What is your Voting Power?

When you upvote a post or a comment, you are using your "voting power", that is between 0% and 100%.
To know your voting power, you can check the page corresponding to your account on steemd.com.

Suppose your user name is "steemdummy" on Steemit. (there is not such account so far).

Steam Dummy
source

Then you would check:
https://steemd.com/@steemdummy

On the left column, you will see a line "Voting power", with a percentage.
If you have never upvoted anything, or if your last upvote was a long time ago, your voting power should be 100%.

Depending on the number of Steem Powers you have, the value of your vote will be maximum when your voting power is 100%.
If your voting power is less than 100%, the value of your vote will be less.

Suppose the value of your vote, with 100% voting power, is $0.40. Then, at 50% voting power, it will be $).20, and at 25%, $0.10.

When you upvote a post or a comment, you may indicate that you don't want to vote at your current voting power, but use only a percentage (from 1% to 100%) of your voting power. I will call this percentage the Vote Strength.

So, if your vote is worth $0.40 at 100% voting power, when your voting power is 50% and you only vote at 50%, your vote will be 25% (50% x 50%) 0f $0.40, that is $0.40.

Changes in Voting Power

As the rules are going to change in 3 days for Hard Fork 19 (HF19), we will use the new rules

Voting power decreases each time you vote and increases continuously over time.

Each time you vote at 100% vote strength, you loses 2% of your voting power. That is, your voting power becomes 98% of itself.
If your voting power is 100%,immediately after your vote, it becomes 98%.
If your voting power is 50%, immediately after your vote, it becomes 49%.

Whenever your voting power is less than 100%, it increases automatically over time at a rate of 20% per day.
So, if at some point your voting power is 70% and you don't vote at all for 24 hours, your voting power will become 90%
If it is 50%, after 24 hours it will become 70%.

Voting at the same voting power

Suppose you always want to vote at the same voting power. How many votes will you be able to give each day?
The answer to this question varies with the voting power you want to keep.

If it is 100%, after each vote, it becomes 98% and you need to wait the necessary duration until it reaches again 100% before voting again.
This duration is one tenth of a day (2 hour 24 minutes), because in one day the voting power increases by 20%.
So, the maximum number of votes at 100% is 10. If the maximum value of your vote is $0.40, the 10 votes will be worth $4.00.

Now, if you want to vote repetitively at 50%, after each vote, your voting power will be 49% and you will need to wait one twentieth of a day before voting again.
So, the maximum number of votes at 50% in a day is 20. If the maximum value of your vote is $0.40, as you vote at 50% voting power, your votes are worth $0.20, and 20 votes in a day are worth $4.00 again.

In fact, if you use the maximum number of votes to keep the same voting power that is lower than 100%, each of your votes will have a lower value, but you are able to vote more often and the total value of all your votes over a period of 24 hours will be the same as if you were voting 10 times with 100% voting power.

For 33.33% voting power, you are able to vote 30 times.
For 25% voting power, you are able to vote 40 times.

I could show you the math behind this claim, but I don't think it is necessary.

So, Should you Care about your Voting Power?

If you are like myself a somewhat prolific curator for rewards, it is my contention that you should not care about your voting power, because reducing the frequency of your votes to keep a high voting power will not increase your rewards.
This mostly applies if you are curating mostly for your own rewards. You may have other reasons to keep a high voting power, for example, if you want to give bigger rewards to your favorite authors.

Steemians that curate mostly for their own rewards (while at the same time rewarding the authors that they upvote) should better focus on aspects other than your voting power to maximize your curation rewards.

For example, you could follow the advice of @liberosist that he gave in this post: Mind Your Votes! II - A guide to maximizing your curation rewards:

Power up
DON'T vote on trending posts
Look for undiscovered posts

I would add another advice:

Try to upvote early (but not too early) posts from Steemians that have a long track record of highly paid posts, such as @trafalgar, @sweetsssj or @papa-pepper.