By Jennifer Ablan

(Reuters) - Billionaire investor Carl Icahn is so convinced he was right to sell some of his Netflix Inc stake that he made a big bet - possibly worth hundreds of millions of dollars - with his son Brett, who disagreed with the decision.

Icahn, whose firm acquired Netflix shares for an average price of $58 against their current price at $330, cut his 9.4 percent stake by more than half to 4.5 percent, booking profits of around $800 million, he revealed on Tuesday.

His son Brett Icahn, 34, who came up with the idea to invest in Netflix, and Brett's investment partner David Schechter, said in a statement they believe the streaming video company is still undervalued. They said they did not want to reduce the stake in the company, which produced the Emmy Award-winning drama series "House of Cards."

So Icahn agreed to make up for any lost profits by injecting money into funds run by his son and Schechter if their views are proven right and it turns out he sold the Netflix shares too soon, according to a regulatory filing which details the agreement. If the shares climb further, then Icahn has committed to make "cash or cash equivalents" available to a new fund under Brett Icahn and Schechter's management, called the New Sargon Portfolio, it said.

Carl Icahn didn't return calls seeking comment. Brett Icahn responded to emailed questions by referring to the filing but declined to elaborate. Schechter couldn't be reached for comment.

The father-son agreement is one of the more unusual bets seen in the investment world. It exposes the dynamic between the corporate raider-turned-activist investor and a son who has been slowly cutting his teeth in money management.

It is unclear whether Carl Icahn needed the agreement of his son and Schechter to reduce the stake and the bet was the result, or whether it was a much more informal arrangement.

"NOTIONAL" VALUE

The payment to New Sargon will be based on a "notional" position in Netflix - as if the stake had not been reduced.

For example, if the Netflix shares, which Icahn sold at between $304.23 and $341.44 to reap a profit of about $800 million, continue to climb to say $500 then Icahn would have missed out on a much bigger potential gain of about $1.3 billion. He would pay the Sargon portfolio a large part of the difference - through a complex calculation that includes assumptions, a hurdle, and is also related to the shares' value at the end of March this year. The agreement expires in August 2016.

Netflix shares have dropped about 15 percent from an all-time high of $389.16 hit on Tuesday, before Carl Icahn did the bulk of his selling. They closed on Wednesday at $330.24.