Albion fans who bought tickets for the club's new Golden Goal jackpot believe the odds have been stacked against them.
Some supporters playing the new scratchcard game expected their chance of winning to be 90-1 but were dismayed to realise the odds were really 5,380-1.
While many clubs reward fans who have the right minute in which the first goal is scored, Albion's contest demands both the exact minute and second the ball hits the back of the net.
The Golden Goal scratchcards were brought in to replace the Withdean Wager, which was a straightforward raffle.
Fans attending the club's home games at Withdean can buy tickets from a network of agents before matches and inside the ground.
One Albion fan thought he had won the £500 top prize when the first goal in last weekend's clash with Swindon Town was scored in the 13th minute.
However, his ticket said 13 minutes, 35 seconds and the goal was actually timed four seconds later.
The supporter, who did not want to be named, said: "I want to help the club and I also want to be in with a fair chance of winning.
"But in this competition the odds are too high and the chance of buying a ticket with the exact time of the goal is just too great.
"If fans felt there was a good chance of winning, the club could sell more."
Fellow fan Dave Bradley, from Hove, said: "The chances of winning the first prize in this competition are virtually zilch. The club should introduce more prizes."
The club produces a ticket for each of the 5,400 seconds of a 90-minute game, except the first ten seconds of each half.
However, only about half the tickets are being sold at each match.
Albion's marketing manager Trevor Watson said: "The Golden Goal is used at other Football League clubs. If we sell all the tickets, everyone has a chance of winning.
"It has proved popular with fans and we are looking at ways of increasing the opportunity of winning with possibly a super jackpot at Christmas."
The person holding the ticket with the right time for the first goal wins £500, while a signed football is on offer for the second goal and £10 for all other goals.
Five tickets saying No Goals are available, offering £100 to each holder if the game ends 0-0.
The game has been backed by probabilities expert Malcolm Lewes, a Lewes-based Open University physics lecturer, who has previously calculated the likely number of pebbles on Brighton beach.
He said: "Statistics show most first goals are scored between ten and 20 minutes of the first half, or just before half-time.
"The odds of winning in this game are a basic 5,380-1 but if you have a first-half ticket between ten and 20 minutes then the chances of winning increase."
Liz Costa, vice-chairwoman of the Albion supporters' club, said: "The Golden Goal game is fun and if all the tickets are sold, everyone has a chance of winning.
"People buy tickets to help the club and there have been instances of people winning the Withdean Wager and giving their winnings back to the club.
"I expect it will also happen in the Golden Goal competition."
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