Please don't judge on my math: (irony: I'm a math minor and never taken statistics)
Well here goes:
Given: 1 share = 1/(2^32) hashes
Group A:
10 GPU's producing 100 Mh/s each
Total: 1 Gh/s
Group B:
1 GPU Producing 1 Gh/s*
Total: 1 Gh/s
*Disclamer: THIS IS THEORY ONLY
Prove: Mining in a proportional pool, you will benefit more from one gpu providing maximum hashing speed, vs multiple cards hashing at slower speeds.
A:
10 Gpu's mining @ 100 Mh/s simultaneously will provide roughly 1 share every 42.9 seconds.
((2^32) hashes / 1 share) * (1 s / 100E6 hashes) = 42.94 s/share
B: 1 Gpu mining @ 1 Gh/s will provide roughly 1 share every 4.29 seconds
((2^32) hashes / 1 share) * (1 s / 1E9 hashes) = 4.29 s/share
ALL POOLS USE A NON-FEE PROPORTIONAL METHOD
Pool has a constant 1 Th/s collective speed.
Scenario 1: (extreme case)
Pool finds a block in 30 seconds.
Total shares: (1 share / (2^32) hashes) * (1E12 hashes / 1 s) * 30 s = 6,980 shares (3 sig figs)
A:
Shares by you: (1 share / 42.9 s) * 30 s = 0.699 shares / GPU = 0 shares
Payout: ( 0 shares / 6980 shares ) * 50 BTC = 0 BTC
B:
Shares by you: (1 share / 4.29 s) * 30 s = 6.99 shares (tough luck) = 6 shares
Payout: ( 6 shares / 6980 shares ) * 50 BTC = 0.430 BTC
Scenario 2:
Pool finds a block in 180 seconds.
Total shares: (1 share / (2^32) hashes) * (1E12 hashes / 1 s) * 180 s = 41,900 shares (3 sig figs)
A:
Shares by you: (1 share / 42.9 s) * 180 s = 4.196 shares / GPU = 40 shares
Payout: ( 40 shares / 41900 shares ) * 50 BTC = 0.477 BTC
B:
Shares by you: (1 share / 4.29 s) * 180 s= 41.95 shares / GPU = 41 shares
Payout: ( 41 shares / 41900 shares ) * 50 BTC = 0.489 BTC
Scenario 3:
Pool finds a block in 3600 seconds.
Total shares: (1 share / (2^32) hashes) * (1E12 hashes / 1 s) * 3600 s = 838,000 shares (3 sig figs)
A:
Shares by you: (1 share / 42.9 s) * 3600 s = 83.9 shares / GPU = 830 shares
Payout: ( 830 shares / 838000 shares ) * 50 BTC = 0.495 BTC
B:
Shares by you: (1 share / 4.29 s) * 3600 s = 839 shares / GPU = 839 shares
Payout: ( 839 shares / 838000 shares ) * 50 BTC = 0.506 BTC
In conclusion:
Stated by my data, the highest hash rate obtainable by one card vs multiple smaller cards will almost always yield more BTC over time.
DISCLAIMER: This is a lottery. You can get get a share the first hash you do with any card. This data represents results over a large period of time.
This is a picture of the results in an excel spreadsheet:
This can be related to 5870's vs 5970's.
~400 Mh/s to ~350 Mh/s
This theory is also in favor of the BFL 850 Mh/s miner. Go figure.
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