The Amazing Race > The Amazing Race Discussion
Some interesting (and some not so interesting) facts and records!
fossil-racer:
TAR 30
Final 3 placed in the top 3 on leg 1
Every team in the final 5 won one of the first 5 legs!
TAR 11 to TAR 15 had MF team win
TAR 16 MM team win
TAR 26 to TAR 30 had MF team win
Will and MM team win 31?
MrDS:
--- Quote from: violetb1911 on March 07, 2018, 02:10:50 PM --- --> The probability of you being a winner of a season and also winning the most legs is 2/5
--- End quote ---
This point intrigued me somewhat as a mathematician to work out (not quite) true probabilities for the likelihood of winning and winning the most legs, so let's actually break down the maths of this (for simplicity purpose, let us assume NELs on leg's 3, 6, and 9, and single eliminations otherwise. In addition, we shall assume every team is equally likely to win a given leg (in practice this is not the case, since there are naturally stronger/weaker teams, the presence of Fast Forwards, U-Turns etc.), and each leg is independent of the next (you can think of this as each leg travelled to a new country with an equaliser at the airport i.e. all teams on the same flight, or an Hours of Operation at the next destination)).
First, the probabilities that arise from this vary so let's take the two extreme examples; winning every leg (I) and winning 2 legs whilst every other team only wins 1 leg (II) (for the calculation we'll assume we win leg 1 as our other leg since this gives us the lowest probability).
For (I), the probability of you winning EVERY leg is Pmin = (1/11) * (1/10) * (1/9) * (1/9) * .... * (1/4) * (1/3) = 1/6286896000 (so, an extremely tiny chance, but possible!).
For (II), assuming that P(does not win a leg) = 1 - P(winning a leg) (and as before stating that we win Leg 1 and Leg 12, and NEL's are the same as above), our calculation becomes (1/11) * (9/10) * (8/9) * (8/9) * ... * (3/4) * (1/3) = 34836480/628689000, approximately equal to 0.005541126... (so again, very improbable, but can happen!). Note that I chose Leg 1 deliberately as this is the lowest probability for this scenario, the highest probability comes from winning the last two legs (why you might ask? Because we are effectively replacing a 3 for a 10, so the numerator becomes bigger hence a bigger probability). In this scenario, we actually end up with a probability of Pmax = 116121600/628689000, approximately equal to 0.018470418..., so the range of probabilities for our overall event is Pmin <= P(winning final leg and winning most legs) <= Pmax, given the set up of our scenario.
To further prove that Pmax is indeed the maximum we can get for our given set up, to get the numerator we multiplied 10 * 9 * 8 * 8 * 7 * 6 * 6 * 5 * 4 * 4 * 1 * 1 = 116121600. If we were to win another leg, we would have to change one of these numbers to a 1 (i.e. P(not winning leg 1) = 10/11 so P(winning leg 1) = 1/11, so the 10 in the calculation would be changed to a 1), giving us a value of 11612160 < 116121600. Any set up involving winning more than 2 legs will yield a strictly smaller numerator hence a lower probability.
If we wanted to be a little more sneaky with how we calculate "true" Pmin and Pmax, we would need to manipulate the scenarios slightly (and use separate scenarios for each one to manipulate the probability to be as small/big as possible). For Pmin, assuming NELs Legs 1-3 and we win every leg, the probability of this occurring is a staggeringly small 1/26564630400 (realistically it is 0 since when has there every been a race with 3 NELs in the first 3 legs of the race??).
Pmax however presents a new set of issues as the numerator will need to be big relative to the denominator (fortunately for Pmin the numerator was going to be 1 so all we had to do was make the denominator as big as possible). Initially my first thought was to have NELs Leg 1, 2, 3 and we win Leg 11 and Leg 12, but this actually was shown to have a smaller value than that calculated earlier! Unfortunately since it is now past 2am and my brain is knackered from doing more mathematics than I care to admit I may have another look at this problem another time.
violetb1911:
--- Quote from: MrDS on July 09, 2018, 08:22:48 PM ---
--- Quote from: violetb1911 on March 07, 2018, 02:10:50 PM --- --> The probability of you being a winner of a season and also winning the most legs is 2/5
--- End quote ---
This point intrigued me somewhat as a mathematician to work out (not quite) true probabilities for the ...
--- End quote ---
Oh no I was just going off empirical probability, based off previous race results. 2/5 clearly won't be your true probability of winning most legs + entire season.
NELs:
Not counting Family Edition, TAR 2 visits the most US states, (in order): Nevada, Hawaii, Alaska, and California.
Season 16 is the only season to have only one US state visited, the state is California.
San Francisco and New York City are tied with most finale visits: 4
TAR 30 is so far the only time Thailand is visited without visiting Bangkok.
Singapore is the only country to have both a Detour and a Roadblock on two separate legs. The Detour is in Leg 1, while the RB is Leg 13, The season is The Amazing Race Asia 2
Guyana, Suriname and French Guiana (France) are so far the only countries in South America to be visited.
Cuba is the most visited country that has been visited on International versions of the show that the US has not visited.
Kenya, Puerto Rico, Bosnia and Herzegovina, Liechtenstein, and Monaco and are the only five countries to not have Pit Stops.
Maanca:
--- Quote from: NELs on July 29, 2018, 11:59:53 PM ---Guyana, Suriname and French Guiana (France) are so far the only countries in South America to be visited.
--- End quote ---
Well, Venezuela. But they'll never go there, it's much too dangerous. I actually know nothing about those other 3.
Navigation
[0] Message Index
[#] Next page
[*] Previous page
Go to full version