23, or even more roughly, 6:5. That's it. Don't bet the farm. For such a short period as a day, you're essentially tossing a coin.

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*  I'm almost certain that this phenomenon is similar to why a tiny preference by people for some attribute leads to a clustering of those attributes around a geographic area over time. In other words, what we expect to be a random distribution of attributes over geographic area instead exhibits a clustering effect. Likewise, for us, what we expect to be a random distribution of stock prices over time, instead behaves -- when there's a slight increase in chance -- as a strong trend of gradually rising prices.