The Paddy Power betting agency on Thursday quotes odds of 8-11 that Hayward won't last the year running the oil company, and even odds that he survives.
The volume of betting against Hayward is three times as large as the bets that he stays, Paddy Power spokesman Darren Haines said.
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Paddy Power is also taking bets on Hayward's successor, with Iain Conn, BP's chief executive of refining and marketing, leading the pack at 3-1.
Robert Dudley, recently appointed to head BP's response to the Gulf of Mexico oil leak, and former CEO John Browne were quoted at 7-2; Peter Mather, head of BP UK, at 4-1; and Malcolm Brinded, head of exploration at Royal Dutch Shell, at 14-1.
Paddy Power is known for listing odds on high-profile figures. In February, the bookmaker took bets on when he made his televised mea culpa following revelations of his infidelity.
For President Barack Obama's inauguration last year, on everything from the name of the Obamas' puppy to whether the new president would be impeached.