update FAQ

faq.md

@@ -36,7 +36,7 @@ For instance, if the game has pt setting $w$ and the players' scores are $[29000
 | West | 27200 | 24.857 | 29.048 | 31.777 | 14.317 |
 | North | 29600 | 37.990 | 28.533 | 23.800 | 9.677 |
 
-Note that these probabilities are esitmates of the **final** rankings at the end of the whole *game*, not after the current *kyoku*.
+Note that these probabilities are estimates of the **final** rankings at the end of the whole *game*, not after the current *kyoku*.
 
 To get the $\Phi_k$​ value for the player sitting in the East seat at South 1, we multiply the probabilities with the pt setting, specifically $[0.29532, 0.32512, 0.27416, 0.10539] \cdot w$.
 It's important to note that Mortal models do not guarantee to use a fixed pt setting throughout its training.
@@ -52,7 +52,13 @@ $\pi_\tau(a|s)$, in simple terms, can be thought of something similar to the hei
 $$\pi_\tau(a|s) = \frac{\exp(\hat Q^\pi(s, a) / \tau)}{\sum_i \exp(\hat Q^\pi(s, a_i) / \tau)}$$
 where $\tau$ is temperature.
 
-Wrapping up, $\hat Q^\pi(s, a)$ is only for advanced users, because it can be very misleading if the user does not understand the subtle details of how Mortal works under the hood. I have been considering whether to just remove the column or not, but in the end I decided to keep it as is. <ins>Just look up $\pi_\tau(a|s)$ as it is easier to understand.</ins>
+Wrapping up, $\hat Q^\pi(s, a)$ is only for advanced users, because it can be very misleading if the user does not understand the subtle details of how Mortal works under the hood. To make it clear:
+
+- $\hat Q^\pi(s, a)$ is not 局収支 (round EV).
+- $\hat Q^\pi(s, a)$ is not pt.
+- $\hat Q^\pi(s, a)$ is not 清算ポイント (end game score).
+
+I have been considering whether to just remove the column or not, but in the end I decided to keep it as is. <ins>Just look up $\pi_\tau(a|s)$ as it is easier to understand.</ins>
 
 ## (Mortal) Why do all actions except the best sometimes have significantly lower Q values than that of the best?
 As mentioned above, $\hat Q^\pi(s, a) + \Phi_k$ is an estimation to the pt EV. However, the evaluation for this value is <ins>the means but not the objective</ins>. To be clear, the real fundamental objective for Mortal as a mahjong AI is to achieve the best performance in a mahjong game, but not to calculate accurate scores for all actions. As a result, the evaluated values of all actions but the best may be inaccurate; they only serve as a means to determine its preference for exploration in training.
@@ -66,9 +72,9 @@ ELI5: <ins>Mortal is optimized for playing, not reviewing or attribution.</ins>
 Mortal is an end-to-end deep learning model that deploys model-free reinforcement learning, therefore we are unlikely to be able to do any significant attribution work on it. If you insist on wanting a reason for a decision made by Mortal, I would say that in contrast to how humans play, Mortal is not based on so-called "precise calculations", but rather just "intuition".
 
 ## (Mortal) The single-line output and the table are in conflict, is it a bug?
-![figure](res/agarasu.webp)
+![agarasu](res/agarasu.webp)
 
-This is an intentional feature, and in the case shown in the figure, it is a rule-based fail-safe strategy against アガラス (win-to-last-place) in the all-last round.
+Not really. This is an intentional feature, and in the case shown in the figure, it is a rule-based fail-safe strategy against アガラス (win-to-be-last-place) in the all-last round.
 
 The single-line output (starting with `Mortal:`) is the actual final decision made by the AI, while the expanded table provides additional, intermediate information that is totally optional and may be altered or even removed in a future version. When they are in conflict, <ins>the single-line output should take precedence.</ins> Furthermore, the table is just a by-product of the AI, and focusing too much on building it may hinder finding better ways to achieve its goal.