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# Ok Math Fellas and Calculating Ladies what's the sweet spot here?

Pandingo
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**820**★★★
So these shard packages always escalate but I'm curious where exactly y'all feel the value falls off. Because if you were to max out these deals (which seems really bad) you're looking at 150 usd for 1/4 of a titan and a whopping near 380 usd (depending where you get the units) for a single 7* basic 11500 so I'm using basic Odins in game for this current question. You could get 50 units shy for 300 usd plus tax in the market. Still seems bad. Anyway. Where's the value start to plummet?

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6,446★★★★★468★★★1,172★★★★36,334★★★★★1,636★★★★For a 6*:

Relative Price of a 6* = (50 + 10(x - 1)) * 10

Where x is the number of times you buy the shards

Depends on what you would say is a fair price for a 6* but let’s give it the benefit of the doubt and say that for the average paragon/valiant player it’s worth 500 units. This means that it’s only worth buying the first 50 unit package. (As 50 * 10 = 500)

But if you value a 6* at 1000 units it’s totally worth buying 6000 shards

For a 7*:

Relative Price of a 7* = (50 + 10(x - 1)) * 50

Where x is the number of times you buy the shards

Recent deals have put the price of a 7* in the 3k unit ballpark (essentially 1 odin). Solve for x you get 2. So basically buying 2 lots of 300 shards for the price is worth it (assuming a 7* is worth 3k units, which is a generous guess in the current IGE)

Finally for a Titan:

Relative price of a titan = (50 + 10(x - 1)) * 100

Where x is the number of times you buy the shards

A titan crystal is worth a lot more, the poolies event had 10k shards worth 900k, which was the price of an Odin. Therefore a titan is worth 6k units. Solving for x you again get 2. Same as the 7* buying 2 lots (or 400 shards) gives you value better than or equivalent to buying a titan wholesale for 6k units.

Pretty sure my maths is spot on here (would hope given my first exam is in a couple weeks) but hope this helps

1,636★★★★Titan:

Basic 7*

Here’s the link to the graphs, you can play around with the y slider based on what you would value the crystals at but these are pretty basic formulae which appear in places like the glory store and loyalty store so it’s good to have a tool like this lying around so you can allocate resources and don’t over/under spend

https://www.desmos.com/geometry/b0vy5ha5gm

587★★★18,937GuardianWhat I mean is this: if you're willing to spend, say, 70 units on 200 titan shards (which would value the Titan at 7000 units) then one way to tackle that problem is to ask how many you can buy until the *average* price rises above your threshold. That would be five bundles for a total of 350 units, averaging 70 units. Six bundles would cost 450 units for an average cost of 75 units. Stopping at five means you're paying on average what you are willing to pay.

That's economically wrong. Each bundle should be evaluated separately, because each one is a separate decision on whether or not to buy. The first one costs 50 units which is below your threshold, so you buy that. The next one costs 60 units with is also below your price point and you buy that. The third one costs 70 units which is exactly your price point and you buy that. The fourth one costs 80 units which is more than you're willing to spend, so you stop buying.

There is a principle in economics called the sunk cost fallacy. It refers to the fact that when a person spends on a particular situation, they continue to judge whether to continue to spend in part based on what they've already spent. But the amount spent should be considered gone. Its gone whether you continue spending or not. The only question is whether you should spend now. This situation is the converse of that. How you judge a deal should be based solely upon the value you get for that deal. It is illogical to buy a deal worse than you are willing to, because you already got deals better than you're willing to. You should decide what you're willing to spend, and then continue to buy until the next one is more expensive that you are willing to spend, and then stop.

There is one psychological variation, however, and that is because we can value the shards in more than one way. If we are just counting numbers, it makes no difference if we get 200 shards today or tomorrow. It makes no difference if we are buying 200 shards and we currently have 15000 shards or 19900 shards. But even in real world economics, there's a difference between getting something now verses later. The presumption is that time is a kind of cost. Getting things now is worth more than getting them later, because you get the benefit of having them for longer.

So completely separate from the question of what you are willing to pay for 7* shards or Titan shards or whatever, there's the separate question: what are you willing to pay to have your next crystal now vs later. If you have 19800 Titan shards, then 50 units for 200 more shards might be worth it, even if you would not ever buy a Titan for 5000 units The quantitative value is the same, but the cost for time is different. A 50 unit premium to open now than later might be worth it, even if the shards themselves are not worth 50 units.

How you value shards and how you value sooner-than-later is completely a matter of preference for the player. But neither of those requires significant math to judge.

820★★★820★★★820★★★1,672★★★★★