According to what I'm reading when you have 7, and you go for the 8th open there is a 1000/1009 chance it will be an item IF you open it successfully. The free open was I think somewhere around maybe 30% chance if you're giving it that much leeway.
That chart is when you have X amount of the item you are collecting, you have y chance of the open giving you the item we are collecting.
The only thing spending gold and the in game cash on affects is the rate at which you open them. You can still expect the same item rate if you spend gold or open them for free.
...[and a logic error just crashed my IDE]
