Is there any reason why the peercoin-qt client can’t show the total probability of minting a block per unit time for an entire wallet? For minters who are staking a non-trivial amount of txns I think it would be a nice feature to sum all of the the mint probabilities. You could also have the option to view the inverse and see how long it will take to find a block per total staked txn.
Also, I think showing the expected rate of return for each staked txn would be really useful feature! Given that ROI is dynamic, I think an estimation of the ROI per staked txn would be a really nice addition to the qt client. Similar to my first idea, the client could then sum the ROI for all staked txn and show the average expected ROI for the whole wallet.
The complication with an aggregated statistical representation is that it would be hard to represent concepts of minting multiple times. If you roll a single die, there is an even chance to get each result. When you roll multiple dice the statistics are skewed. You could talk about an expectation value, but it wouldnt take the form you expect. You can ask “in a given interval of time, how many mint events should i expect?” But if you ask “what is the chance i will mint in a given time interval” you will not get a meaningful result. Calculation of expectation values can be done, but im unsure if it will be generally interpretable.
Expected yearly ROI would be roughly calculated as the expectation value of mint events over the course of a year times the static reward value plus 3% times the wallet balance. Calculation of the expectation value in periods longer than the maturation period (30 days) would again be difficult to do because of the possibility of multiple mint events for a single utxo within the timespan of a year. Doable, but somewhat complicated.
Can’t you just calculate the probability of at least one mint occurring as the compliment of zero mints occurring?
If there are three outputs with mint probabilities of 0.01, 0.02 and 0.05 and probabilities of not minting as 0.99, 0.98 and 0.95, then the probability of minting anything would then be: 1 - (0.99*0.98*0.95) = 0.07831.
Yes, you can just multiply all the conjugate probabilities together, but it is not straightforwardly related to the ROI. The value of such a number as a relevant metric is limited compared to a question like “what is the time interval at which my expectation value of blocks found equals 1?”
You are calculating “Chance of finding at least 1 block in a given time interval”, which is certainly a number and may be helpful for those trying to mint their first block. The original question, however, was about someone with a lot of outputs and I am assuming many mint events. In such a case, that question is not so relevant.
I took this paragraph to mean the probability of minting at least one block. That is easy enough. In the minting tab there is a list of UTXO probabilities, so it would be nice to have an overall probability shown there as well.
Yes, that is correct.
Apologies that it wasn’t clear in my OP.
You were clear, and yes that number can be calculated, but it is not related to your followup question about ROI. To provide a rough sample calculation of ROI, i will make a couple simplifying assumptions. Let’s ignore the maturation period and the possibility for minting multiple blocks within a year. In this case, each output represents a “yes, it did mint” or a “no, it did not mint” over the course of the year. If you add these probabilities (instead of multiplying) you will get a number that can be greater than 100%. That is the expectation value. ROI is linearly related to this expectation value, and is roughly (1.3PPC * X + 0.03 * #coins) where 1.3PPC is the static reward, X is the expectation value, 0.03 is the 3% coinage reward, and #coins is how many coins in your wallet.
Adding the probabilities instead of multiplying is easy to do and provides a more meaningful number. However, if we want a really accurate expectation value we should take maturity and the possibility for minting multiple times into account, which is where it gets a little complicated.
Still, you are right that multiplying the reciprocals provides a number that represents something. I just question the end user usefulness of that number.
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Alright, thinking more, there is an effect that happens on the long timeframe end too with the coinage cap. I think the simplest solution without adding in a bunch of complicated calculations is to show:
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Total percent chance to mint at least one block. This can be done for each timeframe using reciprocal multiplication.
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Rough estimate of ROI. This is done by summing the 90 day mint chance for each utxo and multiplying by 4 (or 365/90). Then, multiply by the current static reward and add 3% of the wallet balance. We use the 90 day interval only to give the best estimate.
It’s not perfect, but it could be informative.
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I think it would extremely informative to add this information by default in the minting tab of the qt client, especially for new users. As it stands, it is not clear how much interest will be earned on your total balance. If we want peercoin to grow, we should provide this information in the official wallet and make it super clear to everyone (even if it is only an estimate).
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I think this is a good idea. For example, Premium Bonds in Britain have an interest rate which has no precise relationship to the “prizes” that people win - but it’s a guide that people can use for comparison with savings accounts, etc.