Like for all miners, solo or pool, each block is always solved by 1 ASIC somewhere. Whether solo or in a pool, the miner (or a pool's miner in the case of pool) needs to solve the block to receive the block reward.
So those who mine solo enjoy the block reward without sharing it, but the probability of getting it is slim (as others have said it depends on hashrate and luck, it's totally random)
Many people mine solo with a small percentage of their hashrate, this allows them to keep a more or less stable income and have a small part of the hashrate left over like a lottery ticket.
OP, here is an quote from the following link that sums it up correctly: https://en.bitcoin.it/wiki/Pool_vs._solo_mining
Pool Mining Pros
Pooled mining generates a steadier income.
Pooled mining can generate a 1-2% higher income (before fees, if any) due to long polling provided by the pools.
Pool Mining Cons
Pool mining can suffer interruptions from outages at the pool provider.
Pools are subject to DOS attacks and have other downtimes, too. Backup pools and solo mining can be configured for these cases.
Pooled mining tends to generate a smaller income due to fees being charged and transaction fees not being cashed out.
There are zero fee pools. Until now, transaction fees are not cashed out by any pool.
Pools might be part of attack scenarios.
Solo Mining Pros
Solo mining is less prone to outages resulting in higher uptime.
Solo mining doesn't incur any fees. For each discovered block, 6.25 BTC and the transaction fees are paid to the miner.
Solo Mining Cons
Solo mining tends to generate more erratic income.
Solo mining wastes time due to only supporting getwork pull.