# Which is more likely?

Red Chipper Posts: 4,944 ✭✭✭✭✭
edited September 2019
This is going to be a multipart question, from a book I'm reading. I'll post the book later in the discussion because I've found it fascinating, but I don't want anyone whose read it to know which it is.

For now, let's say there's a die you're rolling that has 2 Red sides and 4 Green sides. Which of these sequences is most likely? The 1st is 80% Red, the 2nd is 67% Red, and the 3rd is 50% Red. (You must not use a calculator or paper to solve this, you must figure it out on the fly.)

## Which is more likely?

This is a private poll: no-one will see what you voted for.

• Red Chipper Posts: 85 ✭✭
Your 80/67/50 percentages are not what is represented in the poll answers.
• RCP Coach Posts: 1,806 -
edited September 2019
The order does not matter. Each new one is the prior one with a green. This additional green is 66% of the time. If the first is the base line, each additional constraint makes it less likely.
Co-founder Red Chip Poker,
Author Poker Plays You Can Use
Author Poker Workbook for Math Geeks
• Red Chipper Posts: 4,944 ✭✭✭✭✭
NTD12 wrote: »
Your 80/67/50 percentages are not what is represented in the poll answers.

That was simply information and you can do with it what you like. I just want to know which is more likely, the exact number doesn't matter.
• Red Chipper Posts: 4,944 ✭✭✭✭✭
edited September 2019
So this relates to a lot of things we experience at the poker tables, and a lot of things I see provided in hand histories on the forum.

Here's another example from the book.

LInda is 31, single, outspoken, very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.

Put these in order of most likely to least likely:
A- She is a teacher in elementary school
B- She is a bank teller
C- She works in a bookstore and takes yoga classes
D- She is an insurance salesperson
E- She is a bank teller who is active in the feminist movement

One of these is the best answer
1. A, C, E, D, B
2. C, E, A, B, D
3. A, C, B, D, E
4. C, A, E, D, B
• Red Chipper Posts: 669 ✭✭✭
#2 - At first I tried to think of these in order starting with most likely but noticing that D was near the end each time stood out to me.
• Posts: 2,938 -
The only possible answer is #3
Moderation In Moderation
• Red Chipper Posts: 4,944 ✭✭✭✭✭
TheGameKat wrote: »
The only possible answer is #3

Think of what Doug said above for the die problem. Then look at this one with the same concept in mind and pay attention only to B and E. The order of those 2 is the only thing you can know for sure.
• Red Chipper Posts: 49 ✭✭
Love those questions! Makes me think of a book title that I have on my to-read-list, "Fooled by randomness". It's not that, is it?
• Red Chipper Posts: 4,944 ✭✭✭✭✭
No, but I'll take a look at that one too.

The book is "Thinking Fast and Slow" by Kahneman. To be honest it's a bit of a slog at times, but it's really fascinating. It explains so many biases and errors in judgement that we all have. Even professional statisticians are making errors. This is just due to how the human brain is wired and how we evolved. Sometimes I knew what he was getting at and I still was drawn to the wrong answer. It sheds light on how our societies make mistakes, how we vote for the wrong politician for the wrong reason, how we buy the wrong product, how we make the wrong impression at a poker table, how we interpret bad beats and bad runs. Thinking Fast refers to our first, intuitive response, and Thinking Slow refers to our cognitive thought process. Sometimes the latter doesn't get engaged, but both can be wrong anyway.)

It's very intuitive for example to think that Linda is more likely to be a bank teller who is active in the feminist movement than just some random bank teller, because it's simply more plausible based on her description. But it's mathematically impossible.

I've often thought they should teach a "critical thinking" course in high schools, just so kids can learn how to think, and the stuff in this book should be part of it. Definitely recommended.
• Red Chipper Posts: 4,944 ✭✭✭✭✭
So the answer to the first question is RGRRR. While the other options have more of the more likely outcomes, they also require more things to happen. "RGRRR" appears in all answers. The more events you tack on to that, the less likely it becomes, even if those events are the more likely to happen than the alternative events. Look up "parlay betting". https://en.wikipedia.org/wiki/Parlay_(gambling)

• Posts: 2,938 -
Sounds like a book I'd enjoy. I remember when Gladwell's "Blink" came out it was immediately awarded "best book for a poker player to read that isn't about poker".
Moderation In Moderation
• Red Chipper Posts: 4,944 ✭✭✭✭✭
Yeah, while I haven't seen poker mentioned in the book, as I read it I kept thinking of scenarios at the poker table involving profiling and stereotyping, perception of players on a recent "streak", how I might be perceived, how you word things can strongly effect people's response, etc. The applications to business and politics are endless. The examples above were in the middle of the book - it wasn't until then that Bayesian probability was mentioned.
• Red Chipper Posts: 4,944 ✭✭✭✭✭
NTD12 wrote: »
Your 80/67/50 percentages are not what is represented in the poll answers.

Oh, if you meant the 3rd choice was not actually 50% you're right - it's 57%. I missed that. But the overall point is that those numbers are irrelevant.
• Red Chipper Posts: 85 ✭✭
jeffnc wrote: »
NTD12 wrote: »
Your 80/67/50 percentages are not what is represented in the poll answers.

Oh, if you meant the 3rd choice was not actually 50% you're right - it's 57%. I missed that. But the overall point is that those numbers are irrelevant.

Yes, I was trying to correlate the number of Rs and Gs to you percentages as I thought it tied together and it confused me a bit. I was thinking of just percentages as opposed to the exact order.
• Red Chipper Posts: 10 ✭✭
This book was the main focus of my capstone economics course in undergrad (Behavioral economics). Absolutely loved it and would recommend to anyone interested in behavior and tendencies, especially poker players
• Red Chipper Posts: 14 ✭✭