My error or program error?

I'm having trouble (in Matlab) with the following problem:

there are 6 racers in a race. In vectors t1-t6 are previous times for each of the 6 racers (in this case, there are only 3 previous times for each of the racers).

t1=[30.01; 30.42; 30.68], t2=[30.00; 30.31; 30.55], t3=[29.98; 30.54; 30.32], t4=[28.89; 31.15; 30.44], t5=[29.66; 30.08; 31.25], t6=[28.72; 29.96; 31.18]

I want to calculate the probability of each racer to win the race. For example, if first racer wins, he has to do it with either his first time (probability 1/3), second or third with the condition that all other racers have bigger times than him. This group of commands should do that.

p=[0 0 0 0 0 0];
for i=min(t1):0.01:max(t1)
    p(1)=p(1)+ sum((t1==i))/numel(t1) * sum((t2>i))/numel(t2)* sum((t3>i))/numel(t3)* sum((t4>i))/numel(t4)* sum((t5>i))/numel(t5)* sum((t6>i))/numel(t6);
end

for i=min(t2):0.01:max(t2)
    p(2)=p(2)+ sum((t2==i))/numel(t2) * sum((t1>i))/numel(t1)* sum((t3>i))/numel(t3)* sum((t4>i))/numel(t4)* sum((t5>i))/numel(t5)* sum((t6>i))/numel(t6);
end

for i=min(t3):0.01:max(t3)
    p(3)=p(3)+ sum((t3==i))/numel(t3) * sum((t2>i))/numel(t2)* sum((t1>i))/numel(t1)* sum((t4>i))/numel(t4)* sum((t5>i))/numel(t5)* sum((t6>i))/numel(t6);
end

for i=min(t4):0.01:max(t4)
    p(4)=p(4)+ sum((t4==i))/numel(t4) * sum((t2>i))/numel(t2)* sum((t3>i))/numel(t3)* sum((t1>i))/numel(t1)* sum((t5>i))/numel(t5)* sum((t6>i))/numel(t6);
end

for i=min(t5):0.01:max(t5)
    p(5)=p(5)+ sum((t5==i))/numel(t5) * sum((t2>i))/numel(t2)* sum((t3>i))/numel(t3)* sum((t4>i))/numel(t4)* sum((t1>i))/numel(t1)* sum((t6>i))/numel(t6);
end

for i=min(t6):0.01:max(t6)
    p(6)=p(6)+ sum((t6==i))/numel(t6) * sum((t2>i))/numel(t2)* sum((t3>i))/numel(t3)* sum((t4>i))/numel(t4)* sum((t5>i))/numel(t5)* sum((t1>i))/numel(t1);
end

what i get is

 p =

    0.0247    0.0439    0.0562    0.2236    0.1481    0.3333

i've done the calculation manually and probability for fifth racer to win should be 0.1701 and sixth 0.4815. what i don't get is why the probabilities for the first four racers are correct, but the probability for 5th and 6th aren't? The logic is the same for all the racers. Can someone please explain what's wrong?

Answer 1

[Walter Roberson]

Equality comparisons in floating point seldom work.

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

Answer 2

[Doctor Evil]

Thanks! So, to compare equality between a and b I just have to do something like this:

if abs(a-b)<=0.00001 % or something really small, then they're equal

And if I want to see if a is greater than b:

if abs(a-b)>=0.00001  % meaning they're not equal
     if a>b % then a really is bigger
     else % it's not bigger
else % they're equal

Would this work?

[Walter Roberson]

That should work.