user97236: Assuming two miners have a (1/x) chance of finding a block over some time period, is the probability of both miners finding a block within that period simply (1/x^2)?
More generally, would  n miners with equal hash rates have a (1/x^n) chance of all finding blocks within some time period of each other?
This is for a research project where mining probabilities are being factored into a simulation, and I'm not sure if certain configurations are eliminated when the first miner finds a block (ie they would be dependent events)

user60443: 
Assuming two miners have a (1/x) chance of finding a block over some time period, is the probability of both miners finding a block within that period simply (1/x^2)?
More generally, would n miners with equal hash rates have a (1/x^n) chance of all finding blocks within some time period of each other?

I believe these are both correct assuming the miners are working independently of each other.
In practice, however, as soon as a miner finds a block, it is in their best interest to publish that to the network as soon as possible to prevent another from publishing a block before them. So, there is a certain amount of time where the new block will propagate across the network after which a miner will not attempt to mine that old block anymore (usually seconds), so network latency has an effect here.

97236: <p>Assuming two miners have a (1/x) chance of finding a block over some time period, is the probability of both miners finding a block within that period simply (1/x^2)?</p>

<p>More generally, would  n miners with equal hash rates have a (1/x^n) chance of all finding blocks within some time period of each other?</p>

<p>This is for a research project where mining probabilities are being factored into a simulation, and I'm not sure if certain configurations are eliminated when the first miner finds a block (ie they would be dependent events)</p>
 60443: <blockquote>
<p>Assuming two miners have a (1/x) chance of finding a block over some time period, is the probability of both miners finding a block within that period simply (1/x^2)?</p>
<p>More generally, would n miners with equal hash rates have a (1/x^n) chance of all finding blocks within some time period of each other?</p>
</blockquote>
<p>I believe these are both correct assuming the miners are working independently of each other.</p>
<p>In practice, however, as soon as a miner finds a block, it is in their best interest to publish that to the network as soon as possible to prevent another from publishing a block before them. So, there is a certain amount of time where the new block will propagate across the network after which a miner will not attempt to mine that old block anymore (usually seconds), so network latency has an effect here.</p>
