TUWEL quiz optimisation

This R markdown file aims to evaluate the way guessing answers affects the total score in a TUWEL quiz.

Assumptions:

• each statement (not counting the "none of the above" box as a statement) has a 50% chance of being true and a 50% chance of being false, independently of any other statement. This assumption might be only approximative if the total number of true and false statements in a quiz is intentionally made to be roughly equal.
• the score for a batch can't be negative, so negative scores are changed to 0.
• the order of statements in a batch is random.
• with NOTA box format: each batch of questions has four statements, and five boxes, where four boxes correspond to the statements and the last box is "none of the above".
• without NOTA box format: each batch of questions has four statements, and four boxes, where each box corresponds to a statement.

Results:

With a None Of The Above box:

• if you know that one statement is true, and you don't know about the 3 others, you will get the highest score expectancy by guessing 1 or 2 remaining statements to be true.
• if you know that at least 2 statements are true, you will get the highest score expectancy by guessing all remaining statements to be false.
• in all other cases, you will get the highest score expectancy by guessing all remaining statements to be true.

Without a None Of The Above box:

• in general, try to balance out the true and false answers among the four statements. See table below for detailed strategy.

Cheat sheet:

With a None Of The Above box:

What you already answered	Best guess
0T,0F	TTTT
0T,1F	TTT
0T,2F	TT
0T,3F	T or F
1T,0F	TTF or TFF
1T,1F	TT
1T,2F	T
2T,0F	FF
2T,1F	T or F
3T,0F	F

Without a None Of The Above box:

What you already answered	Best guess
0T,0F	TTTF
0T,1F	TTT
0T,2F	TT
0T,3F	T
1T,0F	FFF
1T,1F	any
1T,2F	T
2T,0F	FF
2T,1F	F
3T,0F	F