Bots can solve all kind of captcha.There is services like 2captcha that permit to bots solve the captcha without any problem,In fact there is humans behind these services that solve the captchas in behalf of the bots.Ofcourse it's a paid service,it's not worth it to use it on a faucet that pays pennies anyways.

Quick tip:Just make payments manual instead of instant to avoid cheaters and don't go bankrupt.

Well,if the payments have to be requested first by the users done manually processed by you,the faucet owner you can easily detect if there is fraudulant activity related to the user in question or not.I mean if you see someone requesting a big payment while he didn't register long ago it's obvious he's using bots right?

If you want to do it the hardway,implement an anti-proxy/VPN, implement anti-bot links or other anti-bot means in addition to captcha,hire a coder to check your code and do penetration tests and you should be totally fine.

When I started, I had virtually no clue about cyber security. And let me tell you, it’s an entire field of programming in itself. So, there are a lot of things you can do to limit attack vectors. On the flipside, there are so many different ways you can get hit if someone is really trying.
So, start reading up on it. You will need it at some point...

From my own experience I’ve noticed that once you start hunting bots and malicious code, it quickly becomes a game of judgement calls. Lots of browser compatibility issues to deal with and at the same time, the bots might not even be using a traditional browser. It’s very easy to trip yourself up when trying to lock the site down. I’m still learning new stuff all the time, lol.

Sounds complicated. But thanks.

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Sorry to say this, but I couldn't understand you because your English is not very good.

Your faucet uses captcha, too. Is your faucet being plundered by bots?

Let me try to interpret.
There are companies in countries with cheap labor, that employ people to do nothing except solve captchas all day.
The bot software sends the captcha to the human workers and the human workers solve the captcha for the bot. If the reward is high enough it is still profitable to pay for this service.
I’m sure there are bots out there who are able to solve captchas on their own as well, but once they start using humans to solve them, there isn’t a whole lot you can do to stop them.

My personal tip would be to create your own custom captcha. You might not be able to stop them from solving it, but you can make it unique and force them to write custom code if they want to solve it. Writing custom code for every little faucet isn’t profitable, especially when you can change it any time you like.
Just my $0.02...

Another option is to create algorithms that limit profitability for automated claimers while not impacting real humans.

Don’t know any of the details really, I just read an article about how it’s done. It didn’t go into the technical stuff...

About the starting amount of money you should gather for the faucet, it's a pretty simple process to calculate.
Write down the biggest amount of Satoshi that the user will be able to collect daily. If you will advertise your faucet good enough, or just make an interesting promotion here on the forums or somewhere else, you should expect about 100 to 200 people coming in for the first 3 days.
Now calculate how much would it take to get the advertising revenue, let's say that you are getting the revenue monthly.
So now basically get the max amount of Satoshi per user daily, multiply it by 200 (or more, if you expect more people to come in) and multiply it by 30 days. Now you have the initial starting Satoshi balance to gather, and not run out of money fast!

Also make sure that your website is secure, so the bots and hackers will not drain it faster than you think.
If you are new into faucets and you are using FaucetHUB API, they have a nice feature to alert you, when a certain amount of Satoshi will drain in a specific time (like 30 minutes).

Good luck

Sadly,no there is no way to avoid that.Just to say that captcha alone isn't enough especially if you are offering a generous amount,so having another uncasual way for users to prove that they are humans is a must.