but wait, why is there a confirmed reward number that goes up progressively in pool websites?
Pools use the losing hashes as proof. The pool is estimating your share of the block reward when a block is found. If you contribute 1% of the losing hashes/tickets then (simplified) you will get 1% of a reward when a block is found. Now the pool overall might be lucky or unlucky so it might take longer or shorter for the pool to get paid but by counting your tickets vs entire pools tickets the pool can ensure a) that you are actually working, and b) what "share" you should get. Depending on the pool the "confirmed" reward is likely your share of blocks which have already been found but the pool is waiting for it to mature. The "unconfirmed" reward is your share of the current block miners are looking for a solution to. If the pool is PPS then the pool is simply paying you a flat fee per losing ticket. The pool is taking all the risk and when a block is found faster they get more than they payout and when a block is found slower they payout more than they get. This is why the fee is generally higher for PPS.
To use the lottery ticket analogy imagine you and your friends make a lottery pool you all buy lottery tickets but you can't be together for the drawing, you don't even know when you will get a winner. So you all buy tickets (some can buy more, some can buy less) and everyone saves their losing tickets. Now the losing tickets are worthless but they are proof you helped the pool. When someone wins the lottery everyone comes together and everyone's losing tickets are counted. If since the last winner you bought 120 tickets and the combined total for everyone was 12,000 tickets then you would get 1% of the jackpot regardless of who actually bought the jackpot ticket. Note: don't do this in real life without cryptography this is a very bad setup and very easy for the winner to just walk away with the winning ticket or broke players to grab old losing tickets from the trash to pad their stats. In mining however the use of cryptography means you can't cheat, but the general concept of using losing tickets/hashes as proof of contributing still applies.
