Joining a mining pool

Your portion of the block depends on how much hashing power you have, and the payout method used by the pool. In general, the larger a pool is, the less variance you see. In other words, they tend to close around 100% luck, finding about as many blocks as you would expect.

All things being equal (which they aren't in reality, but for this example, we'll assume they are), if you have two pools, one that is 10 times the size of the other...

You would expect to find 10 times as many blocks in the larger pool. You would receive a 10x smaller reward per block.
You would expect to find 10x fewer blocks, but each block would pay you 10x more in the smaller pool.

The net result? You earn the same in either pool.

Now, I did mention that's a very simplified case where we assumed all things are equal. They never are. Some pools charge fees. Some pools give their miners the transaction fees from mined blocks. They can very drastically alter your earnings. For example, AntPool doesn't charge you any fees, but they don't give you the transaction fees from blocks. That little hidden fee costs you a lot (it also makes Bitmain a BOATLOAD of coin). Look at the latest blocks that AntPool has mined. As of this post, AntPool has found 16 blocks today alone. They have made 23.71029199BTC. For themselves. Today. At an exchange rate of $10000 per coin, Bitmain has made $237,102.92. In 11 hours. That's effectively 11.85% fees they are charging miners.

Had those same blocks been found on my pool, the miners would have made that extra coin. My fee is 0.5%. Huge difference.

Moral of the story? Don't mine on the biggest pool simply because it's the biggest.