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[e] change topic to sound more interesting

Hi guys,

This is my first post in a poe community forum and I thought I share some thoughts on the implied probabilities derived from the assumption of arbitrage free pricing and then share an example which in my opinion shows that this assumption is incorrect but still useful. I hope to get some feedback and maybe you can point out some other interesting examples or maybe there is something wrong with my argument in principle - please let me know. Apologies if this has been posted before - I searched and could not find any discussion.

It started off form me with the question what the probability is to get a lvl 4 empower gem by using a vaal orb on a lvl 3 gem. I searched and it seems that the probability is not known exactly but people are providing data in terms of number of tries until they got a +1 lvl through using a vaal orb etc.

I think that by observing market price data you are able to get a good idea of the underlying probabilities. Here is an example - all prices as of today in standard, using a 35:1 chaos to exalted exchange and my personal bias ;-)

A uncorrupted lvl20 Anger gem costs on average 1.2 exalted (I used Anger because quality is not as important as for other gems and you can find quite a few offers that allows you to do averages etc). A corrupted lvl21 Anger gem costs on average 8.5 exalted and a failed attempt (corrupted lvl20 or lvl 19 gems) costs on average 0.5 exalted.

So applying arbitrage free pricing (and assuming risk neutrality and a number of of other things) and neglecting the cost of the vaal orb we can calculate the probability to get lvl21 Anger by using a vaal orb with the following formula:
1.2 = 0.5(1-x) + 8.5x

This would give you a probability of roughly 9%. If we allow for the market being slightly risk avers then the true probability would be slightly lower. Try this out for other lvl21 skill gems and you might find some interesting examples.

Now the assumption of an arbitrage free market is not correct - neither for the real world nor for poe. But it is a useful assumption because arbitrage opportunities are seen as temporary (because people using these opportunities to make money are accepting increasingly lower margins and thereby closing these opportunities) and they help us understand prices.

In poe some arbitrage opportunities are more stable from my observation. Let me tell you my currently favorite example:
You can get a sacrifice fragment (dusk, dawn, noon) for 1-1.5 chaos each. A midnight sells for roughly 8 chaos. We know that we can use these fragments in the map device to open a corrupted area at the end of which awaits us either a new fragment or a vaal skill gem. We can repeat this procedure until we either get a skill gem or a midnight.

So using arbitrage free pricing we can calculate the implied probability for this game of producing midnights from lesser fragments (and almost everyone should be almost risk neutral since the prices involved are quite low). So with 0 as the value for the vaal skill gems we get
1.5 = 8x + 0(1-x)

That means that the market is convinced that only in 18% of the cases this game will result in a midnight.

In the last week I have bought and found more than 200 fragments (mostly dusk and dawns but some noons as well) and I played this game. My observed value for x is closer to 45% but might be a bit lower or higher. So it is very different from the probability that is implied by the market prices.

You might disagree about the prices I have taken or my observed probability or point out that I neglected the 'labor' to transform any fragment into a midnight but you would have to change this example quite a bit to not be looking at an arbitrage opportunity. And it seems to persist in the market. Probably because people do not know that they can use fragments in the map device or they might not have the character builds to run all of these bosses - I don't know.

To summarize: I think you can use observed market prices to get a rough idea about probabilities that are otherwise not known and you can use known probabilities to detect arbitrage opportunities in the market. But both have to be taken with a grain of salt (since the assumptions of the underlying pricing theory are usually not fulfilled) and we rarely 'know' any probabilities.

so ....

too boring or did I not explain it properly?

Wait is this a quitting post where you are giving away all of your gear/exalts?

Hi there --

I think your observations are interesting. Before I reply, let me see if I understand your hypothesis. You are saying that market prices may inaccurately reflect the good-characteristic-probability that gives them their higher value (i.e. the probability of the desired outcome versus the per-outcome cost). You describe this as an 'arbitrage opportunity' -- an inequity in the predominant pricing versus the actual value as defined by the above probabilities. In economics, I believe this is referred to as an information asymmetry.

To me the issue is other variables, like supply and demand for a given item, the community's attitude toward the item over time, and the accuracy of your probability observations.

My limited knowledge of economic principles brings me to the concept of marginal cost. Introducing another Lvl 4 Empower into the economy adjusts the marginal cost / marginal utility of introducing still more Empowers. Thus, the value of any one additional Empower is nonlinear and cannot be related only to information asymmetry related to probability, as probability is assumed constant and can be rolled into the per-unit cost.

Rates of consumption fluctuate with different items as well. Some items (chroms, alts, etc) are routinely consumed -- the total number of alt in existence has a certain rate of growth, whereas other items (Shavs, Lorica, Voll's) are not 'consumed' in the same way, and may have a different rate of growth or decline because they may be re-introduced into the economy at any point with no additional investment.

Additionally, your theory about information asymmetry assumes that you are the party with best knowledge. The systems in place in this game are intentionally obtuse. Probabilities aren't directly disclosed. If your observations are imperfect, you now become the subject of 'arbitrage,' and potentially lose your ass. Your pre-formed observations about probability may long ago have been sorted out by a mega-algorithm analyzing bots and crafting somewhere in China. This happens in real-world speculation all the time.

In my reading of this forum, straight flipping rarely involves a mathematical determination of how far from a 'true price' an item is. It's a strict measure of current price versus current perceived demand. Whether an item is undervalued to a certain extent is marginally helpful, but having an encyclopedic knowledge of the costs of things RIGHT NOW I think would be more profitable than having an encyclopedic knowledge of one commodity.

All this results in people kvetching about no-lifers sitting in trade 1 and on poe.xyz flipping uniques all day long, saying that flipping is the only way to become rich.

It sounds like you're really interested in economics, and that's really cool. And people say video games rot your brain. Although... I should get back to work.

edit: at the risk of angering the Old Gods of ARPGs, let it also be said that this conversation likely first occurred upon the initial release of the first video game that offered multiplayer trading. Whichever game that was. I'll say Diablo 1.

too many letters

You're thinking way too much. Just buy low and sell high. I've made 20ex in 2 days just by flipping. I don't even play the game, just find low prices in the selling thread & repost them with higher prices. Wait for a PM and log in game to meet. The end.

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Nick043 wrote:

[e] change topic to sound more interesting

Stopped reading here!

This might be true and might not be true. This is probably the only answer we can get unless someone with an abundance of orbs is willing to test this empirically.

I think similar things do happen in the form of corrupting jewelry. I am thinking of Stone of Lahzwar which is common to find and cheap to trade for, but if it gets a good corruption you can sell it for at least an exalted. I think it could be worth while to buy 20 Stone of Lahzwar at a time and corrupt them all to then sell the good rolls. You would spend 20 chaos and 20 vaal orbs with some chance to get lots more back. This should be in line with your example of how the relation of pricing is between the market price for uncorrupted Anger/Empower, corrupted and the chance to successfully corrupt, just much cheaper.

Math and statistics are only as strong as the assumptions we make. You seem to be basing your calculations on the premise that players will behave consistently when comparing different items of value.

I don't buy that.

But anyway, your conclusion of roughly 10% is consistent with experimental data, so it's likely close to that number. Certainly more than 5%.

By the way... I'm using % here to mean "a number I just made up" rather than the traditional "part of a hypothetical 100".