Can someone explain pool hopping for me?

[shads]

I've read about all the payment methods and the apparent 30% gain that can be made by pool hopping between PPS pools but I just don't get it.  Where does the advantage come from?

I presume a 'round' is the number of blocks between the pool's last winning block and next winning block.  So for argument sake let's say we have 4 equal sized pools.  Average round for each pool consists of 1000 shares and I'm a miner who can generate 10% of total shares per round if I stick with one pool for the whole round.

for an average round I generate 50 shares with pool 1 and 50 with pool 2.  Pool1 wins so I get 50/1000 * 50 = 2.5btc, same for pool2
If I stick with Pool1 I get 5 btc but expect to win block only half as often.
For a large number number of 1000 round shares I expect to win on average 1/2 with each pool, say 100 rounds
50 * 2.5btc = 125btc
50 * 2.5btc = 125btc
total = 250btc

For a short round say 600 shares I generate 50 shares with pool1 and 10 with pool2
If pool 1 wins I get 50/600 * 50 = 4.16btc
If pool 2 wins I get 10/600 * 50 = 0.83btc
For a large number number of 600 round shares I expect to win on average 1/2 with each pool, say 100 rounds
50 * 4.16btc = 208btc
50 * 0.83btc = 41.5btc
total = ~250btc

For a long round say 2000 shares I generate 50 shares with pool1, 50 shares with pool2, another 50 shares with pool1, another 50 shares with pool2
If pool 1 wins I get 100/2000 * 50 = 2.5btc
If pool 2 wins I get 100/2000 * 50 = 2.5btc
For a large number number of 600 round shares I expect to win on average 1/2 with each pool, say 100 rounds
50 * 2.5btc = 125btc
50 * 2.5btc = 125btc
total = 250btc

What am I missing?

[shads]

Further to that, why don't pools simply pay out for shares earned during a winning block?  I presume pool members see the round system as an advantage but surely the long term average is just the same as long as you don't happen to switch your miner off during the winning block.

[sirky]

The idea is that you want to maximize your return per block... since the likelihood of finding a bitcoin is independent of when a pool found its last coin.

Think about it... you have 10 equal size PPS pools that you can choose from, and you have 1/10th the hashing power of each... you always want to be mining at the pool with the fewest shares in the current round.

Why? Because each share you submit will increase your bounty more...

For each pool, you have two options. Mine, or don't mine. Mining should either increase your estimated bounty, or keep it constant (if it is already at 5btc). Not mining can either decrease your estimated bounty, or keep it constant (if it is 0btc).

You want to maximize your marginal bounty, by mining at the place where it would have the highest effect (either increasing your bounty the most, or not decreasing it the most). This is done by mining at the pool with the least number of shares currently.

Think about it, what you do in a pool with 10000000 shares already submitted really doesn't matter. What you do in a pool which just started a new round has a massive effect on estimated bounty.

The important point: the likelihood of finding a block is INDEPENDENT of how long the round has been going.

Make sense?

[shads]

I think I get your point... I understand the fact that time since last block has no bearing on likelihood of finding the next.  At any given time there's a 50% chance that the next block will be found in the next 10 mins.

By the theory you put forward then it seems the advantage of pool hopping is proportional to the ratio of total pool hoppers vs single pool miners.  i.e. if every miner mined each block from the pool with least shares the advantage would be cancelled out.  So why is this 30% figure bandied around?  Surely the advantage is highly variable?

[sirky]

I know they exist, but I don't think they are super prevalent...

If I were a pool operator, I would be score based... but if I were a PPS pool operator, I would not be very friendly to those who left at around 800,000 shares every round.

And yes, if everyone was a pool hopper, there wouldn't be much of an advantage to doing it.

The only thing I do, is if I know I need to take down my hardware to do something (reboot, or whatever), I try to do it in a longer round if I can.

[Mousepotato]

I'd rather not sit in front of a computer 24/7 and instead just throw in another 5830 into my system.  Problem solved.

[gentakin]

No need to sit there. It happens automatically.

[organofcorti]

No need to sit there. It happens automatically.

Hopping only happens automatically if you write your own hopping script, or are pointing at Multiclone or (when it's back up) Multipool. Or use the open sourced code to do auto-hopping by yourself without any annoying bash scripting.

http://forum.bitcoin.org/index.php?topic=17970.msg228164#msg228164

edit: I meant to also mention that these pools prove that hopping works. Although I don't know what the hopping algorithm is (although a good look at the code would explain it, I'm just too lazy), it works well. On 110000 shares I got 12% above expected return, and interestingly Deepbit was one of the highest returning - even though they delay their stats.

[Meni Rosenfeld]

Not PPS, "proportional". PPS = Pay per share, which is completely different (and immune to pool-hopping).

[MikesMechanix]

*

[Grinder]

What am I missing?

Your understanding of pool hopping is completely wrong. You don't just jump back and forth randomly, you move all your hashing power to whatever pool started their round last (the last pool to solve a block). Given your example of two pools with the same hashing power they will have the same chance of solving a block, but there will be fewer shares to share with in the one starting last. That results in a higher pay per share on average.