Probability Game (Part 1): Finding Common Sense in the Noise on 祝融说。

Appendix: A Probability Record That Can Be Continued

Sun, 13 Sep 2026 00:00:00 +0800

Start from an Actual Question

This appendix is a set of record structures, not a set of already-filled-in probability answers. To use it, first select a question that actually requires judgment, and save according to the corresponding relations; simple tasks can be recorded briefly, and fields can be expanded when material is ambiguous or evaluation is complex.

The field descriptions in the tables serve to organize the reader's own records; they do not require every item to have a numerical value. Unobtained, unadopted, and pending-check items should be preserved as they are; do not manufacture content just to fill a table. An empty template slot is not the same thing as a judged probability of zero.

All quantities and characters in Chengwan are fictional. The case index serves to check this book's internal continuity; it cannot become a sample for the reader's real tasks. Formulas work only on inputs satisfying the corresponding conditions; they do not make the inputs real.

Chapter 1: How Events Become Assessable Objects

Sun, 13 Sep 2026 00:00:00 +0800

Tomorrow There Will Probably Be Orders

On Thursday morning, Gu Ning stuck a note on the edge of the table at the Chengwan Repair Station that read: "Tomorrow there will probably be orders." Tang Ke glanced at it and said the client had asked about table-and-chair repair the day before, in a friendly tone. Gu Ning was about to write down her judgment in the log, only to discover she did not know at what later moment she should mark it as correct.

The Chengwan Repair Station, Gu Ning, Tang Ke, and the temporary assistants appearing in this chapter are all fictional constructs of this book. We begin with a repair commission still awaiting confirmation and gradually add predictions, messages, and outcomes, without treating their experiences as the author's firsthand accounts or real business data. Here there is first of all no complete statistical table, only a familiar word of approximation.

Chapter 10: Why Updating Is Not Merely Enlarging an Old Number

Sun, 13 Sep 2026 00:00:00 +0800

Where Should 1.8 Be Multiplied

Tang Ke wrote the historical starting point five-eighths on paper, with the message ratio 1.8 beside it. She tried multiplying directly and got 1.125. Gu Ning pointed at the result exceeding one and said this is not an adoptable probability; both numbers can be traced back to history, yet the connection did not preserve their original meanings.

The 1.8 of the last chapter is the ratio of B's appearance probability under A and under not-A, not an increment factor for the target probability. To connect it to the baseline, one must first make explicit what material the old judgment conditioned on, then, within the same model, let the new observation enter the relative shares of the two outcome classes.

Chapter 11: Are Multiple Sources Independent

Sun, 13 Sep 2026 00:00:00 +0800

Both of Them Say It Has Been Received

At 12:50 on Thursday, Tang Ke showed Ye Cheng the original text of the reply R17 obtained at 11:20. After reading it, Ye Cheng told Gu Ning that the message did indeed say the checklist was received and the reception time still needed verification. Tang Ke also said this was exactly what she saw.

Gu Ning now has two people's reading accounts, but no second independent reply from the client. Both return the same original message; what is added is a re-check, not B occurring a second time for R17. The change in the number of people and the change in the original observation must be kept apart.

This chapter continues the fictional Chengwan thought experiment. The previous chapter only preserved a candidate model computation, not adopted as R17's final prediction; complete confirmation is still not obtained. Ye Cheng's reading does not turn the pending reception time into available, nor does it add accepted material for scope and payment conditions.

Chapter 12: When Materials Conflict, Check Quality First

Sun, 13 Sep 2026 00:00:00 +0800

Has the Reception Period Actually Been Settled

At 13:20 on Thursday, Tang Ke found in the in-station draft schedule a note concerning R17, reading "reception period available." The client reply in Gu Ning's hands, however, said "Checklist received, I still need to verify the reception time." Ye Cheng asked whether the two materials conflicted and which should be adopted.

This chapter adds this in-station material to the fictional Chengwan; no new client reply has been obtained. The note does exist within the thought experiment, but whom "available" refers to, when it was written, and which judgment it supports require re-checking; a material's existence does not mean it has already answered full acceptance of the first version.

Gu Ning did not compromise "available" and "pending" into "probably available," nor did she regard the note as newer merely because Tang Ke found it most recently. She first placed the two original sentences together and required that each state separately who was describing whose reception conditions.

Chapter 13: The Selected Sample

Sun, 13 Sep 2026 00:00:00 +0800

Why the Achievements in the Cabinet All Look Smooth

Gu Ning reopened the original stack of eight display cards. They had not become false material through the checks of the preceding chapters: the repair station genuinely completed these jobs, and the cards retain the achievements. But she could now ask a further layer of the question—why did objects of this kind enter the cabinet, and why are other objects not in this stack?

Chapter 3 first identified the acquisition entrance for material, Chapter 4 established a comparable set, and Part Two examined conditions and evidence. Part Three asks a further question about the selection mechanism: if the chance of material entering is related to the target outcome, how does the proportion of visible objects change, and which inference about the whole thereby loses support?

Chapter 14: Survivorship and Unobserved Outcomes

Sun, 13 Sep 2026 00:00:00 +0800

What Should Be Written for Requests Without Achievements

Gu Ning placed the original sixteen registered items back on the table. The eight achievement cards explain what was completed, but what should be written for requests that have no card? Tang Ke suggested filling in "incomplete"; Ye Cheng reminded her that not having found a card and not having been completed are still different, and that not completed does not mean the original window did not receive confirmation.

The previous chapter explained the entrance of selection; this chapter handles the outcomes that were left behind and not observed. An object may not have entered the achievement story yet still possess a known window outcome; it may also be known only that it was registered, with no knowledge of how it ended. Neither should be compressed into a single "did not succeed" column.

Chapter 15: Changing Together Is Not Causing Each Other

Sun, 13 Sep 2026 00:00:00 +0800

Would Requiring Everyone to Reply First Make Confirmation More Likely?

At 3:40 p.m. on Thursday, Tang Ke proposed a method: from now on, always ask the client to reply explicitly that the list has been received. Since the historical group with such messages is more likely to confirm within the window, would obtaining replies uniformly raise the chance of confirmation?

Gu Ning said the proposal can be discussed, but the original table answers how objects with messages behaved, not how requiring everyone to send a message would change outcomes. Turning an easily observable state into an active requirement may have a different generating process.

This chapter continues the thought experiment of the fictional Chengwan. Tang Ke has only proposed a method; the repair station has not implemented a new process, no new client replies have been added, and R17 has still not received complete first-version confirmation. We will not let a proposal obtain a verified effect on the station's behalf.

Chapter 16: What Further Comparisons Does Explanation Require

Sun, 13 Sep 2026 00:00:00 +0800

A Method That Does Not Yet Have Its Own Control

At 2:20 p.m. on Thursday, Gu Ning wrote Tang Ke's proposal on a new sheet: from now on, ask the client to reply explicitly that the list has been received. The previous sheet already preserved several competing explanations; this sheet asks what must be compared if one wishes to judge whether the method is useful.

Ye Cheng said one could compare people who reply in advance with those who do not. Gu Ning pointed to the historical table: that comparison already exists. What is missing is the difference that arises after the station adds a requirement, compared with not adding it. The differences between two groups of people do not automatically become differences between two processes.

Chapter 17: How the Story Overwrites the Original Prediction

Sun, 13 Sep 2026 00:00:00 +0800

Before the Outcome, the Story Can Already Take Shape

At 5 p.m. on Thursday, Tang Ke asked how R17 should be explained to other recorders in the future. From the morning's definition of the problem, through finding the historical table, to seeing the replies, the material was already considerable. She hoped to draft an easy-to-read retrospective account.

Gu Ning agreed to try drafting one first, but titled the sheet "Narrative Draft." R17 has still not received complete first-version confirmation; the outcome window does not close until 5 p.m. on Friday. The 5 p.m. on Thursday is not the endpoint of the original event; the people here do not know the future first.

This chapter continues the thought experiment of the fictional Chengwan. We examine several kinds of narratives that could go wrong and their correction methods, without assigning the main line a confirmed or failed ending. Even when the future outcome becomes clear, it cannot automatically determine what the people at 10 a.m. actually knew.

Chapter 18: How Consensus Changes Visible Material

Sun, 13 Sep 2026 00:00:00 +0800

A Convenient Sentence for Handover

At 5:40 p.m. on Thursday, Tang Ke proposed that when handing over material in the future, the two could open with a single uniform sentence: "After receiving the list, the chance of confirmation is discussed at three quarters." This way later readers could enter the same problem more quickly, without having to re-derive everything from scratch.

Gu Ning said a shared phrase can help with handover, but this sentence cannot yet serve as R17's default prediction. The historical conditional frequency, the candidate model scenario, and the currently adopted final figure are not the same; the original reply still contains reception time awaiting verification, and the historical item-by-item receipt order still awaits rechecking.

This chapter continues the fictional Chengwan. Tang Ke proposed a shared phrase, the three discussed how it might be used, but it has not yet been set as a formal process. There are no new client replies, no new complete confirmation, no new final numerical probability, and no new batch of actual predictive outcomes.

Chapter 19: How a Forecast Record Continues

Sun, 13 Sep 2026 00:00:00 +0800

One Clear Card Is Not Yet a Continuous Record

At 18:20 on Thursday, Gu Ning gathered the papers organized that day. The event definition of R17, the acquisition of information, the historical table, the candidate calculations, and the open questions all had their places. Yet she noticed that if other requests were to be recorded afterward, there was still no single entrance from which all objects could be recovered.

Tang Ke said, isn't one card per request enough? Gu Ning answered that a card can state one object; a continuous record must also state which cards entered, which judgments were actually issued, which outcomes were adjudicated, and how a later adopted version connects to earlier versions.

This chapter continues the fictional Chengwan. The two organize the ledger structure at 18:20; no new client reply or complete confirmation is added. R17 still has no formally adopted final numerical probability, and the ledger will preserve that state; it will not fill in the candidate three-quarters just to make every row neat.

Chapter 2: Prediction Time Points and Observation Windows

Sun, 13 Sep 2026 00:00:00 +0800

When Was the Note Written?

Gu Ning had saved the first-version event card for request R17: by Friday 17:00, whether the repair station would receive the client's explicit confirmation of the specified task scope, payment conditions, and receipt period. At Thursday 10:00, that confirmation had still not arrived. Tang Ke said she was willing to ask once more later, to see whether the other party had any new intention.

This continuing scenario remains the fictional Chengwan. Chapter 1 settled what the event is; this chapter neither adds real samples in advance nor announces that the commission has been formed. We first look at how a prediction enters time, so that future messages can change the judgment while not silently changing the information the original judgment possessed.

Chapter 20: Which Set of Judgments Calibration Compares

Sun, 13 Sep 2026 00:00:00 +0800

One Held Outcome Cannot Yet Answer a Set of Judgments

At 19:00 on Thursday, Gu Ning turned to the next page of the continuous record. Tang Ke asked: if a judgment that adopted three quarters later comes to pass, does that show it was well calibrated? Gu Ning said we can record this outcome, but we still cannot evaluate how a set of three-quarters judgments performed from a single holding.

Three quarters does not hold every time, nor is it a schedule guaranteeing three holdings in every four. To check the correspondence between probability and outcome, one needs to find the corresponding judgments actually issued, state the scope and version, and then look at the frequency of holding among them.

Chapter 21: How Scoring Helps and How It Misleads

Sun, 13 Sep 2026 00:00:00 +0800

A Score First Needs a Convention

At 19:40 on Thursday, after the calibration page, Gu Ning wrote down the scoring question. Tang Ke wanted one short number that could compare reports of different degrees, instead of looking at each probability group separately. Gu Ning said a score can be adopted, but first the number's computation, and whether larger or smaller is better, must be made clear.

The previous chapter's calibration page checks probability groups and their corresponding frequencies. A score can instead give a number to each actual report and its outcome, then summarize over an explicit scope. The two have different uses; one average cannot replace the diagnosis of every condition.

This chapter continues the fictional Chengwan. At 19:40 there is no new reply from the commissioning party, no complete confirmation, and no final probability adoption; R17 still has no numerical forecast paired with an outcome that can be formally scored. The scoring computations use the already-specified independent examples and are not padded into mainline results.

Chapter 22: How Adverse Material Makes Judgment Contract

Sun, 13 Sep 2026 00:00:00 +0800

The New Message Does Not Settle the Original Window

At 20:20 on Thursday, Tang Ke received a new reply from the commissioning party on the agreed channel: "The reception time still cannot be fixed for this one." She handed the original message to Gu Ning, preserving the times of receipt and of delivery. The message concerns R17's current reception period; it is not the station's own scheduling note.

Gu Ning said this material must enter the record. The morning's original reply already said the time would need checking; now the other side states plainly that it still cannot be determined. It has not accepted all the conditions of the first version, nor has it said that confirmation before 17:00 on Friday is impossible.

Chapter 23: How a Provisional Adoption Is Expressed

Sun, 13 Sep 2026 00:00:00 +0800

Judgment Cannot Remain on the Candidate Page Forever

At 21:00 on Thursday, Gu Ning began writing R17's adoption statement. During the day she had already clarified the object, organized the material, checked the candidate computation, and saved a new reply stating that the reception time still could not be determined. Now she must decide whether to form a current judgment that can be handed over.

Tang Ke said, since the gaps are still many, must we simply continue without reporting a number? Gu Ning said one may continue to report nothing, or one may adopt a rough value under disclosed assumptions. Both choices require explanation; reporting a number does not make the gaps disappear, and leaving the value unadopted does not make the probability zero.

Chapter 24: Reopening and Handover

Sun, 13 Sep 2026 00:00:00 +0800

New Material Does Not Follow the Original Point Value

At 16:20 on Friday, Tang Ke received a new reply from the commissioning party on the agreed channel: "The first version's reception slot cannot be used; please move the discussion to next week." She saved the original message and handed it to Gu Ning. The "first version" here clearly refers to the task conditions R17 had previously saved; the message does not fully accept the original reception period.

This chapter continues the fictional Chengwan and explicitly adds mainline material. The 0.5 issued at 21:20 on Thursday remains the forecast of its time; Friday's reply is not a basis of the original forecast, and it does not let Gu Ning know the original window's final adjudication in advance.

Chapter 3: Where Samples Enter From

Sun, 13 Sep 2026 00:00:00 +0800

Eight Cards That Look Very Confident

Having saved the event and time notes for R17, Gu Ning watched Tang Ke take eight display cards from the cabinet. Each had photographs of tables and chairs before and after repair, a task name, and a completion note. She said these commissions had all been finished, and now the other party was asking in a lot of detail, so Gu Ning could use them for reference.

These eight cards and the numbers below are settings newly added to the Chengwan thought experiment in this chapter, not real business statistics. Gu Ning is still at the Thursday-morning stage of organizing information, and R17 has not received complete confirmation. The appearance of historical material does not preemptively generate an outcome for the current request.

Chapter 4: What Comparison Class Does a Base Rate Need?

Sun, 13 Sep 2026 00:00:00 +0800

Which Ratio Answers the Original Question?

Gu Ning now has before her sixteen historical registrations, eight completion display cards, twelve requests with locatable original material, and four requests whose raw material is temporarily missing. Tang Ke says at least half were finished. Ye Cheng says three-quarters of the material has been found. Each statement can be accurate on its own, yet neither answers whether R17 will receive full confirmation within the specified window.

This chapter continues with the fictional Chengwan and does not treat these quantities as real statistics. Chapter 3 established the source range; this chapter further examines historical versions and windows and adds outcome counts. What we want is not a number guaranteeing the current commission's success, but a starting point with a clearly stated comparative use.