Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it

Quote from: kTimesG on Today at 04:23:45 PM

My brain's fried, let's ai:

Quote

There’s nothing syntactically “wrong” with this code, but there are a few logical and statistical issues in the way you’re comparing the two search methods:

1. You’re averaging “checks” only over wins

Code:

avg_success_rate_sequential = total_checks_sequential / wins_sequential

This gives you the average number of checks taken only in the cases where sequential_search “won”, ignoring all the other runs (losses and ties).

That means if one method rarely “wins,” you’ll divide by a very small number and get a deceptively large average.

Conversely, if it wins almost every time, you’ll be averaging only its best performances.

What you probably want instead is the average number of checks per trial, across all trials, regardless of whether it “won,” “lost,” or “tied” on that trial:

2. “Wins” as a performance metric is crude

You’re counting a “win” whenever method A uses strictly fewer checks than method B on a single trial. But that ignores how much better it was. A method that “wins” by 1 check a thousand times but “loses” by 10 checks just once will look like a bad runner‑up even though it’s dramatically faster on average.

Better alternatives:

Compare the distribution of checks (mean, median, percentiles) rather than just counting wins.

Compute the mean difference in checks per trial:

3. Ties are effectively ignored in your averages

You increment results["ties"], but then never use that count in any of your averages or analyses. If ties are frequent, you’re throwing away a lot of information.

Code:

=== FINAL RESULTS ===
Wins:
Sequential: 174
Prefix: 295
Ties: 31

Total Checks:

Sequential: 25723799
Prefix: 25388472
Total Time:

Sequential: 713.658067 seconds
Prefix: 741.870805 seconds

Averages (Total Time / Wins):

Sequential : 4.101483 seconds/victory
Prefix : 2.514816 seconds/victory

Checks per Win:
Sequential : 147837.93 checks/win
Prefix : 86062.62 checks/win

Code:

Analysis of Results in the Context of Key Cracking
The provided data compares two search methods (Sequential vs. Prefix) in a scenario simulating key cracking (searching for a target hash in a key space).
The key is correctly interpreting the metrics to determine which method is more efficient in practice.

Key Data Summary
Metric Sequential (A) Prefix (B)
Wins 174 295
Ties 31 31
Total Checks 25,723,799 25,388,472
Total Time 713.65 sec 741.87 sec
Time per Win 4.10 sec 2.51 sec
Checks per Win 147,837 86,062

Interpretation for Key Cracking

In this context, the goal is to find a valid key with minimal effort. Thus, the critical metrics are:

Wins:

The Prefix method (B) wins 295 times vs. 174 for Sequential (A).

This means B is 1.7x more effective at finding solutions.

Checks per Win:

B requires 86,062 checks/win vs. 147,837 for A.

B is 1.72x more efficient per win (uses almost half the resources per success).

Time per Win:

B takes 2.51 sec/win vs. 4.10 sec for A.

B is 1.63x faster per win.

Why the Prefix Method is Better for Cracking
Success Efficiency:

In cracking, what matters is the cost to find a valid solution (not the overall average).

The prefix method optimizes the search using heuristics (like comparing hash prefixes) to quickly discard useless blocks.

Practical Example:

If searching for a needle in a haystack, the sequential method checks the entire haystack in random order.

The prefix method uses a magnet (the hash prefix) to rule out areas without needles, reducing the search space.

Why Global Metrics Aren’t Enough
Total checks and time are similar (25.7M vs. 25.4M; ~714 sec vs. ~742 sec).

This might make the methods seem equal, but they’re not.

The difference lies in how they distribute resources:

Sequential: Spends more per win but wins less.

Prefix: Spends less per win and wins more.

In cracking, cost per success matters, not total cost.

Example: If A spends 1,000,000 ops for 1 win and B spends 1,000,000 ops for 10 wins, B is clearly better, even if the global averages are similar.

Conclusion
The prefix method (B) is superior for key cracking because:

Wins more often (295 vs. 174).

Requires fewer operations per win (86k vs. 147k).

Is faster per win (2.51 sec vs. 4.10 sec).

The sequential method (A) is less efficient in this context, as it wastes resources on unproductive searches.

Recommendation
If the goal is maximizing success per invested resources, the prefix method is the best choice. The per-win metrics (checks/win, time/win) are the correct ones to evaluate this.
Ignoring these metrics is comparing apples to oranges.