The only thing that affects gambling is character level.
Items generated for the gamble stock are -5 through +4 levels of your character's level with a minimum item level of 5. Note, this does not apply to level requirements often seen on items also known as required level. This applies only to the item level. This item level is never seen by the player in game and is used primarily in formulae that choose what affixes an item can get. Ancient armor has a quality level of 40, which means you can see it in the gambling screen at level 35. You will see it more often in the gambling screen when you are level 44 because at this point, you will always meet the required level. Look at the bottom of this page for a list of base items and their proper quality levels.
Chance to gamble:
Chance to get exceptional item:
Gambling +2 skill amulets
Lvl Chance 86 10 87 20 88 30 89 40 90 50 91 60 92 70 93 80 94 90 95 100Characters 95 and above will always gamble an amulet with an ilvl sufficient for +2 skill prefixes.
Gambling Tri-res rings.
Gambling dual-leech rings