Steemit How to optimize your vote (mathematical analysis)
Do you know how much you get as a reward for your post healing? Should we vote for a post that is already on the trending page? How about voting for an impop post
ular? How much does it matter? How much does steem power influence our healing rewards? How to vote before the 30-minute rule? Do you vote at 20, 25, 27 minutes? Maybe you've ever wondered one or more of these questions. Would you like to know the answers? Well, this post is for you. I have done a thorough study of the entire rewards system and I am expressing it in this post. You will find many mathematical formulas, but do not worry! do not go yet, in the end you have a summary title where I leave the main conclusions I have reached and that can help you.
a healing formula
In my previous post we talked about the entire reward system for authors and curators. There we get to the healing formula: where P0 is the post payment before you vote, P1 is the post payment right after your vote, v is the value of your vote, PT is the post payment after 7 days and t is a value between 0 and 1, and is a function of the 30-minute rule (if you vote at 0 minutes then t = 0, if you vote at 30 minutes then t = 1, if you vote at an intermediate point then t will be proportional to that moment, and if you vote after 30 minutes t continues to be 1). Note: In steem, the formula for calculating the square root is not exact but approximate so that the operations are fast. Then the calculations we make here may differ somewhat from reality. Let's look at an example with healing: Your vote is valued at $ 0.24. Then you vote a post valued at $ 5. Your vote is given after 30 minutes. What is the healing gain if after 7 days the post grows to $ 50? You will receive $ 0.094. But as you know your healing work is paid in steem power, so it must be transformed using the price of the steem (this price can be consulted on steemd.com in the feed_price section). If 1 Steem is worth $ 5, then you will receive 0.018 Steem Power. As you can see it is easy to calculate, but now we will stop to analyze this formula in more detail.
Rewriting the formula We will rewrite the formula taking into account the value of the vote. Suppose the vote is k times the P1 payment, and that the final payment PT is sometimes the P1 payment (the scale): For example, if you are the first voter then k = 1 since there is no previous payment and therefore the payment of the post right after your vote corresponds to your vote P1 = v. But if you vote late for a post (in this case P0 is large) and you are a minnow (v is small), then k will tend to 0. How can you see k is a constant that varies between 0 and 1, and defines some characteristics of the vote on the time, on its value, and also on the popularity of the post. By making a couple of calculations we get that: If we include all this in the healing formula we get: Here we can group the first fraction into a large capital K: Then, by rewriting the formula we get: The value of K But what does this great K mean in that formula? It represents the transformation of k into money. As we saw earlier, k is a value that varies between 0 and 1. Now let's look at the range of values of K. If k = 1 we have: If k = 0 we have: This day is undetermined and is a bit more complicated. To solve it we will apply the L'Hopital rule: Super interesting !! It means K varies between 1/8 (when voting late) and 1/4 (when voting first). Below is a graph representing the values of said K. On the x-axis we have the voting rate with respect to the payment before the v / P0 vote. For example, suppose that before voting the payment is P0 = $ 5 and the value of the vote is v = $ 0.5, so the division v / P0 is 0.1, which corresponds in the graph with K = 0.128. If we want to reach a value close to 0.25 the vote v must be many times greater than the P0 payment, in the graph we see that it must be around 1000 times, a super high value. Here we have 2 options: 1) Be the first voter, since here P0 = 0 and any value of v will be a thousand times greater. 2) Be a whale but at the same time vote when the post has few cents, that is P0 is very small and you look very large, so that v / P0 is equal to 1000 or more. If our vote v has the same value as the payment P0, then the relation v / P0 = 1, and K = 0.146. As long as our vote is less than the P0 payment, the value of K will decrease until it reaches its minimum 0.125. Healing Examples Let's look at some examples of the healing formula
Example 1: A minnow is the first to vote for a popular post Assume the vote of a minnow (valued at $ 0.10) whose contribution is made after 30 minutes and apart from that it is the first to vote. What is your reward if the post reaches $ 5 after a week? First let's see how much it climbed: from P1 = 0.1 to PT = 5 there is a scale s = PT / P1 = 50. Then: We see that you get an amount greater than your vote was worth !! This would be the ideal case, but it is also very difficult to achieve. Let's see: He was the first to vote and voted at 30 minutes (all the healing of 30 min goes to him) and apart from that the post climbed by 50 !! Something to note here is that the earnings scale with the square root of the scale of the post. As the post payment increased by 50, then the healing gains increased in square root of 50, which has been approximately 7 times. Example 2: A whale votes a trending post Suppose now a whale, whose vote is valued at $ 40, which votes a post valued at $ 460. After this vote the post does not grow much more. What are the healing gains? After voting the post reaches P1 = 460 + 40 = 500, then k = 40/500 = 0.08, and K = 0.1276 (close to 1/8 since he voted late). So: Despite having voted late, he receives $ 5, a good amount. Why? because his vote worth $ 40 is large and this in the multiplication pays off. Therefore we can conclude that the Steem Power that each one has is very important. The more steem power you have the more you will receive for healing, it is directly proportional. And in this example we see that the curator receives an eighth of his vote. Example 3: A minnow votes a trending post Assume the same example above but in this case the value of the vote is $ 0.10. In this case, the post payment will be $ 460.10, k = 0.1 / 460.1 = 0.000217, and therefore K = 0.125. The cure payment will be: The result is the same as the previous one, the curator receives one eighth of his vote. Note that the value of K is very similar to the previous one. Therefore we can conclude that the value of K will be close to 1/8 when the post is already in trending regardless of whether we are minnows or whales. This is a great simplification, since by definition K the value of the vote depends.
Maximizing the vote
In my previous post we also concluded how to calculate the value of a vote, where Vp is the voting power, SP is the steem power, w is the weight given to the vote, and g is an equal global variable for everyone . You can calculate your vote by entering steemnow.com.How to maximize our vote? Here I am going to focus on something that I have not mentioned before, the voting power. As you can see the value of our vote is directly proportional to the voting power, so the more power we have the better. On the other hand, this power is consumed each time it is used and regenerated at a rate of 20% per day.If this is the rate of regeneration, what we must do is spend said power at that same rate, 20% per day . Why? Suppose you spend at a higher speed, it means that a point will come to an end because regeneration is slower. And if you spend a smaller cup what will happen is that the power will be 100% regenerated and it would be there for a long time without being used, which is also not profitable. If we spend our voting power at the same speed as the regeneration cup, it means that said power will always remain at a constant value. And therefore we must leave it at 100% to maximize the value of the vote. Seen in another way: Let your voting power reach 100%. Do a couple of cures and wait again for it to reach 100% and continue like this, the less you let it fall better.
Summary
Your healing gains are calculated using the following formula: where:
K is a value that varies between 0.125 (if you vote late) and 0.250 (if you are the first to vote). It is very difficult to reach 0.250 or a close value, you should be the first, or be a whale that votes very early). And on the other hand, it is very easy to fall into the value of 0.125. All this depends mainly on your steem power and the moment you vote.
v is the value of your vote. You can easily calculate it by entering steemnow.com.
t is the 30-minute rule, and corresponds to a value between 0 and 1. If you vote at 0 minutes of publication then t = 0. At 10 minutes t = 0.33. At 20 minutes t = 0.66. At 30 minutes t = 1. And after 30 minutes it remains 1.
s is the scale of growth of the post after you vote. If the post has $ 20 right after your contribution, and after 1 week it reaches $ 100, then s = 100/20 = 5.
This payment is finally transformed into Steem Power, therefore it is divided by the price of the steem. This price can be found on steemd.com in the feed_price section.
Some conclusions
The rewards increase with the square root of the growth scale of the post.
Rewards increase linearly with the value of the vote. The more steem power you have, the more profit you will have.
If you vote late for a trending post the reward will be v / 8 regardless of the total value of the post.
If after 30 minutes you vote and you are the first then you will receive a minimum v / 4, regardless of whether the post is popular or not.
The 30-minute rule says that if you vote at this time later then you will have all the reward, but as long as you do it before a part of it will go to the author. The best way to vote before 30 minutes is this: If you think that after 30 min the post will have a growth scale greater than 900 / Dt² (time being Dt in minutes) then it is better to vote before, but better wait.
I hope you liked it as much as I liked writing these analyzes and scrutinizing the rewards system.