## 8 Numerical Examples  
We conducted experimental computations in which we modeled the information extraction process for two AI chatbots with different characteristics; we varied the number of rounds of the algorithm, the scanning time, and the overlook probabilities, includingvery large and very small ones. The computations consistently confirmed our judgement that the considered paradoxical phenomenon exists and is easily reproduced. In this section, we considered numerical examples for two chatbots with six locations, randomly selected from our experiments. The examples convincingly confirmed the existence of the paradox. The input data are presented in Table 2. The notations are introduced in Section 3 as follows:  
* \(p_{i}\) is a known probability that location \(i\) contains the information we are looking for; \(i=1,\ldots,6\);
* \(t_{i}\) is the time (in minutes) spent by a human user in conversation with the chatbot to evaluate the chatbot's answer about the scan of location \(i\); at each round, the time is assumed to remain the same;
* \(a_{i}\) is a non-zero operlook probability;
* \(r_{i}\) is a known Likert-scale satisfaction level obtained by the human user when the target information is found at location \(i\) (at any round) before discounting; recall that the level of satisfaction that a human user receives for a correct answer from the chatbot is measured on the 10-point Likert scale. This is the IBM SPSS rating system, in which the highest score of 10 signifies \"very satisfied\" on a 10-point scale ranging from 1 to 10, while the lowest score of 1 means \"very dissatisfied\" [4];
* \(\pi=(\pi_{1},\pi_{2},\ldots,\pi_{k})\) is a finite sequence of conversation stages (rounds);
* \(\pi_{k}\) is the number of a location (a database) scanned at the \(k\)th round of the sequence \(\pi\), \(\pi_{k}\)\(A=\{1,\ldots,6\}\), \(k=1,2,\ldots\);
* \(n\) is the _a priori_ unknown round of the sequence \(\pi\) at which the chatbot successfully extracts the targeted information;
* \(T_{\pi,n}=\sum_{i=1}^{n}t_{\pi_{i}}\) is the total time spent by a human user in conversation with the chatbot from round 1 to round \(n\) in sequence \(\pi\);
* If the search for the target information required \(T_{\pi,n}\) time units in \(\pi\), the level of satisfaction in round \(\pi_{n}\) was discounted by \(e^{-dT_{\pi,n}}\), for a known discount factor \(d\), \(d\in(0,1)\), i.e., the discounted level of satisfaction was computed as follows: \(R_{discount}(\pi)\)\(=r_{\pi_{n}}e^{-dT_{\pi,n}}=r_{\pi_{n}}e^{-d\sum_{i=1}^{n}t_{\pi_{i}}}\). The numerical parameters of the times and probabilities were randomly selected. These and numerous other examples stored in our dataset confirmed our theoretical judgements. Calculations of the proposed iterative algorithm are presented in Tables 2 and 3 for chatbots 1 and 2, respectively, for 12 consecutive rounds. The table columns correspond to the six locations considered; the rows represent rounds of the search example considered. The elements in the cells are the coefficients \(Q_{i,j}\) calculated for 12 rounds, row by row. The number in the cell (\(i\),\(j\)) of these tables represents the parameter \(Q_{i,j}\), calculated by Formula (4), where \(i=1,\ldots,12\); \(j=1,\ldots,6\) for two chatbots. The tables represent the matrices \(M_{k}\) for two chatbots, introduced in Section 5.2. The calculations in Table 3 for \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Round**Location** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \(p_{i}\) & 0.1 & 0.05 & 0.15 & 0.2 & 0.3 & 0.2 \\ \hline \(t_{i}\) (Min.) & 3 & 2 & 4 & 1 & 3 & 5 \\ \hline \(r_{i}\) & 5 & 10 & 4 & 7 & 2 & 10 \\ \hline \(a_{i}^{(1)}\) & 0.2 & 0.05 & 0.2 & 0.04 & 0.1 & 0.3 \\ \hline \(a_{i}^{(2)}\) & 0.3 & 0.1 & 0,4 & 0.1 & 0.2 & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input data, for example, \(d=0.1\). chatbot 1 can be observed; similar calculations were performed in Table 4 for chatbot 2.