Propability and outcome

I’m hoping you can assist me. I’m using a simplified analogy for the problem, but it accurately represent s what it is I’m looking for. Suppose I have 5 people in a room numbered #1-#5 who each have a die. They pay 5 cents each to roll the die and in this room, they all roll the die continuously and simultaneously so long as they pay. Rolling a “6” constitutes a win. Consequently, each person’s toss is independent of the other four, and will either be a win or a loss. As soon as a person rolls a “6”, they stop and wait to report the win to me so I can pay them. Outside the room, I stand and collect the money anonymously, oblivious to which person (or persons) have successfully rolled a 6. However, every 30 seconds, I ask for an update so I can pay a winner the lump sum of the money collected from the players. Now here’s the catch: The people in the room MUST report to me – in order of sequence (#1, #2, #3…) whether they are a winner or not AND, I will ONLY pay the FIRST one the lump sum (even as I collect money from other players that haven’t rolled a “6.”
SO, I have a situation whereby each roll is independent of the others, but the awarding of the winners happen according to order. Thus, what could happen is that person #4 rolls a “6” and waits, but while they’re waiting for me to ask who the winners are, #2 rolls a “6” as well. Based on the scenario above, even though #4 won “first,” I will pay #2 instead and #4 will be awarded a lesser amount only because he/she is fourth instead of second.
The questions I have are: a) How does one determine if a bias will develop whereby person #1 will receive winnings disproportionately higher than the others based on their place in the row (as opposed to #2 who should be less, #3 less winning still and so forth…). B) If a bias does occur, what is the formula to calculate this?
Thanking you in advance.