Statistical analysis of POV outcome

The only problem with his analysis is that he assumes that every player has an equal chance of winning. This is bogus. While it's hard to rank everyones chances clear down the list , common sense tells you that Dani and Jeff rank in the top two with Adam possibly as #3. After that....anyone's guess.

Of course he does qualify it by using "possible".....

'Big Brother 13' Spoilers: Who Are the Week 7 Nominees?
Friday, August 19, 2011

John Kubicek
Senior Writer, BuddyTV

Some weeks on Big Brother 13 seem more inevitable than others, and this is one of them. The outcome was essentially decided the moment the HoH competition was over. Nothing can be done and while the Power of Veto competition might offer some hope, it won't change things that much.

SPOILER WARNING: This article contains Big Brother 13 spoilers.

Jeff is the HoH and he nominated Porsche and Kalia.

The nominations make sense since Jeff promised to put up Kalia when she nominated him and since Porsche has been floating and Jeff wants her to actually have to play the game. And now it's doubly bad for them since Kalia and Porsche are already Have-Nots for the week. Of course, the real target is Daniele.

It might seem stupid to some people not to nominate Daniele, especially since she has the Veto Ticket, but it's actually the smartest move if they want to evict her. Let's look at the possible PoV outcomes.

-If Porsche or Kalia win, they save themselves and Daniele gets backdoored and evicted.

-If Jeff, Jordan, Adam or Shelly win, they save someone (probably Porsche), backdoor Daniele and evict her.

-If Rachel wins, she's a wild card. She'd probably backdoor Daniele, but she might also see that Daniele is the only other player who can help Rachel get rid of Jeff and Jordan. Sure, Rachel is BFFs with Jeff and Jordan for now, but she knows she's expendable to them.

-If Daniele wins, she saves Kalia and Porsche gets evicted regardless of who the replacement nominee is.

Assuming Rachel would backdoor Daniele, that leaves Daniele with a 1 in 7 (or 14.3 percent) chance of winning the Power of Veto and not being evicted.

Now let's look at the other option. If Daniele were nominated next to Kalia or Porsche, then the one of them not nominated could play in the PoV competition and win, then decide to save Daniele. Thanks to my math major in college, I've crunched the numbers and figured out that the odds of Daniele coming off the block would be 26.7 percent if she was an original nominee (I've included my work below for any high school math teachers interested in using Big Brother as an example to teach probability and statistics).

In other words, from a purely mathematical perspective, there's a greater likelihood of Daniele getting evicted if she's NOT nominated right away, assuming everyone else would use the veto and, if not nominated, Kalia or Porsche would use it to save Daniele.

Whether or not Jeff was able to do the math in his head or come to the same conclusion isn't obvious (though I'm sure Brendon would've smeared chocolate sauce on the HoH walls to come up with a Good Will Hunting-esque formula to explain it all). However, at the end of the day, if Daniele is the real target, Jeff made the smartest move.

Now, as promised for all you nerds, here's how the math of Big Brother works.

Big Brother 13 Math: Why Jeff Didn't Nominate Daniele

Let's assume Jeff nominated Daniele and Kalia (though mathematically, it's identical if he nominated Daniele and Porsche).

Then there would be 10 possible groups of players to compete for the Power of Veto:

Jeff, Daniele, Kalia, Adam, Porsche, Jordan
Jeff, Daniele, Kalia, Adam, Porsche, Rachel
Jeff, Daniele, Kalia, Adam, Porsche, Shelly
Jeff, Daniele, Kalia, Adam, Jordan, Rachel
Jeff, Daniele, Kalia, Adam, Jordan, Shelly
Jeff, Daniele, Kalia, Adam, Rachel, Shelly
Jeff, Daniele, Kalia, Porsche, Jordan, Rachel
Jeff, Daniele, Kalia, Porsche, Jordan, Shelly
Jeff, Daniele, Kalia, Porsche, Rachel, Shelly
Jeff, Daniele, Kalia, Jordan, Rachel, Shelly

Since each possible scenario has six possible PoV winners, there are a total of 60 different outcomes.

NOTE: The presence of the "HGs Choice" chip in the selection bag may create a very slight statistical variation in the likelihood of these scenarios, but I'm going to ignore that. Let's just refer to that as the margin of human error.

Daniele could win in each scenario, so that's 10 outcomes where she's safe. Additionally, Porsche would play in six of the 10 scenarios, and so there are six possible outcomes where she wins and saves Daniele.

So there are 16 out of 60 possible outcomes where Daniele would come off the block, thus, 26.7 percent.

I bet you thought you'd never have to use math again after graduating from high school, but as you can see, it can definitely help if you ever have to play Big Brother.