Probably somebody have done this before but I have counted probabilities of making score worse by pure guessing (all expectations are evidently zero).

It seems that it's strongly recommended to guess on =4(mod 5) questions.

It's better to guess on =0(mod 5) questions but there is a huge probability of not changing the score at all.

Number of questions to be guessed Probability of worsening of the score

1 0.800

2 0.640

3 0.512

4 0.410

5 0.328

6 0.655

7 0.577

8 0.503

9 0.436

10 0.376

11 0.617

12 0.558

13 0.502

14 0.448

15 0.398

16 0.598

17 0.549

18 0.501

19 0.455

20 0.411

21 0.586

22 0.543

23 0.501

24 0.460

25 0.421

26 0.577

27 0.539

28 0.501

29 0.463

30 0.428

31 0.571

32 0.535

33 0.500

34 0.466

35 0.433

36 0.566

37 0.533

38 0.500

39 0.468

40 0.437

## Pure guessing

### Re: Pure guessing

The key here is that the expected value is 0 for any guess. It is true that the majority of "=4(mod 5) guesses" will have a positive outcome. Yet, the magnitude of the negative guesses is on average higher. So, it is unwise to recommend guessing, (unless you consider something like Score Select, or you otherwise do not have a risk averse utility function.).Jenn wrote:Probably somebody have done this before but I have counted probabilities of making score worse by pure guessing (all expectations are evidently zero).

It seems that it's strongly recommended to guess on =4(mod 5) questions.