Diablo 3: Gold to RMAH Exchange Rate

After playing around with the Diablo 3 Auction House FAQ, I've stumbled upon a tension that ought to have been quite obvious to me after first looking at the data.

Compare these two numbers:

RMAH:  $250 maximum list price.
Gold AH:  100,000,000,000 maximum list price.

If you had the rarest item in the game, and wanted to sell it, how would you determine which AH to use?  The maximum list prices can be used to answer this question, and in so doing indicates a standard for determining the exchange rate of money to Gold.

When we do some division, we find the flat exchange rate between the highest list prices:  $1 = 400,000,000 Gold.  However, determining the actual exchange rate isn't quite that simple:

Fees:

• Gold AH / RMAH Commodities:  15%
• Gold AH Equipment:  15%
• RMAH Equipment:  $1
• Transfer to PayPal:  15%

Let's break this down.  First, note that we're ultimately transferring everything to PayPal.  Let's first figure out the profits from a $250 RMAH sale:

250 - 1 = 249  (List price cut)

(249 *.15) = 37.35 (PayPal xfer)

(249 - 37.35) = $211.65 profit.

When we sell our item on the RMAH for the highest list price, $211.65 is sent to PayPal.  The next question is:  If we list that item on the Gold AH, and then sell that Gold on the RMAH, how much would we have to sell the gold for in order to gain the $211.65 we would have made by selling the item on the RMAH?

MATH!

You list the item for 100,000,000,000

Blizzard's 15% cut:  15,000,000,000

Your gold profit:  85,000,000,000

Now, how can we turn a $211.65 profit with our 85,000,000,000 gold?  Let's start by selling all of our gold, as one lump sum, for the highest possible list price:  $250.

85,000,000,000 gold listed for $250:

(250 * .15) = 37.5 (List price cut)

(250 - 37.5) = 212.5

(212.5 * .15) = 31.875 (PayPal Cut)

(212.5 - 31.875) = 180.625

If we sell our 85,000,000,000 gold for $250, then $180.625 is sent to PayPal.  That's $31.025 less than if we'd sold the item on the RMAH in the first place!  To get the $211.65 profit we could have made on the RMAH, we'll have to break this gold into chucks, and sell off those chunks.  Let's sell two chunks.

85,000,000,000 / 2 = 42,500,000,000.

What must each chunk sell for in order to match the $211.65 we made from selling the item on the RMAH?

(146.47 * .15) = 21.9705   (List Price Cut)

(146.47 - 21.9705 = 124.4995 (we'll round this up in the next step)

(124.5 * .15) = 18.675    (PayPal cut)

(124.5 - 18.675) = 105.825

(105.825 * 2) = 211.65

In order to make the $211.65 we would have made by selling the item on the RMAH, we would have to sell our two chunks of 42,500,000,000 gold for $146.47 each.

For the sake of curiosity, let's pretend there was no highest list price on the RMAH for gold sales.  In this scenario, how much would we have to sell our total gold for, to match the profits we made selling the item in the RMAH.

292.94 * .15 = 43.941

292.94 - 43.941 = 248.999

248.999 * . 15 = 37.34985

248.999 - 37.34985 = 211.64915

If there were no highest list price on the RMAH, for gold sales, we'd have to sell our 85,000,000,000 gold for $292.94 in order to make the $211.65 we made selling the item on the RMAH for $250.


So, what have we learned?

RMAH Highest Profit for one equipment:  $211.65

If we turn that equipment into gold, and sell the gold:

1)  Split our 85,000,000,000 gold into two stacks.

2)  Sell each stack for $146.47.

What, then, is the actual exchange rate between the Gold AH and the RMAH?

42,500,000,000 gold / $146.47 =

290,161,807.8787465 Gold / $1

So,

If gold costs more than $1 for 290,161,807.88, turn the item into gold and sell the Gold.
If gold costs less than $1 for 290,161,807.88, sell the Item.


You're Welcome.