Gambling

[MadScientist]

I wanted to do some calculations about gambling but I encountered some difficulties. First, let me summarize what formulas I use: the chance of an item being unique is fixed at 1/5000, set fixed at 1/2000, rare fixed at 1/10 and thus magic fixed at 8993/10000. The chance of the item being exceptional is 90*(ilvl-qlvl_exceptional+1)/10000 and elite 33*(ilvl-qlvl_elite+1)/10000 where ilvl is evenly distributed in the interval [clvl-5,clvl+4] and qlvl_xxx the quality level of the exceptional/elite version of the item in question. If the number in brackets is negative, the value is set to 0.
So the actual chance of getting an exceptional item at clvl x is now [sum(i=x-5,i=x+4)theta(i-qlvl_exceptional+1) (i-qlvl_exceptional+1)]*9/10000 and analogous for elite with "9" being replaced by "3.3". theta(x) is the theta-function (duh!) which is 1 if x>0 and 0 if x<0. The chance of getting a normal item is then 1-p_excep-p_elite.

What happens if you gamble and there does not exist a set/unique version of that item? Is the item downgraded one category (unique->set, set->rare and unique+set->rare if both do not exist)?

And if I happen to be wrong with the formulas in the first paragraph, please correct me!

The Mad Scientist

PS I don't care if the chances to gamble a Cranium Basher are infinitesimal - the whole thing is just mathematical gymnastics for me :D

[adeyke]

If the game tries to spawn a unique but (1) there either isn't a unique of that type, or (2) all uniques of that type have too high a level to be picked, or (3) it picks a unique of that type and that unique has already spawned in that game, the unique will instead be a rare with 3x durability.

The first two criteria also apply to set items, which become magic items with 2x durability.

[MadScientist]

Well, I thought maybe there was some other behavior when it comes to gambling...

Feel free to try a very beta version of my Gambulator! The numbers are quite discouraging but one can always hope to get a good rare!
However, gambling seems to be a reasonable way to get exceptional and elite items since the chance to get one increases with your level at the cost of the chance of normal items. I don't know how the Hell-merchants are in 1.10(s) but in 1.09 they were very reluctant selling me elites :angry:

What does happen when your gambling efforts yield a set/unique ring/amulet? How does the game decide which one you get? For monsters it is governed by their monster level what they could possibly drop then the actual item is created by looking at the frequencies, right? Do I just have to replace the monster level with the ilvl of the gamble? Anything else?

I have read that uniques are created just one for each game so could you open a game and have a char gamble for rings until he has everything but a, say, SoJ and other chars are bringing him money to keep the gambling alive until you get your desired ring? Very time consuming, I know :P

The Mad Scientist

[adeyke]

I think it is just decided by the ilvl.

The ring gambling trick won't work (though it did in an earlier version). It first decides which of the unique rings should be spawned (choosing from the ones whose level is low enough and weighted by their rarity). Then, if it picked one that has already spawned in a game, it'll downgrade to a rare.

What this means is that, if you gamble a Nagelring successfully and continue to gamble, your chance to get the other unique rings is the same as it was before, your chance to gamble a Nagelring is 0% and your chance to gamble a rare ring is a little bit higher than it was before.

[Jarulf]

The downgrading of uniques and sets is part of the actual item generation code which is used for ALL items in the game. It is independant on the actual source of the item. The item creation code doesn't even know it is an item that is supposed to be gambled. All it knows is that it is an item of a specific type and a desired quality. It also has a item creation level (commonly refered to as ilvl) to use. That is basically it. If it can't create the item of the desired quality, it will downgrade the quality until it suceeds (which it always do for rare and magic items I think although it has built in ability to downgrade those too should one change the game so that rare items can't always be created, like no affixes being available in some cases).

As for the gamble code, it just decides the item type and then a quality it wants. It sends this info to the general item creation functions and get an item back (usually with the desired quality, but thus, not always).

As for the level used to determine for example which uniques are possible, it is the item creation level that is used by the function creating items (as I mentioned above). For items from monsters, it is set to equal the monster's level. For gamble, it is set to be a random value from 5 levels below the character's level to 4 above it (the character gambling).