﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.00,0:00:04.00,Default,,0000,0000,0000,,Now, since it seems complicated to solve this game in this form, Dialogue: 0,0:00:04.00,0:00:08.00,Default,,0000,0000,0000,,one way we can address it is to change from this matrix form Dialogue: 0,0:00:08.00,0:00:11.00,Default,,0000,0000,0000,,into the familiar tree form. Dialogue: 0,0:00:11.00,0:00:13.00,Default,,0000,0000,0000,,We'll move this over here, Dialogue: 0,0:00:13.00,0:00:15.00,Default,,0000,0000,0000,,and we'll draw it as a game tree. Dialogue: 0,0:00:15.00,0:00:20.00,Default,,0000,0000,0000,,Max will be the even player, and min will be the odd player, Dialogue: 0,0:00:20.00,0:00:25.00,Default,,0000,0000,0000,,and for the moment, let's look at the game Dialogue: 0,0:00:25.00,0:00:28.00,Default,,0000,0000,0000,,of what would happen if max had to go first Dialogue: 0,0:00:28.00,0:00:31.00,Default,,0000,0000,0000,,rather than having them move simultaneously. Dialogue: 0,0:00:31.00,0:00:36.00,Default,,0000,0000,0000,,So, max would make a move either 1 or 2. Dialogue: 0,0:00:36.00,0:00:41.00,Default,,0000,0000,0000,,And then min--so max is even and min is O-- Dialogue: 0,0:00:41.00,0:00:46.00,Default,,0000,0000,0000,,would also make the move, 1 or 2, 1 or 2. Dialogue: 0,0:00:46.00,0:00:50.00,Default,,0000,0000,0000,,And then the outcome in terms of E would be 2 here Dialogue: 0,0:00:50.00,0:00:54.00,Default,,0000,0000,0000,,-3 here, -3 here and 4 here. Dialogue: 0,0:00:54.00,0:00:57.00,Default,,0000,0000,0000,,And now what does min do? Well, try to minimize. Dialogue: 0,0:00:57.00,0:01:01.00,Default,,0000,0000,0000,,So, we choose 2 here, so this node would be -3. Dialogue: 0,0:01:01.00,0:01:06.00,Default,,0000,0000,0000,,We'd choose 1 here, so this node would be -3, Dialogue: 0,0:01:06.00,0:01:08.00,Default,,0000,0000,0000,,and then E tries to maximize. Dialogue: 0,0:01:08.00,0:01:11.00,Default,,0000,0000,0000,,It doesn't matter what he chooses, Dialogue: 0,0:01:11.00,0:01:14.00,Default,,0000,0000,0000,,and we get a -3 up here. Dialogue: 0,0:01:14.00,0:01:17.00,Default,,0000,0000,0000,,So, that's giving E the disadvantage of having to reveal Dialogue: 0,0:01:17.00,0:01:21.00,Default,,0000,0000,0000,,his or her strategy first. Dialogue: 0,0:01:21.00,0:01:23.00,Default,,0000,0000,0000,,What if we did it the other way around? Dialogue: 0,0:01:23.00,0:01:25.00,Default,,0000,0000,0000,,Let's take a look at that. Dialogue: 0,0:01:25.00,0:01:29.00,Default,,0000,0000,0000,,What if O had to go first and reveal a strategy of 1 or 2 Dialogue: 0,0:01:29.00,0:01:35.00,Default,,0000,0000,0000,,and then E as the maximizing player goes second Dialogue: 0,0:01:35.00,0:01:37.00,Default,,0000,0000,0000,,and does a 1 or 2? Dialogue: 0,0:01:37.00,0:01:41.00,Default,,0000,0000,0000,,And then we have these 4 terminal states here, Dialogue: 0,0:01:41.00,0:01:45.00,Default,,0000,0000,0000,,and I want you to fill in the values of the 4 terminal states Dialogue: 0,0:01:45.00,0:01:49.00,Default,,0000,0000,0000,,taken from the table and the intermediate states Dialogue: 0,0:01:49.00,9:59:59.99,Default,,0000,0000,0000,,or the higher up states in the tree as well.