At Berkshire Hathaway's (BRK.A 0.64%) (BRK.B 0.54%) annual shareholder meeting on April 30, Warren Buffett revealed that Berkshire had increased its stake in Activision Blizzard (ATVI) to 9.5% of the company. And most of this stake was accumulated after Microsoft (MSFT -1.84%) had agreed to buy the video game maker for almost $69 billion.

Buffett's move drew criticism from some investors, especially since he had just made negative comments about the stock market turning into a casino. After all, a merger arbitrage play (more on what that is in a bit) is certainly a more bet-like investment than Buffett typically makes. However, when you take a step back from the deal, it starts to make a lot more sense.

Warren Buffett smiling for photos.

Image source: The Motley Fool.

Buffett's Activision Blizzard stake

Berkshire Hathaway first bought Activision Blizzard stock in the fourth quarter, a short time before Microsoft announced its plans to buy the company. Buffett has said that Berkshire Hathaway had no prior knowledge that the deal was in the offing when it made the investment -- it was simply buying a stake in the video game giant to hold in its portfolio.

However, the initial position was about $1.1 billion, rather small by Berkshire Hathaway's standards.

Investors were surprised to learn at the annual meeting that Berkshire Hathaway had acquired more Activision Blizzard, boosting his stake by nearly $5 billion. Buffett confirmed that since the acquisition deal was announced, his conglomerate had increased its stake in the video game maker to about 9.5%, a position now worth about $5.8 billion. And he specifically mentioned that the goal of the investment is to make a profit when the deal closes, a strategy known as merger arbitrage.

Merger arbitrage 101

Without getting into a textbook definition of what arbitrage is, the best way to think of it is as a "risk-free bet." For example, if you can buy a stock on one exchange for $20 and simultaneously sell it on another exchange for $20.50, that's a form of arbitrage. Arbitrage typically takes advantage of short-term price discrepancies in financial markets.

When it comes to merger arbitrage, the general idea is that after a company agrees to be acquired at a specific price, its shares will typically rise to a level close to -- but not quite equal to -- the bid price.

Consider this example. Student housing company American Campus Communities (ACC) recently agreed to sell itself to Blackstone (BX -2.33%) investment funds at a price of $65.47 per share in cash. The stock jumped after the deal was announced, and as I write this, shares trade for $64.70.

So, if you were to buy 1,000 shares of American Campus Communities now and hold them until the deal was finalized, you would receive $65,470 for a $64,700 investment, a profit of $770. That's the basic idea behind merger arbitrage.

Now, American Campus Communities stock is trading for about 1% less than the takeover price, indicating that the market views it as extremely likely that the deal will go through. Planned mergers and acquisitions do fall through from time to time -- sometimes regulators block a deal, for example. And the greater the perceived risk that a deal will hit a roadblock, the larger the spread between the current and takeover prices can be.

Why Buffett is particularly interested in Activision Blizzard

Buffett frequently did merger arbitrage deals in his younger years, but they've been quite rare throughout his 57-year tenure at the helm of Berkshire Hathaway. So, why is this one worth such a large bet?

In a nutshell, Buffett sees a big disconnect between the current price of Activision Blizzard shares and the $95 per share in cash Microsoft is planning to pay for the company. Even after the price uptick that came after Buffett announced his large position, Activision Blizzard still trades for less than $79 per share -- more than 20% below the deal price.

If Microsoft closes on this acquisition, Berkshire Hathaway stands to earn a profit in excess of $1.2 billion on its $5.8 billion investment.

Buffett clearly sees the deal as far more likely to go through than the stock price indicates. And while he admits that there is a fair amount of regulatory uncertainty in the U.S. as well as internationally, he correctly points out that Microsoft already has the cash to make the acquisition, which eliminates one major potential roadblock.

What happens if the deal doesn't go through?

To be fair, there is some degree of probability that the deal won't close. But here's why I still say that this arbitrage play isn't a gamble.

Obviously, Buffett wants to see the deal to close, have Berkshire Hathaway pocket its billion-dollar-plus profit, and move on. But let's say that it doesn't happen for one reason or another. Then Berkshire Hathaway will own 9.5% of a business that it already wanted to own a piece of before it was a takeover target. It's also worth pointing out that before the deal was announced, Activision Blizzard shares were trading for just over $65, compared to their 52-week high of more than $99, so he likely feels that the downside is rather limited if the deal falls through. In Buffett's mind, holding nearly 10% of a great business isn't a gamble, even if there's the potential for a short-term reward.