WEBVTT 00:00:00.000 --> 00:00:04.000 Now, since it seems complicated to solve this game in this form, 00:00:04.000 --> 00:00:08.000 one way we can address it is to change from this matrix form 00:00:08.000 --> 00:00:11.000 into the familiar tree form. 00:00:11.000 --> 00:00:13.000 We'll move this over here, 00:00:13.000 --> 00:00:15.000 and we'll draw it as a game tree. 00:00:15.000 --> 00:00:20.000 Max will be the even player, and min will be the odd player, 00:00:20.000 --> 00:00:25.000 and for the moment, let's look at the game 00:00:25.000 --> 00:00:28.000 of what would happen if max had to go first 00:00:28.000 --> 00:00:31.000 rather than having them move simultaneously. 00:00:31.000 --> 00:00:36.000 So, max would make a move either 1 or 2. 00:00:36.000 --> 00:00:41.000 And then min--so max is even and min is O-- 00:00:41.000 --> 00:00:46.000 would also make the move, 1 or 2, 1 or 2. 00:00:46.000 --> 00:00:50.000 And then the outcome in terms of E would be 2 here 00:00:50.000 --> 00:00:54.000 -3 here, -3 here and 4 here. 00:00:54.000 --> 00:00:57.000 And now what does min do? Well, try to minimize. 00:00:57.000 --> 00:01:01.000 So, we choose 2 here, so this node would be -3. 00:01:01.000 --> 00:01:06.000 We'd choose 1 here, so this node would be -3, 00:01:06.000 --> 00:01:08.000 and then E tries to maximize. 00:01:08.000 --> 00:01:11.000 It doesn't matter what he chooses, 00:01:11.000 --> 00:01:14.000 and we get a -3 up here. 00:01:14.000 --> 00:01:17.000 So, that's giving E the disadvantage of having to reveal 00:01:17.000 --> 00:01:21.000 his or her strategy first. 00:01:21.000 --> 00:01:23.000 What if we did it the other way around? 00:01:23.000 --> 00:01:25.000 Let's take a look at that. 00:01:25.000 --> 00:01:29.000 What if O had to go first and reveal a strategy of 1 or 2 00:01:29.000 --> 00:01:35.000 and then E as the maximizing player goes second 00:01:35.000 --> 00:01:37.000 and does a 1 or 2? 00:01:37.000 --> 00:01:41.000 And then we have these 4 terminal states here, 00:01:41.000 --> 00:01:45.000 and I want you to fill in the values of the 4 terminal states 00:01:45.000 --> 00:01:49.000 taken from the table and the intermediate states 00:01:49.000 --> 99:59:59.999 or the higher up states in the tree as well.