# Trade Goods: Buy Tokens, not Radios (mostly)

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**32**
I wanted to determine the trade-off between turning my TGs into radios (or saving them for radios) versus buying the tokens outright. To do this, I used the probabilities from this site: https://twdnomansland.wordpress.com/radio-call-drop-rates/. If someone has better probabilities, I'd love to see them!

Here's a picture of the calculations:

The keys points are:

1. Trading in TG for tokens directly is slightly better than the expected number of tokens from radio calls

2. It's very close, though, and small shifts in the probabilities could sway that

3. This assumes you're taking the maximum number of tokens presented to you.

We expect to get 5.7767 tokens for each radio we spend on a 15x call, which isn't as good as a guaranteed 8 tokens for the cost of 1 radio.

For those interested, here's an explanation of the math. The left side of the calculations gets the expected number of tokens for a single slot in the radio call. To get the probability of having some number of tokens as a maximum, we need the Cumulative Distribution Function (CDF) of the tokens. This means the probability of getting at most some number of tokens. The probability of getting at most 128 tokens is the probability of getting 32 tokens + the probability of getting 128 tokens, for example. Then we get the CDF of the maximum for all three slots in the radio call. These are just the cubes of the CDF of one slot (cubed b/c 3 slots). CDFs are turned into probability mass functions (PMF) easily (subtracting the CDF of 128 from the CDF of 256 gives you the probability of getting 256 exactly). From there, the PMF gives us the expected number of tokens when we take the maximum of the radio call.

Here's a picture of the calculations:

The keys points are:

1. Trading in TG for tokens directly is slightly better than the expected number of tokens from radio calls

2. It's very close, though, and small shifts in the probabilities could sway that

3. This assumes you're taking the maximum number of tokens presented to you.

We expect to get 5.7767 tokens for each radio we spend on a 15x call, which isn't as good as a guaranteed 8 tokens for the cost of 1 radio.

For those interested, here's an explanation of the math. The left side of the calculations gets the expected number of tokens for a single slot in the radio call. To get the probability of having some number of tokens as a maximum, we need the Cumulative Distribution Function (CDF) of the tokens. This means the probability of getting at most some number of tokens. The probability of getting at most 128 tokens is the probability of getting 32 tokens + the probability of getting 128 tokens, for example. Then we get the CDF of the maximum for all three slots in the radio call. These are just the cubes of the CDF of one slot (cubed b/c 3 slots). CDFs are turned into probability mass functions (PMF) easily (subtracting the CDF of 128 from the CDF of 256 gives you the probability of getting 256 exactly). From there, the PMF gives us the expected number of tokens when we take the maximum of the radio call.

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## Comments

861,0612,065This counts even more for Hero's then...

Tokens won't buy you new survivors though...

I usually make sure I can buy both tokens and phones in TG shop.

I agree though. When you must choose between buying tokens or buying phones.

Buying tokens directly is statistically significantly better and chance is eliminated.

Lucky people should buy phones though

1601 -

Heavy gunner suggestion32One thing I left out is a look at the relative effort of upgrading a survivor up so many traits vs. getting one that is much better.

135From a raw math standpoint single radio calls clearly win, but for people looking to build a capable and diverse survivor pool, pulls using 15s are still probably ideal. You can cherry pick your preferred 32-250 tokens for the class you need most with the rare chance of scoring a nice and well balanced survivor worth keeping vs scrapping.

Once you have a well kitted squad with lots of legendaries, singles are the way to go.

With regards to trade goods, buying tokens for a desired hero class is probably the best option, but it's going to take a long time to acquire enough tokens to make meaningful upgrades.

15 calls will rarely reward you with 128-250 hero tokens though ... and that is always a nice surprise.

2,065I don't think this was up for debate in this discussion.

Empirical data shows that there actually isn't much difference. (See link give in OP)

I'm tempted to calculate it but maybe later.

Would you care to share your maths with us?

|edit|

After looking a little closer to the bronze calls data (136 calls)

74% was 2 tokens

24% was 8 tokens

0.74% was 32 tokens

0.74% was 128 tokens

0.74% was 256 tokens

If this would represent the real odds, then indeed bronze phones would be better for tokens.

Token/radio becomes ≈ 6.4

But I find this outcome rather suspicious.

The amount of calls was to little to have certainty about even the 32 tokens percentage.

Let alone to determine what 128 or 256 percentages could be.

And look at it. I don't believe 32, 128 and 256 are equal in chances.For now

I think it is better to at least not count the legendary drop.

The 1 call

Token/radiobecomes ≈ 4.6The 15 call

Token/radiois still ≈ 5.7I honestly don't believe there is any advantage about 1 radio calls.

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