Leonardo DiCaprio will finally take home the best actor Oscar on 28 February, according to Las Vegas bookmaker Ben Eckstein. Eckstein, who has a nationally syndicated odds column and publishes betting odds on his website AmericasLine.com, has DiCaprio at 1/50 for his role as a fur trapper bent on revenge in The Revenant.

The best picture race, though, is tighter, with Alejandro Inarritu's dark drama competing against Tom McCarthy's journalism tale Spotlight, with financial farce The Big Short in third place.

"The Revenant, now, has moved into favourite. It's really a dogfight between The Revenant and Spotlight. We think that The Revenant is going to do it, because of the fact that the director just got the nod – Inarritu – and he's certainly going to win best director," he said.

Eckstein compiles his odds by looking at a film or actor's performance across the awards season, and gets tips from movie industry insiders. He sees Sylvester Stallone, who has picked up a Golden Globe and a Critics Choice award for reprising his role as Rocky Balboa in Creed, as a front runner for the supporting actor Oscar. British actor Mark Rylance, though, tightened the race when he was named best supporting actor at the British Academy of Film and Television Arts (Bafta) awards for his Soviet spy role in Bridge of Spies.

"We have Sylvester Stallone, Rocky, as the favourite. But a slight favourite over Rylance. Now, the reason we updated our odds and made it a little tighter, because Rylance just won the Bafta for best supporting actor. And we really take into account the Baftas, even though it's so far away, it's across the ocean, sometimes we like the English, sometimes we don't. But that is a very important benchmark, when you win the Bafta. So we made that a little tighter, but still, right now Stallone is the favourite to win," Eckstein said.

For best supporting actress, Eckstein favours Sweden's Alicia Vikander for her role playing the wife of transgender artist Lili Elbe in The Danish Girl. Close behind are Rooney Mara, who plays a shop assistant who has an affair with a married woman in 1950s New York in Carol, and Kate Winslet for her portrayal in Steve Jobs of the late Apple co-founder's colleague Joanna Hoffman.

"Alicia Vikander is going to be our favourite. This, again, is not a really competitive race. She's kind of out in front, not way, way out in front, it's 1/2 odds. We have the other two girls, Rooney Mara and Kate Winslet at 7/2, so if there is an upset in this category, I would look for Rooney Mara or Kate Winslet to take it," he said.

The Oscars will be handed out in Hollywood on 28 February in a star-studded television show viewed around the world.