Twitter (NYSE:TWTR) is finally public and yesterday the stock jumped an astonishing 73% from its $26 IPO price. In most places you'll read that that kind of jump is the result of a wildly successful IPO. But is that really true?

Let's take a look at the winners and losers of yesterday's IPO.

Twitter is tweeting mad
In its simplest form, an IPO is a way for a company to raise cash. From Twitter's perspective, they want to raise the cash they want from investors for the fewest shares possible. Any gain the day the stock begins trading is money left on the table. In fact, Twitter itself would love it if the stock dropped on day 1.

Yesterday, Twitter sold 70 million shares, of the fully diluted 705 million available, for $1.82 billion. If underwriters exercise an overallotment (which they will), it will sell a total of 80.5 million shares for $2.093 billion.  

The problem is, as of yesterday's close those 80.5 million shares were worth $3.614 billion, meaning Twitter left $1.521 billion on the table. From Twitter's perspective, the IPO was a complete disaster.

Underwriters win no matter what
Goldman Sachs (NYSE:GS) was Twitter's lead underwriter with JPMorgan and Morgan Stanley taking a significant role as well. These underwriters take a cut of Twitter's proceeds but their real upside is the overallotment I mentioned above.  

Underwriters generally have a 30-day option to buy another 15% of the IPO, in this case 10.5 million shares for $26 if there's demand for shares. We don't know exactly when underwriters sell shares or who gets them, but let's assume they sold shares at yesterday's closing price of $44.90.

Under this scenario, underwriters could have walked away with an additional $198.5 million in profit. If you're an investment bank, under-pricing an offering pays.

Twitter's first public investors
Who did get to buy shares of Twitter at $26? The lucky investors who got a 73% gain yesterday are in large part big institutional investors, who have a good relationship with the underwriters. These are hedge funds, wealthy investors, mutual funds, pension funds, etc. Sometimes, online brokerages are allotted some shares and if your broker is Goldman Sachs or another underwriter you have a better shot than most individual investors. But for the most part, you and I are out of luck when it comes to getting IPOs at their advertised price.

We're stuck paying for the stock after its pop yesterday. The big fish are the ones who made out like bandits yesterday.

Who won the Twitter IPO?
Investors who paid $26 for shares were big winners yesterday, notching a 76% gain in a matter of minutes. Investment banks who underwrote the offering were also big winners, potentially locking a $198.5 million in profits on overallotment, on top of its standard fee.

On the other hand, Twitter itself was the biggest loser in the IPO yesterday. The company left more than $1.5 billion on the table by pricing shares lower than the public markets were willing to pay.

Most headlines won't tell the story from Twitter's side, but it should be steaming mad today.

Fool contributor Travis Hoium has no position in any stocks mentioned. The Motley Fool recommends Goldman Sachs. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.