Skill focus probabilities

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====== Skill focus probabilities ======

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There are four choices of skill focus. Below you can find the expected value of each choice. //Expected Value// is the average roll you will get when rolling a skill check. Skill focuses improve your skill rolls, increasing the average roll. The expected value of a Skill Focus can be thought of as the average value it will add to your skill checks

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**Clutch**\\
//Once per day when making a check with this skill, you may upgrade a “5” to a “6”, increasing the result by one point//

The expected value of this skill focus is 1


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**Grit**\\
//Whenever you make a check with this skill, you may reroll any dice that comes up as a “1”//

The value of this skill focus increases with each additional dice that you can potentially reroll

^Dice Rolled^Expected Value of Rerolling 1's^
|4d6	|0.11|
|5d6	|0.14|
|6d6	|0.17|
|7d6	|0.19|
|8d6	|0.22|
|9d6	|0.25|
|10d6	|0.28|
|11d6	|0.31|
|12d6	|0.33|
|13d6	|0.36|
|14d6	|0.39|
|15d6	|0.42|
|16d6	|0.44|
|17d6	|0.47|
|18d6	|0.50|


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**Jack of all Trades**\\
//You have 4d6 which you may assign to any skill check. You must assign the dice to the check before the check is rolled. You may assign the dice on separate checks or on a single check, in whatever configuration you wish. At the beginning of each day, any dice you have spent are replenished. You may only take this skill focus once//

The expected value of adding a single dice varies slightly but it is about 0.17

Jack of all trades can synergize with Grit, increasing the expected value

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**Resourceful**\\
//You may ignore disadvantage on all checks made for this skill. Additionally, once per day you may make a check with this skill at advantage. You may choose to roll at advantage after the results of a check are known//

The expected value of gaining advantage is 0.5, or half a point. Preventing disadvantage avoids a penalty but can also be thought of as a value of 0.5
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