dumb math question

I play lord of the rings Hello Kitty online. There are two ways people mostly use to roll on loot. For this question I'll assume 12 players rolling and 4 coins dropped.

1. One roll where the top four rolls win a coin. Winning one disqualifies you from winning another.

2. Four rolls where top roll wins each time, and if you win you don't get to roll again.

Either way, 12 players, 4 coins, 4 winners.

Some people insist that four rolls gives you better odds of winning. My friend keeps insisting that the odds are better with separate rolls. Common sense tells me that you have a 1/3 chance of winning either way, and that odds can't improve for EVERYONE in the group with the same number of coins and the same number of players.

He asked his calc teacher. At first the teacher agreed with me but then he kept badgering him and got him to agree that since the odds are 1/12, 1/11, 1/10, 1/9 for four separate rolls, it's better odds of winning. The exact thing happens when you do one roll with 4 chances to win of course but whatever.

Please give me ways to get it through his thick skull and make him stop talking about it because it is hurting my head. Common sense isn't enough evidence of course so be as mathy as desired.

For those who may actually be able to answer, how do I explain it to him in a way that will make him shut up?

p.s. This is not a homework question.
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• Hajiomatic’s gone, as in deleted; anyone know why he made that decision?

He’s been such a hardy perennial here that I was wondering.

• What do you do with a stand mixer?

Hi peeps, a few years ago, our neighbours moved and we bought their old stand mixer. It's one of those coveted Kitchen Aid ones in candy apple red.…

• Here's a Puzzler

Do you enjoy doing jigsaw puzzles? What is it about the activity that you do and/or don't like?