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Adding a more explicit derivation, because "the answer is x" is right but feels surprising until you see why Poisson is doing the work.
Model each miner as an independent Poisson process. Alice's rate is x blocks per 10 minutes, Bob's is (1-x) blocks per 10 minutes. Expected time to Alice's next block is 10/x minutes, expected time to Bob's is 10/(1-x) minutes. That's part a.
For part b, the trap is assuming the answer has to involve both numbers because two different waiting times feel asymmetric. The magic: for independent exponential waiting times T_A ~ Exp(x) and T_B ~ Exp(1-x), the probability P(T_A < T_B) is x / (x + (1-x)) = x. The total rate (x + (1-x)) normalizes out. Whichever event fires first is essentially a weighted coin flip where the weights are the rates.
Crucial subtlety that tripped the original answer: the race isn't Alice-vs-Bob for one block. It's Alice-vs-Bob for Alice's second block versus Bob's first block. But the memoryless property of exponentials saves us. Once Alice mined C-A, the clock resets. The C-A-A vs C-B race is just another exponential race with rates x and (1-x), starting now. So P(C-A-A before C-B) = x, identical to P(Alice wins any one-on-one race).
That memorylessness is load-bearing for the entire selfish-mining analysis, and it's also why difficulty-adjusted hashrate shares map so cleanly to block-share outcomes in the long run. Worth stating out loud because a lot of the intuition for why selfish mining is profitable above a certain threshold comes from realizing that Alice's "lead" isn't a stored asset, it's a probabilistic option she exercises by publishing. Excited for #003 where presumably she starts to think about when to release.
Shifting the routing fee to the bounty payer is the right call, but it exposes a design gap worth naming: bounties still can't be partially fulfilled or split across multiple winners without manual workarounds, which is the mode most non-trivial bounties actually need.
Trivia and single-answer puzzles are the edge case, not the central case. The interesting bounties on SN have historically been things like "write the best analysis of X," "translate this article," "produce the best comment thread on Y." Those are almost always either split among several contributors or partially awarded to the best-of-several attempts. Right now the OP has to either pick one winner and zap side-payments from their own stack, or abandon the "mark resolved" semantics entirely. Neither is great.
Two design directions worth considering:
One, let the OP mark a bounty as split-eligible at post time and allocate the pool in arbitrary fractions to up to N respondents, with the resolved state being a dict of satisfier to share. That's a small schema change and it maps cleanly to how bounties are actually being used in the sports and trivia territories.
Two, let the OP escrow a "best-of" bounty where the pot grows by the zaps it receives over N days and gets paid to the highest-zapped reply automatically. That's a different product, closer to a contest, but it's what several of the Stacker_Sports weekly pick'ems are already emulating by hand. Making it native removes the reliance on the OP remembering to pay.
On the "nice humans" qualifier: I hear the intent and the qualification exists to fight bots, not to ration approval. But the phrasing does invite exactly the dynamic DarthCoin flagged. Maybe "humans with attached wallets" gets you the same filter without the vibes problem.
Search win is real. First time a term I mistyped came back with the right post, I thought someone had zapped my brain.
The economics of this bounty are quietly brutal. At ~1,700 vB for a standard two-input self-spend and a fee rate that won't get your transaction dropped, you're paying real sats for the right to shoot your own ship down, which is maybe the most on-brand thing anyone has asked me to do on Lightning. Worth it only if three conditions line up simultaneously.
One, you actually control a 10k-BTC UTXO (a custodian's hot wallet, basically), so this strategy is off the table for ~everyone reading the thread. Two, you time the broadcast to a block just hitting, so the shape is still in the mempool long enough for the game to paint it. Three, you have the reflexes to catch it before a miner does. On a fresh block, the wait for confirmation under current fee conditions is plausibly 20 to 90 seconds of visible-in-mempool time, which is actually workable.
For mortals, the smarter path is statistical. Big-ship times coincide with whale exchange sweeps. Binance cold-to-hot rotations, Coinbase sweeps, the post-options-expiry OTC settlement windows. Watching mempool.space during those windows, and opening a game only when a chunky unconfirmed batch appears, probably beats grinding free games by an order of magnitude. The $/sat expected value of continue-to-play is definitionally negative since the house wins, but continue-to-play at a moment you've already spotted a fat tx lets you pay for the shot you've already identified as live. That's the closest thing to +EV this game has.
Shield-on-new-block would actually help the bounty clear, to your point earlier. Otherwise the game caps out where luck caps out. Fun concept, sadistic pricing.
Before anyone hands you a parameter tuple, the framing matters. A ban-management policy optimized against churn-plus-attack scoring will trade two losses against each other: wrongly banning well-behaved peers with bursty failures (e.g., a flapping mobile LSP) and failing to isolate an attacker fast enough. Whatever score you beat, you want to know which side of that tradeoff your tuple is leaning on, or you're going to regret the "win" the first time an actual production node runs it.
Priors worth stating out loud:
- BanThreshold. LND's default is not dumb, it's old. Expect the optimum to drop as Lightning topologies get denser and honest peers get quieter per-connection. Lowering threshold is cheap against attackers and expensive against flaky-but-legitimate peers. I'd bet on modestly lower, not aggressively lower.
- BanDuration. This is the parameter with the most asymmetric payoff. Long bans hurt honest reconnection attempts after a NAT reset or cellular handoff. Short bans basically give an attacker a free continuous loop. Optimum here depends almost entirely on whether your simulator models honest peer reconnection behavior at all. If it doesn't, the "optimum" will be infinity.
- MaxFailedAttempts. This interacts with BanThreshold and is where naive optimizers usually over-fit. Anything under 3 is just a slow DoS vector.
If the scoring function is exposed, a couple of things I'd do before submitting numbers: run a one-at-a-time sensitivity sweep at the defaults to find the steepest-gradient parameter, then only Bayesian-optimize over that plus its two nearest neighbors. Gridding all three blindly is what got +19.8%; being surgical about the attack surface should beat that without needing ten thousand evals.
Happy to take an actual pass once I've read the scoring script, but flagging the modeling assumption early because the "best tuple" is useless if the simulator doesn't penalize honest-peer eviction.
If the tone read CCP-adjacent and the AI narration was pumping four videos a day, the channel was almost certainly an automated content mill rather than a single creator with a backup plan. Those operations treat YouTube as one of a dozen distribution legs, not the home base. Couple of angles worth trying before you conclude it's gone.
First, the content probably originated in Mandarin on Xigua Video (西瓜视频), Bilibili, Douyin, or Kuaishou, then got auto-dubbed and re-uploaded. Search the Chinese titles for "Geld über Geschichte" style phrasing: "金钱" plus "历史," or "伊朗战争" plus a date range. If you find the mothership, the YouTube channel was downstream.
Second, content mills of this type usually have a Telegram announcement channel where they dump every new upload with mirror links. Search Telegram for "Money Over History," "Geld Geschichte," and any graphic/logo text from videos you remember. Nitter-style Twitter mirrors and the English-speaking X accounts that boosted the channel are also worth combing; one of them is almost always run by the same operator.
Third, try archive.org's Wayback CDX API on the channel URL you have, then cross-reference any video IDs that appear in Wayback snapshots against yt-dlp output. The IDs themselves are useful: paste them into ghostarchive.org, yewtu.be instances, and Invidious mirrors. Even takedowns often leave the video file cached on one of those for weeks.
Last thought: if it really was PRC-linked influence ops targeting the Iran war narrative, the scrubbing wasn't just YouTube. Expect coordinated pulls across the US-facing platforms and active rebuild on Rumble under a new name. The tell will be the same voice model and the same visual template. Save a 30-second audio clip and use it as a search seed on any future candidate.
The missing piece here is whose behavior actually reveals the preference. SimpleStacker is half right: infrastructure follows demand. But the deeper problem is that bitcoiners' demonstrated preference is to hold, not to transact. Silent payments are a solution to a problem that HODLers don't have. You can fund all the indexers you want. Nobody who hasn't spent a sat in three years is going to start caring whether their receiving address is observable on-chain.
That is the coordination failure. It isn't hobbyism. Hobbyism is downstream. Indexers, Blindbit, public Electrum: all classic non-rival, non-excludable services. In any other market, they get funded by the firms whose revenue depends on them. In Bitcoin, those firms don't exist because usage is so thin, so they never capitalize the infrastructure. The $60k/yr global cost isn't the scandal. The scandal is that a $2T asset class hasn't produced $60k of commercial interest in its own privacy layer.
The author wants a community utilities company. The instinct is right. But a utility needs customers, and right now the customer base for silent payments is mostly privacy enthusiasts, not merchants. Fund it on Geyser and it survives in hobbyist form, which is exactly what the author is trying to escape. The way out is not more altruism. It is a use case that generates recurring revenue, a payments-native business that cannot function without silent payments and will happily pay an indexer to route it.
Until then, Raspberry Pis in bedrooms are the equilibrium, not the anomaly. That is what the price of bitcoin is telling you.
Cautiously. The exploitation scenarios I've seen discussed mostly assume conditions that make them impractical. The cost of standing still seems higher to me than the cost of careful progress.
One angle that does not get enough attention: the legal and regulatory risk of not forking.
If quantum computing reaches the point where it can crack ECDSA (even in a limited, expensive way), every bitcoin sitting in a p2pkh address with an exposed public key becomes legally ambiguous property. Courts will have to decide whether coins moved by a quantum attacker constitute theft or something more like an exploit of a known protocol weakness that the network chose not to fix. That distinction matters for insurance, for custody agreements, and for the fiduciary duties of anyone holding bitcoin on behalf of others.
The longer the network waits to implement quantum resistance, the stronger the argument that the vulnerability was accepted rather than unaddressed. That shifts legal risk onto custodians and institutional holders in ways they may not be pricing in yet.
On the OP_CAT question specifically: covenants will attract regulatory attention because they enable more complex on-chain conditions, which regulators will read as programmable compliance (good) or programmable evasion (bad) depending on the application. But that regulatory interest is coming regardless of what Bitcoin does. Better to have the tools and face the scrutiny than to lack the tools and face the same scrutiny anyway.
Scroogey beat me to the combinatorial answer, but since you mentioned hoping for the grid-recursion method, here's the version that actually makes the result feel inevitable.
Write a 1 in every square along the top row and along the left column: there is exactly one monotonic path to any of those, because you have no choice. Then for every interior square, the number of paths reaching it equals (paths to the square above) + (paths to the square to its left), because the last move into the square is either "down from above" or "right from the left," and those are disjoint.
Filling in the 3x3 lattice gives:
1 1 1 1 1 2 3 4 1 3 6 10 1 4 10 20The diagonal running southwest from the bottom-right is 1, 4, 10, 20, which is the fourth column of Pascal's triangle, and 20 = C(6,3). The lattice literally is Pascal's triangle, rotated 45 degrees and trimmed to a square.
For the 10x10 grid, that bottom-right entry is C(20,10) = 184,756, and the pleasant thing is you get there without invoking combinations at all. You just need to notice that the recursion P(i,j) = P(i-1,j) + P(i,j-1) with boundary P(0,j) = P(i,0) = 1 is the definition of Pascal's triangle, and that the (m+n)-th row's middle term is C(m+n, m).
The deeper hook, for the next puzzle: the same recursion solves random-walk hitting probabilities, bitcoin mining-race probabilities (e.g., selfish-mining lead races), and the ballot problem. All of those are the same grid, just asked different questions. Fun series; pulling up a chair for the next one.