Update README.md

1 files changed, 23 insertions, 11 deletions

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@@ -12,16 +12,28 @@ int D = 0, R = 0, B1 = 0, B2 = 0; // Initial power-up status
 ```
 
 Change these values to alter the initial state:
-* **start** - Starting amount of money
-* **goal** - Ending amount of money
-* **max_it** - The maximum number of iterations to solve
-* **MPQ** - The initial level of the money per question upgrade (Starts from 0)
-* **SB** - The initial level of the streak bonus upgrade (Starts from 0)
-* **M** - The initial level of the multiplier upgrade (Starts from 0)
-* **D** - The status of the discounter power-up (0 is unpurchased, 1 is purchased and used)
-* **R** - The status of the rebooter power-up (0 is unpurchased, 1 is purchased and used)
-* **B1** - The status of the mini bonus power-up (0 is unpurchased, 1 is purchased and unused, 2 is used)
-* **B2** - The status of the mega bonus power-up (0 is unpurchased, 1 is purchased and unused, 2 is used)
+- **start** - Starting amount of money
+- **goal** - Ending amount of money
+- **max_it** - The maximum number of iterations to solve
+- **MPQ** - The initial level of the money per question upgrade (Starts from 0)
+- **SB** - The initial level of the streak bonus upgrade (Starts from 0)
+- **M** - The initial level of the multiplier upgrade (Starts from 0)
+- **D** - The status of the discounter power-up (0 is unpurchased, 1 is purchased and used)
+- **R** - The status of the rebooter power-up (0 is unpurchased, 1 is purchased and used)
+- **B1** - The status of the mini bonus power-up (0 is unpurchased, 1 is purchased and unused, 2 is used)
+- **B2** - The status of the mega bonus power-up (0 is unpurchased, 1 is purchased and unused, 2 is used)
 
 ## How it works
-*Coming soon*
+Without considering player interactions, the *state* of a Gimkit game can actually be represented with only eight parameters: money, the levels of the money per question, streak bonus, and multiplier updates, and the status of four power-ups. For any such state, we want to minimize the number of questions ("iterations") needed to reach that state. However, money can range over a large range of values, so instead, we will swap money and the number of questions answered. Realistically, a player will only answer at most 200 questions, so this will reduce the total number of states. Note that a state only contains information about the current status in the game, not the particular path used to reach that state.
+
+State parameters
+- **it** - The number of questions answered
+- **MPQ** - The level of the money per question upgrade (Starts from 0)
+- **SB** - The level of the streak bonus upgrade (Starts from 0)
+- **M** - The level of the multiplier upgrade (Starts from 0)
+- **D** - The status of the discounter power-up (0 is unpurchased, 1 is purchased and used)
+- **R** - The status of the rebooter power-up (0 is unpurchased, 1 is purchased and used)
+- **B1** - The status of the mini bonus power-up (0 is unpurchased, 1 is purchased and unused, 2 is used)
+- **B2** - The status of the mega bonus power-up (0 is unpurchased, 1 is purchased and unused, 2 is used)
+
+Now that we have our state, we must determine the state *transitions*. Some transitions include answering a question, using a power-up, or buying an upgrade. These transitions allow us to go from one state to another. For example, consider the transition of answering a question. The new state's iteration will be one larger, while everything else stays the same. Starting from the initial state, the algorithm traverses transitions in an attempt to reach a state with money greater than the goal.