user123385: Why do we need so many miners, if we anyways only can add one block every 10 minutes? I mean if the current block height is x and we now need the block of height x+1 only one miner will be rewarded right? And all others who also tried, go away empty-handed.

user50349: One way to think about bitcoin mining is to phrase it in terms of a lottery. The bitcoin network essentially hosts a sequence of lotteries, and the protocol is designed (and enforced by nodes) such that, on average, the time between one lottery and the next is ten minutes.
Those who are interested in buying tickets for these lotteries (miners or prospective miners) are able to use their knowledge of the protocol to compute a valid ticket. The computation is the non-refundable purchase of the ticket.
However, a valid ticket is not necessarily a winning ticket. Naturally, miners want to acquire as many valid tickets as possible so as to maximize their chances of winning the lottery.
Alas they must balance this desire to win with the cost to acquire all those tickets and compare this cost to the miner's perceived value of the reward (block subsidy + fees). When the miner includes in this analysis the risk not winning even though they purchased all these tickets, many of them choose to join mining pools. Doing so reduces their likelihood of walking away completely empty handed, albeit they will not walk away with the entire lottery reward either (it is shared among the pool members).
Lastly, to address the first part of your question, bitcoin does not need so many miners. Just a handful would do. However, the reason why there are so many miners is simply because the expected value of winning these lotteries is such that it, in the eyes of those participating, it is worth the expected value risk/cost of participating in them. The difficulty adjustment algorithm essentially regulates the expected costs associated with winning the lottery. Ultimately, what we know is the number of lotteries that have been held (blocks), but the exact number of miners participating in any one of them is unknown.

user13866: We need more than one miner because ...

We must avoid centralisation as a goal of Bitcoin is to avoid the need for trusted third parties.
We need miners to invest sufficient work to make the Blockchain effectively immutable. Otherwise we lose any agreement about who has money. This requires a competitive set of participants who undertake mining. It requires that there be a set of miners participating whose combined computing power is sufficiently large that it is uneconomic for one of them to attempt to seize control and commit fraud.

We get more than one miner because it is necessary to provide a monetary incentive to those who do the work of ordering transactions and securing the Blockchain. In a purely peer to peer system this attracts multiple participants.

123385: <p>Why do we need so many miners, if we anyways only can add one block every 10 minutes? I mean if the current block height is x and we now need the block of height x+1 only one miner will be rewarded right? And all others who also tried, go away empty-handed.</p>
 50349: <p>One way to think about bitcoin mining is to phrase it in terms of a lottery. The bitcoin network essentially hosts a sequence of lotteries, and the protocol is designed (and enforced by nodes) such that, on average, the time between one lottery and the next is ten minutes.</p>
<p>Those who are interested in buying tickets for these lotteries (miners or prospective miners) are able to use their knowledge of the protocol to compute a valid ticket. The computation <em>is</em> the non-refundable purchase of the ticket.</p>
<p>However, a valid ticket is not necessarily a winning ticket. Naturally, miners want to acquire as many valid tickets as possible so as to maximize their chances of winning the lottery.</p>
<p>Alas they must balance this desire to win with the cost to acquire all those tickets and compare this cost to the miner's perceived value of the reward (block subsidy + fees). When the miner includes in this analysis the risk not winning even though they purchased all these tickets, many of them choose to join mining pools. Doing so reduces their likelihood of walking away completely empty handed, albeit they will not walk away with the entire lottery reward either (it is shared among the pool members).</p>
<p>Lastly, to address the first part of your question, bitcoin does not <em>need</em> so many miners. Just a handful would do. However, the reason why there are so many miners is simply because the expected value of winning these lotteries is such that it, in the eyes of those participating, it is worth the expected value risk/cost of participating in them. The difficulty adjustment algorithm essentially regulates the expected costs associated with <em>winning</em> the lottery. Ultimately, what we know is the number of lotteries that have been held (blocks), but the exact number of miners participating in any one of them is unknown.</p>
 13866: <p>We <em>need</em> more than one miner because ...</p>
<ul>
<li>We must avoid centralisation as a goal of Bitcoin is to avoid the need for trusted third parties.</li>
<li>We need miners to invest sufficient work to make the Blockchain effectively immutable. Otherwise we lose any agreement about who has money. This requires a competitive set of participants who undertake mining. It requires that there be a set of miners participating whose combined computing power is sufficiently large that it is uneconomic for one of them to attempt to seize control and commit fraud.</li>
</ul>
<p>We get more than one miner because it is necessary to provide a monetary incentive to those who do the work of ordering transactions and securing the Blockchain. In a purely peer to peer system this attracts multiple participants.</p>
