Bitcoin 2013, San Jose
Meni Rosenfeld
Bitcoil
5/19/2013
Written by Meni Rosenfeld
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Outline
 Mining primer
 Simple reward methods
 PPS
 Proportional
 Advanced methods
 DGM
 Reward method triangle
 Shift-PPLNS
 The future
 Questions
5/19/2013
Written by Meni Rosenfeld
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Mining primer
 Bitcoin mining exists to:
 Determine initial distribution of coins
 Synchronize transactions
 Miners calculate hashes in an attempt to find blocks and
be rewarded with bitcoins
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Written by Meni Rosenfeld
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Mining rewards
 One in 232 hashes will be a share
 A share has probability p = 1 / D to be a block
 Currently D ≈ 10 M
 A block is rewarded with B bitcoins
 Currently B = 25 (+ tx fees)
 Expected reward per share: pB
 Example: a 10 GH/s miner finds:
 8K shares per hour (73M per year)
 Per year, on average, ~7 blocks (180 BTC)
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Written by Meni Rosenfeld
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Variance
 Actual number of blocks found is random
 Follows Poisson distribution
 Variance is equal to mean
 Relative variance: D / #shares
 Example: 10GH/s miner, one year, B = 25, D = 10M
 Average reward: 180 BTC
 Standard deviation: 68 BTC
 Reward range: 25 – 350 BTC
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Written by Meni Rosenfeld
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Mining pools
 Group of people mining together sharing rewards
 Relative variance based on combined hashrate
 Allows continuous rewards similar to expectation
 Contribution is measured by number of shares
 Actual calculation of rewards is not trivial!
 Hence the need for (and variety of) “reward methods”
5/19/2013
Written by Meni Rosenfeld
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PPS (Pay per share)
 Pool operator takes an active role
 Pays miners a fixed amount pB per share (minus fees)
 Operator keeps all block rewards
 Advantages:
 Simple
 Miners completely shielded from randomness and variance
 Payment sent instantly
5/19/2013
Written by Meni Rosenfeld
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PPS (Pay per share)
 The problem
 Variance is entirely assumed by pool operator
 Operator requires high fees to compensate for risk
 Bankruptcy chance: 𝛿
= exp
−2𝑓𝑅
𝐵
 Still viable
 But difficult to get right
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Written by Meni Rosenfeld
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Proportional
 Mining is organized into rounds
 Finding a block ends previous round and starts new one
 Block reward distributed among miners in latest round in
proportion to shares they submitted this round
 Operator has no risk; miners do have variance
 Problem: Method is completely broken!
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Written by Meni Rosenfeld
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Pool hopping
In good times…
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Written by Meni Rosenfeld
and in bad?
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Pool hopping
 Proportional method based on wrong intuition
 Suitable for deterministic tasks
 Not for random, memoryless tasks
 Reward per share = B / (#shares in round)
 #shares in round = #past shares + #future shares
 #future shares unknown but always look the same
 #past shares is known and variable!
 Mining most lucrative when #past shares is low
5/19/2013
Written by Meni Rosenfeld
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DGM (Double geometric method)
 When miner submits a share, his score increases
 Score decreases geometrically when:
1. A share is found
2. A block is found
 Miners are rewarded for blocks according to current score
 Independent of everyone else’s scores!
5/19/2013
Written by Meni Rosenfeld
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DGM (Double geometric method)
 Reward per share depends only on pool’s future
 Hence, method is hopping-proof
 Works like a capacitor
𝑟 ≔1+
𝑝 1−𝑐 1−𝑜
𝑐
𝑆 ≔ 𝑆 + 1 − 𝑓 1 − 𝑐 𝑠𝑝𝐵
𝑤≔
5/19/2013
1−𝑜 𝑆
𝑐𝑠
Written by Meni Rosenfeld
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Reward method triangle
5/19/2013
Written by Meni Rosenfeld
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Shift-PPLNS
 Work is divided into “shifts”
 Ending a shift is arbitrary
 But not based on finding blocks!
 Miners are paid for shares submitted in last N shifts
 Method can work asynchronously
 Suitable for scalable, parallel implementations
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Written by Meni Rosenfeld
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Pool landscape
5/19/2013
Pool
Method
BTCGuild
Shift-PPLNS / PPS
50BTC
PPS
Slush
Slush
Bitminter
Shift-PPLNS
Bitparking
DGM
Eclipse
DGM / PPS
Deepbit
Proportional / PPS
Ozcoin
DGM / PPS
Itzod
RSMPPS
Eligius
CPPSRB
P2pool (decentralized)
PPLNS
Written by Meni Rosenfeld
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The future
 Currently: “Standard” pools
 Pool assigns work to miners
 Miners submit proof of completed work
 Pool pays miners
 Problem:
 Pool performance improves with pool size
 Mining tends to concentrate at biggest pools
 Control of mining is centralized
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Written by Meni Rosenfeld
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The future
 Some combination of:
 Multi-pool mining
 p2p pools
 Variable-difficulty shares
 Smart miners
 Distributed insurance agents
 Proxy pools
 Will allow:
 PPS payments (simple, no variance)
 Low fees
 Decentralization of power
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Written by Meni Rosenfeld
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Questions?
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Written by Meni Rosenfeld
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Thank you
 Meni Rosenfeld
 meni@bitcoil.co.il
 https://bitcoil.co.il
 1DdrvajpK221W9dTzo5cLoxMnaxu859QN6
 “Analysis of Bitcoin Pooled Mining Reward Systems”
 https://bitcoil.co.il/pool_analysis.pdf
5/19/2013
Written by Meni Rosenfeld
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