A Complete Description Of A New Casino Game

ECM on 100 digits (prescribed threshold)

I had to retract my claim of “a practical description,” because I failed to account for the necessary computation of probability for automatic SIQS. I hope others will be interested enough to compensate this potential lack.

ten sided dice—x5 or x20 each roll (to remove order as a concern.) It takes time to record or enter x25 digits. x20 digits takes a little time, but there is “action,” in between.

After data entry

300 curves on one core—ruling out factors < 10^25. 

Note: for complete factoring, any count of factors, each < 20^25.

Although summary SIQS is plausible any time after 300 curves, it is desirable to run fully 2100 curves for the 100 digit range, before coercing SIQS. In this game we describe 2400 curves.

SIQS as a mathematical choice only accounts for two (2) unique factors. Full number should be reduced to two factors (at least as a statistical probability) before attempting SIQS.

2100 - 300 =1,800 

1,800 / 300 =6 

Practical solution: Instances of a browser. These can be cascaded (coincides with 6 cores on an Intel Core i5 12,600; sufficiently “tall,” but more secure on network than comparable AMD/since hw ram register.) For game play, one core may suffice. Customer research should experiment with duration; while inflexible, it can be compensated by concurrent processing. account for excitement of wagering v number of opportunities 

After 2,100 curves, coerce manual SIQS (prefer “tall cores.”) SIQS requires all processing to be completed on a unique single core. 

For hw: investigate multithreaded SIQS

Game play:

  1. If prime, player wins outright.
  2. If factors in < 300 curves, player loses. As an explanation; even numbers cannot be prime (alert the media,) but they can remain challenging to fully factor. 300 curves not only eliminates some 90% of factors <25 digits: it accounts for all occurrences of every possible factor <25 digits. This can reduce the challenge of the final question by many more digits than merely 25 digits, and there is no deterministic or predictive process for finding integers that require more than 300 curves to factor. To contribute knowledge from experience; it can be a little tedious to discover a good prospect; allowing for variety, as many as 20 trivial numbers when testing them sequentially. I recall making that choice early on, based on lotto strategy; I do not recall what my experience was rolling unique 100 digit numbers one at a time—convenience, including the ease of adding one to the last digit (for data entry,) factored in.
  3. Introduce background computation 2100 - 2400 game play. All curves must complete [and no subprocess effort succeed] for player to ultimately lose - if number factors in this range player wins outright; computation runs concurrent for time; it is the slowest range, and coprocessing accommodates game play.
  4. Player proceeds to win or lose on an alternating basis 300-600 win; 600-900 lose; 900-1200 win; 1200-1500 lose; 1500-1800 win; 1800-2100 lose.
  5. There exists a mathematical condition that triggers SIQS automatically. Subject to review, SIQS represents factorization: so whether automatic SIQS or manual SIQS (required to provide obligatory results after 2400 curves) house wins on SIQS.
  6. Calculating probabilities for Wagering might involve summations of lesser included probabilities for a largest co-factor of: (ex:) 35 digits + 36 digits + 37 digits … 50 digits, uniquely represented at the threshold of each range, since curves represent % probability of factor length of relevant i, where number is x * 10^i. I balked at this requirement-I was not completely satisfied it was sufficient. However, if probabilities are not possible, a professionally developed system of ODDs, would still be a practical (viable) solution. A math professor could provide probabilities for individual instances.
  7. We suppose that 2100 - 2400 completes before the rest, but if it is still running, the computation is a useful prerequisite to manual SIQS, and should not be discarded- game play ends at 2400 curves.
  8. Choice of subsequent number goes with player; next odd integer if he choses to play again; re-roll dice for new player.

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