Archive > The Amazing Race 22
TAR 22 Speculation and Discussion **of Spoilers**
apskip:
--- Quote from: MrDeerShank on February 18, 2013, 09:17:33 AM ---
--- Quote from: apskip on February 18, 2013, 08:31:55 AM ---
--- Quote from: RachelLeVega on February 17, 2013, 08:23:45 PM ---
--- Quote from: Jimmer25 on February 17, 2013, 08:18:48 PM ---I'm just going to express again that I hate luck tasks, especially with Bates and Anthony checking in 2nd after like searching 2 sandcastles. I don't blame the task for Matt and Daniel's elimination, since they were too arrogant with the boat task.
I'm shocked they all took the penalty. If I was racing, I would have not agreed to take the penalty hoping that I have kept good track at which sandcastles I knocked down, but then again, I wasn't out there for 3 hours either.
--- End quote ---
Ain't nobody got time for a 4-hour penalty when almost half of the sandcastles are already knocked down. Even if you didn't take the penalty, it will still take less time to knock down and rebuild them. Forget the pact, I'm worrying about myself.
--- End quote ---
Let's look at the mathematics of this. There are 400 sandcastles at the start and 10 clues; the first team has a 2.5% chance each try. It appeared to be slow going and I thought the average time per sandcastle was running at about 3 minutes. That means it would take on average 1 hour of attempts to find a clue. For each succeeding team, the odds went down until for the final 3 teams there are 3 sandcastles left, for a probability of 0.75% for each try. That means is would take 3.3 hours for them to find a clue. They appeared to have gone beyond that, so the statistics of the situation (which had worked for all prior teams) did not appear to be working out for the last 3 teams. Their election of taking the 4 hour penalty together meant that one team would almost certainly be eliminated and the other two would be fighting against elimination at the end of leg 2.
--- End quote ---
Wasn't there 11 clues at the start? ??? If there were only 10 clues, somebody was guaranteed not to get one and thus forced to take a penalty. Going with that new addition, the first team had a 2.75% chance of getting the clue at each sandcastle. Going with the assumption that each sandcastle would take on average 3 minutes to knock down and rebuild, there would be a 55% chance that a team would get it within the first hour of searching. Obviously this will decrease as teams find clues, but at the same time, I think from watching it, no teams rebuilt the last sandcastle they knocked over (the one with the clue), so going with that assumption...
10 teams: 50.12% chance within one hour
9 teams: 45.22% chance within one hour
8 teams: 40.3% chance within one hour
7 teams: 35.35% chance within one hour
6 teams: 30.38% chance within one hour
5 teams: 25.38% chance within one hour
4 teams: 20.36% chance within one hour
3 teams: 15.31% chance within one hour
This is based also on another assumption that the teams are doing it independently of one another (very poor statistical assumption but is basic enough to see the effects of finding the clues are). Thus, if Katie, Jennifer and Daniel had continued with the Roadblock, they would have taken about 6 and a half hours to complete (with all the assumptions used)! :ascared
However, going with the assumption that the Roadblockers DID rebuild the last sandcastle, the effects of chance change significantly:
10 teams: 50% chance within one hour
9 teams: 45% chance within one hour
8 teams: 40% chance within one hour
7 teams: 35% chance within one hour
6 teams: 30% chance within one hour
5 teams: 25% chance within one hour
4 teams: 20% chance within one hour
3 teams: 15% chance within one hour
Although insignificant in some respect, if the last sandcastle was to be built back up again, the chances of find the sandcastle would be reduced. Once again, these calculations are done with the assumption that all the teams performances are independent of each other. Thus, the time taken for the three teams to find a clue at 3 teams left would be slightly greater at 6 hours 40 minutes.
However, these models are really simplistic, ignoring a number of factors including:
* How quickly teams are constructing the sandcastles
* Fatigue
* How many sandcastles teams know have been searched
* Teams potentially "missing" the clue (remember how Dave said he might have missed a clue for not digging deep enough?)
* How many sandcastles other teams deconstruct before finding a clue
There are other factors but I think these could be considered as the most important. At the end of the day, looking over the calculations here would suggest that taking the penalty would have been a good decision, however, incorporating the factors affecting how long the teams take, it may not have been such a wise decision after all. I guess time will tell...
--- End quote ---
Mr. Deer Shank,
I discovered my error about 11 initial clues vs. the 10 I erroneously used (and am correcting it). Your mathematics are not significantly different than mine. Your point about the several other factors that influenced the actual situation are all valid. However, we have no knowledge of the specific impact of each one or even the aggregate of them. So we are left with just the mathematics, which does tell us some very interesting things about why it was taking the last 3 teams so long.
BuuYaa:
--- Quote from: apskip on February 18, 2013, 08:31:55 AM ---
--- Quote from: RachelLeVega on February 17, 2013, 08:23:45 PM ---
--- Quote from: Jimmer25 on February 17, 2013, 08:18:48 PM ---I'm just going to express again that I hate luck tasks, especially with Bates and Anthony checking in 2nd after like searching 2 sandcastles. I don't blame the task for Matt and Daniel's elimination, since they were too arrogant with the boat task.
I'm shocked they all took the penalty. If I was racing, I would have not agreed to take the penalty hoping that I have kept good track at which sandcastles I knocked down, but then again, I wasn't out there for 3 hours either.
--- End quote ---
Ain't nobody got time for a 4-hour penalty when almost half of the sandcastles are already knocked down. Even if you didn't take the penalty, it will still take less time to knock down and rebuild them. Forget the pact, I'm worrying about myself.
--- End quote ---
Let's look at the mathematics of this. There are 400 sandcastles at the start and 10 clues; the first team has a 2.5% chance each try. It appeared to be slow going and I thought the average time per sandcastle was running at about 3 minutes. That means it would take on average 1 hour of attempts to find a clue. For each succeeding team, the odds went down until for the final 3 teams there are 3 sandcastles left, for a probability of 0.75% for each try. That means is would take 3.3 hours for them to find a clue. They appeared to have gone beyond that, so the statistics of the situation (which had worked for all prior teams) did not appear to be working out for the last 3 teams. Their election of taking the 4 hour penalty together meant that one team would almost certainly be eliminated and the other two would be fighting against elimination at the end of leg 2.
--- End quote ---
I also think it was smart of them to take the penalty. I meant they could just stay there and depended on their luck but were you really gonna do that after 4 hours of digging, searching, building, repeating, in almost 100 degrees. It was still leg 1 and you knew you have 11 legs coming and had to stay fit.
I think what's interesting in this RB is that they're gonna have to re-build the Sandcastles. Back in Tar 6 and Tar 15, in the hay RB, they didn't have to roll the hay back, they just roll it open and search, and if no clue in it, repeat. So teams coming behind were spared some works and had the chance to catch up. or in Tar 18 in the tea-tasting RB, once you drank a cup,if wrong, that cup would not be re-filled again.
this RB, either they arrived first or last, they all started from zero. of course teams arriving behind may notice which sandcastle had been torn down and which hadn't, but i think it was still hard to differ, especially with 100 degrees up on your head. almost everything depended on their luck.
It was fair actually but I did pity the racers. Why would they just put 11 clues instead of like 20? The more clue found, the more miserable teams became.
BuuYaa:
--- Quote from: Leafsfan on February 18, 2013, 10:39:52 AM ---I wonder why Matt and Dnaiel did not go back and finish the roadblock. If I remember correctly teams that quit the meat roadblock went back and finished it (Susan and Patrick).
--- End quote ---
I think because they already declared to take the penalty.
Once you took it, it will be assessed no matter what
Susan&Patrick never really declared to take the penalty.
They were second to last and they still needed to wait for Debbie&Bianca to start the RB before the penalty time was started to count
So it would be best for Patrick to attempt the RB so they remained ahead of Debbie&Bianca.
Kamineko:
--- Quote from: BuuYaa on February 18, 2013, 10:46:45 AM ---I think what's interesting in this RB is that they're gonna have to re-build the Sandcastles. Back in Tar 6 and Tar 15, in the hay RB, they didn't have to roll the hay back, they just roll it open and search, and if no clue in it, repeat. So teams coming behind were spared some works and had the chance to catch up. or in Tar 18 in the tea-tasting RB, once you drank a cup,if wrong, that cup would not be re-filled again.
--- End quote ---
Umm.. I think it's TOO CRUEL to be implemented... Actually, making one hay bale (from a source I read) takes more than 1 day in order to dry the hay. Also, I think that they used tractor to make it, not by bare hands... :res:
BuuYaa:
--- Quote from: Kamineko on February 18, 2013, 10:58:50 AM ---
--- Quote from: BuuYaa on February 18, 2013, 10:46:45 AM ---I think what's interesting in this RB is that they're gonna have to re-build the Sandcastles. Back in Tar 6 and Tar 15, in the hay RB, they didn't have to roll the hay back, they just roll it open and search, and if no clue in it, repeat. So teams coming behind were spared some works and had the chance to catch up. or in Tar 18 in the tea-tasting RB, once you drank a cup,if wrong, that cup would not be re-filled again.
--- End quote ---
Umm.. I think it's TOO CRUEL to be implemented... Actually, making one hay bale (from a source I read) takes more than 1 day in order to dry the hay. Also, I think that they used tractor to make it, not by bare hands... :res:
--- End quote ---
aw lol sorry then I guess I had no idea. but still, the hay bale RB spared some works on teams arriving behind. in the sandcastle RB, you need to have keen eyes to differ which has been torn down and which hasn't. the amount of hay bales in tar 6 was only 200 something, and in tar 15 was 100 something. amount of clues hidden inside were more than the amount of remaining teams.
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