First, off, I will knock out the notion that die roll strongly correlates with item won. It's not that there's a correlation so much as selective memory bias. If you actually go through and catalog each roll and the result, the correlation is actually pretty weak. I've gotten no medals on just about every possible roll, and 2 medals on just about every possible one.
Just today, i landed on a gold twice, using the same roll (1) to get there both times. I got a 115 neut the first time and a 30% item the second. All told, I have landed on the gold 8 times. I have gotten 2 +10 medals, 1 each neut & EBB coupon, and the rest +30% items. For the record, I got the EBB on a 5, and at least one of the +10 medals on a 4. I don't remember the others because . . . I wasn't paying attention and didn't record them.