Thursday, January 31, 2019

Odds of guessing my way to $1M--assumptions

If you have seen my run on Who Wants to be a Millionaire (aired on 1/29/2019 and 1/30/2019, available to stream here: Rich Day 1: Aired 1/29/2019 , Rich Day 2, Aired 1/30/2019 ) then you know that early on Day 1, Chris Harrison and I talk about a probability math question related to the show.  Specifically, what are the odds that I would answer all 14 questions correctly by sheer guesses, assuming that I have no idea what the answer is on any question?  I immediately state the rounded answer (1 in 135 million), and then make the vending machine joke.  Typical source--you'll find more if you search  Believe it or not, I think that this little exchange is what helped me pass the interview to get on the show!

I'm hoping people will "check the math", and try to corroborate (or disprove) my answer.  There are some important assumptions in my work:

First, as stated in the show, I assume that I have absolutely no clue on any of the 14 questions.  This is admittedly a rather ridiculous assumption, given the intentionally easy questions they pose in the earlier rounds, but we are assuming the worst case scenario here, so for the purposes of this problem, I will need to guess on every single question.

Next, I will certainly take advantage of my three lifelines, but I am again assuming the worst case:
  • I will use my "ask the audience" lifeline, but for the purposes of this question, we will assume that the audience also has no clue, and that this lifeline does not help me out at all (assume after I ask the audience, each answer gets 25% of the vote).  Ugh.
  • I will use my "plus-1" lifeline, but sadly for the purposes of this "worst case" scenario for the problem, he too is unable to help me in any way.  Strike two.
  • I will use my "50/50" lifeline at some point, where two of the wrong answers are eliminated, and I only have to guess between the other two.  Yes!!  This will definitely help me, as my chances of getting that question right are 1/2, rather than the 1/4 chance I will have on the other 13 questions.  
Okay, now that we are on the same page with the assumptions, you can check my math--what are my chances of guessing my way to a million bucks?

If your probability is rusty, consider this easier question, which might get you on the right track:


Imagine that somehow I have answered 12 of the 14 questions correctly, using all of my lifelines along the way.  So in this fantasy scenario, I only have 2 more questions to go to win the $1,000,000.  What are my odds of winning $1,000,000 at that point, if my strategy is to just guess on the final two questions?

Odds of guessing my way to $1M--the answer

For those who have an understanding of probability, I hope you have taken a stab at this yourself--check out the "Assumptions" post before reading this if you want to try to solve this on your own.

Let's start with the simplified question that I pose at the end of that post:

Simplified Question:
Imagine that somehow I have answered 12 of the 14 questions correctly, using all of my lifelines along the way.  So in this fantasy scenario, I only have 2 more questions to go to win the $1,000,000.  What are my odds of winning $1,000,000 at that point, if my strategy is to just guess on the final two questions?

Solution to Simplified Question:
In this case, in order to win $1M, I need to first guess the first question correctly (probability = 1/4), and then also guess the second question correctly (probability = 1/4).  Since these are independent events, the probability of them both happening is the product of the two individual probabilities, or

1/4 * 1/4 = 1/16.

Alternatively, you could calculate my odds of NOT winning $1M using this strategy.  In this case the math goes as follows:

3/4  + 1/4 * (3/4)

(first term represents 3/4 of time I miss the first question.  Second term says of the 1/4 times I get the first question right, I will then miss the second question 3/4 of the time.)

= 3/4 + 3/16 = 12/16 + 3/16 = 15/16.

This agrees with the first result.  I have 1/16 chance to guess right, and 15/16 chance to fail.

***

Original Question:
Now, on to the original question...what are my chances to guess right on all 14 questions at the start of the game?  As I mention on the air, it is important to factor in the 50/50, so the odds I state on the air (rounded) are the odds of guessing 13 questions where I have 1/4 chance on each, and one question where I have a 1/2 chance.

Last chance to work it out on your own!  Look under pic for the solution.






Okay, the same logic applies as with the simplified question...we multiply the probabilities of guessing each of the individual questions right, so this works out to:

(1/4)^13 * (1/2)

(the "^13" there means 'raised to the 13th power')

= (1/2)^26 * (1/2) = (1/2)^27

Or, one over 2 raised to the 27th power.

or 1/134,217,728 (I rounded to 'about one in 135 million' on the show.)

As for the vending machine statistic...I did not cite my source, but it is from the internet (so it must be true!)  I saw it referenced in several places, though I suspect there is some original source somewhere, and then others keep referencing that.  Here is one of the pages I found:

Lottery and crushed by vending machine stats




Monday, January 21, 2019

Pre-airing rambles about my experience on Who Wants to be a Millionaire--long post!

I had quite a fun/exciting experience in Las Vegas earlier this summer...on a hot Vegas Tuesday afternoon, 7/17/2018, I was in the audience of the US TV game show “Who Wants to be a Millionaire?” It is a blast to be in the audience, and tickets are free. I have done it each of the last three years. They have a good comedian who keeps things interesting during breaks in the action. You get to watch others compete, and even participate when the contestants use their "Ask the Audience" lifeline. Every audience gets to see several episodes tape, so it ends up being a fun four hours or so. If you like Millionaire and you are in Las Vegas in July/August, I highly recommend this!

One thing you get the opportunity to do as an audience member is take a multiple-choice test to try to qualify to be a contestant on the show. This happens early in the process, before you are seated in the circular studio to watch the show. The test is not easy...as on the show, the questions can be about anything (pop culture, history, geography, movies, math/science, etc). Also, you only have 10 minutes to answer 30 questions, so you need to be speedy to get through the full test. I just finished when they called time, and thought I might have a shot. I can say that test-taking strategies from actuarial exams came in handy here!

Later in the afternoon, during a break in the action, the comedian announced that 4 people in the audience of about 130 passed the test, and sure enough, I was on the list. The three (ahem) other nerds and I were instructed to hang around after the last episode to speak to Kristin, a representative from the show. She ended up doing a quick group interview with the four of us, and it seemed to me that none of us made a great impression, though I felt like I scored a point with one of the comments I made. She escorted us out of the building, saying they had our information, and they would contact us if they were interested (she didn't put it this way, but it was a definite "don't call us, we'll call you"-type-moment.) I got in my baking-hot rental car, disappointed that I did not make a more favorable impression.

As I was driving away from the studio, my cell phone rang... "Hello? This is Rich." What do you suppose I heard on the other end of the line? (Let's do this Millionaire-style):

A. (Robo-voice): "Act now, and you can consolidate your student loans…"
B. "This is your wife, Paula. Our house in NH was hit by a power surge during an electrical storm, and all the electronics are fried …"
C. Long pause, then an irritating voice: "Hello? Helloooo?...Is this Doris??"
D. "Hi Rich, this is Kristin from Millionaire, I was just talking with you. Could you come back to the studio? My Supervising Producer would like to meet you."

Most of the calls on my cell phone are of the A or C variety, and B would come later that day. But happily, if you guessed "D, Final Answer", you are right! I whirled my rental car around, and in minutes was back in the studio.

I then had a great talk with Kristin and Eric Waddell, the Supervising Producer. After about 15 minutes, he informed me that he wanted me to be a contestant on the show! Needless to say, the disappointment from the rental car had entirely evaporated. Woo hoo! He was 'hoping' they could get me on this year, but if not he said that I would be called next summer to appear next season. I spent quite some time--perhaps an hour--filling out paperwork.

When I left the studio I felt a bit uneasy about how long I might have to wait to get the call (I could picture waiting a whole year, getting my hopes up each time my cell phone rang). However, on the positive side, he was clear that he was going to get me on the show, and most likely before they were done taping this season, which would have been August 23rd. Awesome! I assured him that I would have no troubles getting back to Vegas whenever they could get me in.

By now it is late afternoon. I visited with my Vegas friends Mark and Leslie (Leslie had just had a major surgery one week prior) to share the good news, and then headed to my hotel room to call my wife, Paula. This is when I learned about the lightning strike, so poor Paula was dealing with all sorts of trouble and strife back home.

As we were talking, at about 6:10 that evening, we were interrupted by another call on my cell phone...

"Hi, this Ines from Millionaire. Has anyone told you yet that we want you to come in tomorrow at 9:00 am to be a contestant on the show?"

I laughed, figuring she really just needed more paperwork, and was pulling my leg. But after an awkward pause, I realized that she was serious. Whaaa??!?! This is definitely *not* their normal procedure, but they knew I was in town for the rest of the week, and they were willing to squeeze me in the next day, if I was willing to scramble. Yowza.

That night was a whirlwind, I had so much to do. First I had a long talk with Ines, going over her checklist of standard communications to cover when they call a contestant to tell them what their tape date is. She said I would be contacted by Marina, who would be my support person during the taping the next day. I then called Paula back; offered her absolutely no support for what she was dealing with (lightning strike), and added to her burden by asking her to send me a picture of my Social Security card. (She found it--thank you dear!)

Then sure enough Marina King from the show called, and we had another long conversation. Contestants are asked to wear their first outfit when they get to the studio at 9:00 am, and have two others in reserve in case they last more than one episode. There are several guidelines for what you can wear...no blue, because it blends in with the stage floor, and no logos of any kind. I told her I only had one shirt with me that might work (a funky Hawaiian shirt). She asked me to text her a pic of it, and said she loved it, and that I should wear that to the studio. (Marina was very helpful and supportive.)

Next, and importantly, I had to talk with my Las Vegas friend Mark, as I wanted him to be my "Plus 1" lifeline on the show. I needed him to drop everything (including caring for Leslie, who had undergone a total hip replacement one week earlier) and commit to what could be a full day at the studio. Thankfully he and Leslie were fully supportive, and quickly agreed to the commitment. Whew!

Next Mark and I headed to a Vegas Stein Mart (clothing store). We arrived there at 8:47 pm, and the store closed at 9:00 pm. As we were walking through the door, they were announcing that people needed to finish shopping and bring their purchases to the registers.  After some seriously speedy shopping, I had my two extra outfits.

Mark and I ate a late dinner, then I went back to my hotel room to iron my clothes and somehow try to quiet my mind and get some sleep. Remarkably I slept okay for about 5 hours, but woke up at 4:45 and couldn't get back to sleep. I had a good breakfast at my hotel (Red Rock casino), and fired off some text updates.

I picked Mark up at his house, and at 9:00 that morning, Wed 7/18, we report to the studio.  The very first thing we had to do was give up all electronics—they took our cell phones (and iPads, and even smart-watches) as soon as we arrived, not to be returned until after I was finished.  This meant I couldn't text updates to Paula, as I had promised, and I didn't even get a chance to warn her that I was about to "go dark".

Next I met my support person Marina King, and the other contestants.  There were a grand total of eleven contestants (with our eleven 'plus one' lifelines) there to be taped that day, and we spent most of that morning together. Two contestants had sat through the full day of taping on Tuesday, and had not been picked. Therefore they were guaranteed the first two spots on Wednesday. The order for the remaining nine of us would be determined at random.

We learned that we would not get to watch each other compete…all contestants who have not competed are sequestered in a room (watching Season 15 and Season 16 reruns) until it was our turn to go out on stage.  It was fun to talk to the other contestants. They were amazed that I had been in the audience just the day before, as they all had known for several months that they would be on the show. Most of them had been studying and preparing in one way or another.

The next three hours flew by in a buzz of activity. Mark and I both had quite a bit of additional paperwork to fill out. Then Eric Waddell, the supervising producer, addressed the group of contestants to give us general strategy advice. He told us that from his perspective, the two most common mistakes made on the show were: 1), contestants not reading the question carefully, and 2), contestants burning lifelines early (just to "make sure"), even when they are pretty confident that they know the answer. Good advice, for sure.

We also met with a lawyer (remember the movie "Quiz Show"? There are some pretty interesting rules and regulations to ensure game show integrity.) Much of that had been covered in the reams of paperwork I had signed, but they had him talk through the most important items with us. We then went to the stage to get familiar with where we were supposed to enter and exit, and then how to stand at the podium. We all got a mock question to answer, to get a feel as to how things would look and feel under the lights.

We were finally allowed to go use the rest rooms, and I was surprised to see that the first audience of the day had been seated…I had no idea that three hours had passed, and it was already past noon. (Just 24 hours earlier, I had been up in the audience, waiting for the first contestant to appear.) Pretty soon the first of the two contestants from Tuesday was called to compete, and I learned that I had been randomly picked to go first out of my group of 9, right after those two. Okay, then, ready or not, I'm about to go.

But first, I get to go do hair and makeup...now *that* is something I've never done before. Not much for them to work with, but at least my big forehead was less shiny than normal. The first contestant wrapped up her game while we were doing makeup.  After that Mark and I were walked over to a secluded trailer to get mic'd up, and then we were left to chat with Marina until the contestant before me was finished. Marina and Mark wondered if I was nervous, but I was not. I was really looking forward to getting my questions (MY questions...what a thrill!) and doing my best.

Naturally at this moment, it is critical to be in the correct frame of mind, beaming with positive thoughts, and soaking in the positive energy and encouragement of your friends and family. I'll share with you a text that my 23-year-old son Jed sent me that morning. So inspirational, it brings a tear to my eye. He said, and I quote: "Well, good luck. Please don't be too embarrassing/nerdy." Geez, thanks, Jed!! ðŸ˜€ðŸ˜€

Marina gets a chirp in her ear, then turns to us and says "okay, it is time to make our way to the stage!" We walk to the perimeter of the stage, and the comedian who keeps the audience entertained asked me if I had a request for a "pump up" song. I was ready for this. 52 Girls by the B-52s. He found it and liked the song choice. He didn't crank it to sufficiently ear-splitting volume, but it was fun to hear.

He also did a double-take when he saw me, and asked if I had been in the audience recently. Yep, I confirmed, 24-hours ago. He announced to the audience "Ladies and Gentlemen, our next contestant was sitting in the audience yesterday afternoon, in that seat right there!" It was again clear that this next-day process that I was experiencing was rare for the show. Chris Harrison (the host of the show) joked to the crowd that he personally guaranteed that anyone who passed the test in that audience would be placed on the show the next day...an empty promise, as they then informed him that nobody in my audience had passed the test. (Not the best of news for me and my "Ask the Audience" lifeline!) All this happened prior to the start of my episode, so you will not see it on TV.

I admit to being in a bit of a fog, but the show is run like a well-oiled machine, and the Millionaire crew guided me through the whole process step by step. Right off the bat, Chris asked me about the fun math-related fact I had given at the group interview the day before (I am convinced that this is what got me on the show), so you will see what that is all about before I get any questions.

At every commercial break I would go and chat with Marina, and she had water for me and would make sure that my teeth and nose were clear of spinach and boogers (do I have to add, "respectively"?!) It was fun to meet Chris Harrison, he is easy to talk with, and impeccably dressed in his skinny suits. If I was worried about anything, it was along the lines of blowing a math question, bringing shame to the actuarial profession, or something silly like that. And of course I needed to remember to not embarrass Jed. Once the game started, it seemed to go really fast.

And now, as your reward for reading through all of this, you get nothing. I'm afraid I can offer you absolutely no spoilers. Much of the legal advice and paperwork that I signed centered around the fact that I am not allowed to tell anyone anything about my game-play that day. I have not even told my wife Paula, much to her chagrin! This includes how much I may or may not have won on the show, nor am I to disclose any of the questions that I faced. They want you all to tune in when "my" episode(s) air. 

And you have to admit, it will be more fun not knowing, right?! It will air this upcoming season, which could be anytime from mid-September 2018 to May 2019. It is a syndicated TV show, and it generally airs nationally 5 weekdays per week on ABC or their affiliates. It airs at different times depending on where you live. Here in NH it is shown on WMUR at 3:00 in the afternoon. Channel 5 in Boston shows it at 12:30 pm. Back in CO, it airs at 9:00 pm, and in Vegas it is 2:30 pm.  You can go to the Millionaire website and find when it airs in your locale if you do not know.

They will notify me 10 days before my episode airs, so I will definitely let you know when I know.  It may be somewhat correlated with the order in which it was taped, and if so then I'd guess late October/early November as most likely, since I was there in their 2nd week of taping out of 6-7 weeks for the entire season. But no guarantees, it could be delayed and aired later in the season. Any amount that I may or may not have won will be paid 30 days after it airs.  (update, I just found out the episode dates are Tues January 29th and, if necessary, Wednesday January 30th!)

When it is over, it ends abruptly. No matter how psyched (or depressed) I might have been, I was asked to sign a form acknowledging how much money I won. Then Mark and I were given back our electronics and told to gather our outfits.  We said our good-byes to Marina, and boom, we were out in the parking lot blinking at the Vegas blast-furnace sun. We did not get to see how any of the other contestants did...we'll have to wait until their episodes air.

Before my time onstage, I imagined that when it was all done, I'd be filled with multiple regrets, wishing that I had been wittier, or more importantly, smarter. In the end, I have fewer regrets than I anticipated. It was a thrill to be on the show, just as I imagined it would be.

That said, one thing that I regret a bit is that we never talked about what I would do with the Million dollars if I won it. (Chris often asks contestants to talk about this.) Part of my response would have been that I have two people in my life who unexpectedly were diagnosed with MS. One is Paula's cousin Cassie, and the other is my best friend Mark, who lives in Las Vegas and was my "Plus-1" lifeline on the show. They are both doing great in face of this difficult disease. I will be donating a portion of any amount I won to MS charities in their names.

Please feel free to ask questions here if you have any for me…I'll be happy to answer anything that is not related to winnings or my game-play. (Seeing how long this write-up is, there must not be too many questions out there.) Once my episode airs, I expect I will have a couple of "behind the scenes" stories to talk about it. I appreciate your interest, thank you for reading through this long story!