meta 10 minutes*

hello and welcome to episode #546 of

**matt gaffney’s weekly crossword contest**, “What Are the Odds?”. for this week 3 puzzle, matt challenges us to name a

**5-letter proper noun.**what are the theme answers? there are five long across answers that are yes/no questions:

- {Question that may determine whether you go to work on a given morning} IS TODAY A WEEKDAY?
- {Question that may determine a spade’s value in certain card games} IS A NUMERAL ON IT?
- {Question that may determine whether one’s opponent wins at roshambo} DID YOU PLAY PAPER? the use of the alternate name “roshambo” is a nice way to get around the duplication of PAPER in the name “rock-paper-scissors”.
- {Question that may determine whether the other football team kicks off or receives} DID YOU SAY TAILS?
- {Question that may determine whether a Yahtzee was converted on the last turn with the final die} DID YOU ROLL A FIVE?

before i’d really had a chance to work on the meta myself (i spent most of the middle of the day friday watching chess), andy kravis pinged me and asked me if i wanted to co-solve. so i solved this with andy, even though in retrospect, it seems like the kind of thing either of us could have done on our own.

the first obvious thing to do is answer the question in the title: what are the odds? each question relates to the probability of some random event, so it’s a matter of just calculating the odds. we’re going to make the default assumption that each of the possible outcomes is equally likely, even though in some cases that doesn’t necessarily has to be the case (in particular, your strategy in calling coinflips or playing roshambo doesn’t have to be balanced).

- IS TODAY A WEEKDAY? if you’re equally likely to ask this on any day of the week, then 5 out of 7 are weekdays. so the probability of this being a “yes” is 5/7; but we’re not asked for the probability. we’re asked for the odds, and the odds against today being a weekday are
**2 to 5**(two nos for every five yeses). - IS A NUMERAL ON IT? if you draw a random spade from the deck, the probability is 9 in 13 that there will be a numeral on it (2 through 10 yes, J/Q/K/A no), so the odds against are
**4 to 9**. - DID YOU PLAY PAPER? if your strategy is a uniform random distribution among the three choices, the probability of playing paper is 1 in 3, so the odds against are
**2 to 1**. - DID YOU SAY TAILS? if you are equally likely to choose heads or tails, odds against are
**1 to 1**. - DID YOU ROLL A FIVE? for a fair die, the odds against are
**5 to 1**.

once we’ve got all the odds written down, the next step is not too tough: for 2 to 5, just circle box 25 in the grid, and then similarly 49, 21, 11, and 51. i’ve circled them in the screenshot above, and reading off the letters in those squares in that order gives **MACAO**, which is a 5-letter proper noun. and as it’s the gambling capital of the world, macao is a very apt answer for a meta about betting odds.

i liked this meta. the mechanism is pretty much given away by the title, which seems like it might be more suitable for a week 1 or 2 puzzle. but exactly how betting odds work is not quite common enough knowledge for a week 1 or 2 (even if it is lookupable), so the week 3 placement seems just about right.

speaking of not quite common knowledge gambling terms, {Loan shark’s charge} VIG (short form of “vigorish”) is a term i only know from gambling.

that’s all i’ve got this week. have a great thanksgiving weekend! or if you’re canadian and already celebrated thanksgiving six weeks ago, have a great ordinary week!

I figured out all the odds (probabilities) but never thought of odds against. Phooey. Shows what I know about gambling.

Same here. Couldn’t figure out what to do with 9/13.

Yeah, 9/13 killed a lot of potential avenues I was trying out, it was just very unhelpful!

I initially wrote down all the odds as odds *for*, and didn’t get anywhere. The 9 to 4 gave me 94 which was no help, as there was no matching number in the grid. I figured I must be on the wrong track. I’m neither a gambler nor a math guy, so I’d never really had cause in my life to dwell on the difference between odds for and odds against, and I put the meta aside for a few days.

But this morning I took a fresh look, and some googling made me realize that I could flip the odds-for to get odds-against. And voila. An eleventh-hour save. Fun meta!

That’s exactly the pit I fell into. Now the word ‘odds’ has taken on a whole new meaning for me.

Doh, I actually did employ the correct trick to find the letters, but was definitely using probabilities and not odds, so I was looking at 57 instead of 25, 13 instead of 21, etc., leading to a mess. Debated between HOYLE and BAYES as potential answers, based on some of the letters I kept hitting on with the probabilities.

Feels like a dumb reason to have missed the meta, but like you said, the title does say “odds,” so it’s my own fault.

I didn’t get this one, but I have to say I’m not impressed. I in fact have “2:5, 4:9, 2:1, 1;1, 5:1” written next to the grid, but the leap from there to “square 25, square 49…” seems unmotivated. Or rather, perhaps: that’s a reasonable thing you can do; but it’s no more reasonable, and no more obvious, than hundreds of other things you can do with them (e.g., indexing into things).

To each his own, but this comment baffles me. In an effort to solve a puzzle you wrote down 5 ordered pairs of digits on a page that also contains a bunch of two-digit numbers. I am struggling with the notion that it seems strange, or far-from-obvious, to you to experiment with the idea that those number pairs could map onto the corresponding two-digit numbers in some way. More specifically, and especially where the instructions call for a word of length equal to the number of theme entries, “create a function mapping elements of the set {theme entries} to the set {numbered grid squares}” is to me one of the most obvious meta mechanisms to try.

But why to “numbered grid squares”? Certainly I was trying to map each of the odds to a letter–but there are any number of ways you could do that. You could use the numbers to index into the clues; you could look for other words (FOLIO? that’s even got “paper” in the clue?) that you can index into; you could take the second letter of “five”, the fourth letter of “nine”, the second letter of “one”….

Maybe the problem for me was that “2:5” is just not the same thing as “25”, so at no point did it look like a two-digit number? I don’t know. It just felt like an unmotivated leap to me.

I’ve seen this mechanism many times in the last couple years between the MGWCC and WSJ contest. It is definitely a common method in metas to get from a set of seemingly random numbers to a word.

> But why to “numbered grid squares”?

I could answer this in a number of ways but to me the two best answers are “because it ended up working” and “why not?”

More broadly, I think that where you see an “unmotivated” step that is therefore a reason to downgrade the puzzle’s rating, I see a “somewhat well-concealed” step that is therefore a reason to upgrade it.

For my part, realizing that the odds ratios (2:5, etc) could be re-interpreted as two-digit numbers (25, etc) and hence as grid numbers was the big “Aha!” moment of the puzzle: and far from seeming like an unmotivated leap, it was, for me, a clever mechanism, which it was very pleasurable to hit upon. A great meta!

I thought the puzzle was good, but I must admit that I tried the correct thing thinking there was no way it would work.

“I tried the correct thing thinking the was no way it would work” strikes me as a sign of an excellent puzzle

Grrr! I got everything right in about 30 minutes…until I couldn’t figure out the last step over the next 3 days. I seemingly thought of everything EXCEPT looking at squares 25, 49, etc. Nothing ruins a mood like a 98-yard drive that ends with a fumble at the 1-inch line.

I agree. This has been me all year. Almost all the ones I’ve missed, I’ve had the first few steps, but couldn’t finish!

I got this, on about my 100th try. The way the clues are worded, it could be odds for or odds against, so I tried them both. And I didn’t rule out expressing this as 5/7, etc. as Joon mentioned abouve. But my major problem was I thought we were doing grid coordinates. So I plotted them in every possible way. Then I must have triple checked twice. Even when I asked myself what else you can do with two numbers, putting them together to make single numbers was about my tenth guess. When it came out MACAO, I was convinced I’d have to argue for an alternate answer, despite the solid click with gambling. I’m amazed it was right, and that over a hundred people followed the same path. Though probably not as tortuously as mine.

Unbelievable. I had Macao, wasn’t familiar with it, googled it, and the first thing that comes up is “Macau” so I discarded it and kept digging for something else. How can google return a presumed typo as an answer when the real thing exists? Booooo google.

If you had clicked through to the Wikipedia entry, you would have seen that both “Macau” and “Macao” are considered acceptable spellings.

Yeah, I noticed that about an hour ago :) I also noticed that scrolling down the google results would have shown “Macao”. Definitely not faulting Matt and the puzzle, just annoyed at my over-confidence on google results. I’m mentally giving myself credit for this week anyway!

You don’t even need to click through – the first google result (for me) is the wikipedia entry, whose first sentence giving both spellings is displayed right there in the search results. But I can understand finding it frustrating, if you’ve never heard of Macao or Macau, to google the former only to find the immediate suggestion “this is almost, but not quite, a real thing”

I suspect I will be one of a number that didn’t consider, or even fully understand, the subtlety of odds vs probability.

Stayed stuck on 5 of 7, 9 of 13, 1 of 3, etc.

I stayed extra stuck because 7, 13, 3, 2, and 6 are across only answers. Started to think more about the words – 5 out of 7, or 5 IN 7.

I was convinced I had it when I tried the 5th letter in the clue for 7 across, the 9th letter in the clue for 13 across, the 1st letter for 3 across, etc.

Alas, it produced gibberish and a DNF.

I was stuck where you were until I googled “convert probability to odds” and got this response: “To convert from a probability to odds, divide the probability by one minus that probability. ” A little math, and I had the right digits. I had them backwards at first, but with no square 94 it was a quick conversion.

Yep, shoulda googled!

Seems like I always get stuck in google rabbit holes on weeks when google won’t help at all – and vice-versa.

That said, this illuminates a cool aspect to doing the MGWCC. It’s not just knowledge or cleverness that’ll help you solve. It’s often about implementing a bunch of different ways to approach the same problem.

I’m getting better at reminding myself when stuck that I need to try my ever-growing list of alternate approaches. Re-check the title, look for tells like pangrams or unusually occurring letters, look at the clues for patterns or oddities, that sort of thing.

So it was a complete coincidence that the lowest common denominator of all the probabilities (5/7, 9/13, 1/3, 1/2, 1/6) was 546? For MGWCC #546? What are the odds? No chance of recovering after seeing this.

this factoid is so wild to me i can’t even decide whether i think it’s more likely this was planned or a coincidence

I am really, really, really glad that I am not good enough at math to have discovered this, for it would surely have been my undoing as well.

This was absolutely my undoing. Curious if it was a known fact or just a wild coincidence.

I teach statistics to business students. I don’t dwell much on odds because, to me anyway, the vast majority of people confuse them with probability. When an awful lot of people hear the odds of 1 to 5 they think the probability is 0.20 when it is 0.167.

I originally wrote the odds as the odds for an event. After looking at the letter strings from 2 to 5 (LOGA) for example, I moved to the using the odds numerals to point to one letter. The 9:4 didn’t work so I switched to the odds against.

I was disappointed to discover that 254-921-1151 isn’t the phone number of a flat in Waco, TX where Arthur Dent went to a fancy dress party, and met a very nice young woman whom he totally blew it with.

I’m entertained by this reference because I was just thinking this morning that the last time in my life I remember thinking of odds in terms of “_______ to one against”–before solving this puzzle–was when I read the Hitchhiker’s Guide to the Galaxy as a teenager.

“We have normality. Repeat: We have normality.” I love that this reference reminds me of one of the few places I can hear the word “normality” instead of the word “normal.”

I meant “normalcy.” Stopped typing before I was done thinking. :)

I was traveling this weekend and didn’t have much time to think about this meta, so I flipped a coin to choose between VEGAS and MACAO as last-minute wild guesses – picked the wrong one though!

I had all the odds backwards: 5:2, 9:4, 1:2, 1:1, 1:5, so I never had a chance. I even read up on how to express odds versus probability, and I noticed how some of the questions were phrased (“… one’s opponent wins at roshambo.”) But I wouldn’t have put any money on my seeing the next step of combining two numbers to create a new number anyway. But maybe, because I did study the letters in the odd numbered boxes. Finally, I’ve never heard of Macao, much less it being the gambling capital of the world. So odds were stacked against me solving this meta. (And it’s only a week three!) I enjoyed the challenge though. Maybe next time the odds will be more in my favor.

I pulled out another Monday night solve (a trend for me lately), but I don’t think this would have been out of place for a Week 4. Mildly terrified for the next two weeks.

The questions in the themer clues seemed to imply odds for (going to work, completing a Yahtzee, etc.) not odds against – was there a hint somewhere to indicate odds against? That’s where I got stumped forever.

i did not even know until today that “odds for” is a thing. “odds against” is vastly more common in my experience.

that said, the most practical reason to prefer odds against is that there’s a 49 in the grid, but no 94.

Took me 3 days to get this meta but only after a healthy push from a solving friend that I needed to get out of the probability hole. I don’t know gambling odds. Someone up the thread said the odds of 1 to 5 is not 20% and that still baffles my mind. Especially since I assumed “probability” and “odds” were synonyms.

So I had 9 out of 13 for the longest time until the friend gently said, “no, 9 vs 4” and that I needed to subtract 9 out of 13. What?!? I still feel like I need a ELI5 on this.

This one felt like a week 4 to my addled brain that can’t grasp odds vs probabilities. I’m sure those that understand that math thought it a week 1 meta.

Once again, the ol’ math degree comes in handy when solving a meta. (Full disclosure: I did get caught up on 9/13 AND 9/4.) Loved this puzzle.

Then there’s the additional tidbit that 25, 49, 21, 11, and 51 are all odd numbers.

I’m surprised at the people who have never heard of Macao. It seems to me it’s been in a lot of grids lately. I always get the spelling wrong–if I enter MACAU, it turns out to be MACAO and vice versa.

I still don’t get the difference between odds and probability.

I was going to enter VEGAS as a guess, but it’s never satisfying when you don’t actually figure it out yourself.

That was the neat thing about this puzzle for me, a person whose skill set skews hopelessly toward the verbal side: although I was dimly aware that there is a difference between odds and probability, I couldn’t have told you what it was until this puzzle forced me to learn it (and also to learn the order in which one puts the numbers when stating odds-for and odds-against, respectively). It took me so much time reading and re-reading explanations online to grasp it that I think I’m now likely to retain it.

Thanks for the lesson, Matt!

I certainly got an education regarding odds/probabilities. I have one question for Joon if he could please answer me. Referring to a number of places I read such as

stats.seandolinar.com, it talks about the difference between odds and probabilities also. But it also talks about odd for versus odds against. In your description you made the correct assumption that we were talking about ‘odds against’. However, in each one, such as the first in seeing if one would go to work, and the answer is “is today a weekday?” It seems we are looking for the odds of “going to work” which would be “5 to 2”. Or “is a numeral on it” to determine a spades value. Wouldn’t that be “9 to 4”? That is to say, by using the word “odds” does not necessarily imply “against” but one has to say either for or against, and in Matt’s wording it seems that the answers are opposite to the way you explained it. Now I’m not at all correcting you because you obviously got the answer quickly. I’m just asking for either you or Matt to explain it to me, because I’ve gone to a number of sites including the one above and still am having problems getting the fine point of this.

Thank you for listening.

as i wrote in reply to nate above, “odds for” is just not commonly used in my experience. “odds against” is. (i guess wikipedia doesn’t mention this?) for example, if you wanted to lay a wager on the outcome of the upcoming soccer match between west ham and manchester city, you could go to a betting website and see the odds listed: west ham win 12-to-1 (very unlikely), man city win 2-to-7 (very likely), draw 96-to-17 (rather unlikely). it just says “odds” (and sometimes people will say “the odds of [x]”) but it’s technically odds against. so i would say that in general, “odds” without “for” actually does necessarily imply “odds against”. that’s just the common usage.

Thanks for clearing that up. I didn’t realize that and thanks for responding so quickly. Maybe if there is a next time, I’ll get it right.

I agree that in general that gambling odds are “against” odds. In probability this is not the case. The odds are neutral. An important distinction is that gambling odds are not fair odds. In American roulette a bet of “0” pays 35 to 1 while the odds against this bet are 37 to 1. If they were fair odds casinos would not make money. The odds in the puzzle are fair odds making the jump to gambling not as obvious.