The pair, who have become close friends during their time in the house, made the deal after initially suggesting they bet on their chances of victory in Monday's (August 13) final.
Believing that Adam had proposed they wager £5,000 on the former LA gang member winning, Luke A replied with shock: "I'm not doing that. Have I got five grand to spare?"
Both then stated their belief that the other was more likely to win, before shaking hands on a deal to hand over part of their potential £50,000 winnings.
Luke A is already guaranteed a spot in the final after escaping this week's nominations alongside Sara McLean. Luke Scrase is also through after receiving a free pass in last week's 'White Room' task.
Adam, however, will only make it to the end of the show if he survives this week's double eviction over fellow nominees Ashleigh Hughes, Deana Uppal and Scott Mason.
Copyright: Channel 5The Big Brother prize money was cut down to £50,000 from £100,000 after controversial contestant Conor McIntyre walked out with half at the end of the 'White Room' challenge on Friday (August 3).
Digital Spy readers have reacted angrily to Conor's win due to his aggressive behaviour towards Deana earlier in the series, which attracted over 1,225 complaints to Ofcom.
Big Brother continues nightly on Channel 5.