A Problem Squared - 143 = What Comes After Thrice and Coffee Roulette Advice

Episode Date: September 14, 2026

📖 What comes after thrice?☕ How can I increase my chances of winning a free coffee?🎹 And we have some Any Other Beatness Thank you to everyone who sent in audio or visuals of the Thue-Morse pattern!Here is Damien’s Thue-Morse Visualiser which is really fun to play with: https://damienkee.github.io/thue-morese_visualiser/ And here is the keyboard visualisation of Thue-Morse sonified by Seta Lyas: https://www.reddit.com/r/AProblemSquared/comments/1vl0m8s/140_thuemorse_sonified Head to our BlueSky/Twitter/Instagram to see the full run down of Bec’s post-thrice words.Do you have a problem for Bec and Matt to solve? Tell us about it: https://www.aproblemsquared.com/ Matt has extended his tour - and he’s filming the show in London in October - all the dates, venues and tickets can be found here: http://standupmaths.com/shows Join us on Patreon for early releases and our monthly bonus podcast I’m A Wizard!If you’re already on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on our pinned post!   If you want to (we’re not forcing anyone) please do leave us a review, share the podcast with a friend, or give us a rating! Please do that. It really helps. Finally, if you want even more from A Problem Squared you can connect with us and other listeners on BlueSky, Twitter, Instagram, and on Discord.

Thank you for installing a problem squared into your ears, which should now be able to provide you with some solutions to 100% highly practical problems sent in by previous users. First, we have a couple dependencies. You have to install the Beck Library, writer, performer, comedian. You actually, if you previously installed the Beck Library, you probably want to install with the upgrade. Dashash Upgrade. Oh, yes. She's been at the fringe, so. Oh, yeah, no, that's true.

Yeah. You're doing a work in program? show, so. Yeah, I'm still upgrading, to be honest. Yeah, it's going to be a long buffer. Yeah, exactly. And you want to import Matt as maths. I'm here to provide, math, maybe maths-ish.

I'll give it a go, close enough mathematical approximations to all your problem needs. And on this episode, I'm going to solve a problem not once, not twice, not thrice. Oh. But more than thrice. More than thrice. Mm. I've run the numbers on how to play your cards right in a cafe. And we have some any other booting up.

Oh. Mm. Love it. So back. Yes. How have you been? I'm good. Great.

I'm tired. Right. Got back from, well, essentially got back from Edinburgh last night. Yes. So I am still. adjusting. Because the last three weeks of July were really full on.

I did Berlin Fringe, almost immediately followed by like a big corporate gig and a charity gig. You were all go. I think you dialed in from Newcastle at one point. Latitude. And then Manchester Leeds, Newcastle.

Edinburgh. I'm in that place where I'm like, how do I life again? But then you were home for at least 10, 12 hours. Yeah. And then I was like, oh yay. Okay. After Surrey. I've got a lot to do.

So I'm good. Yep. But I am fully aware of how much I've got to do. Yes. Yes. But Edinburgh was great. Oh, great. How to go?

I was very disappointed to not get up there. Yes. I've seen any shows. Firstly, got to go see one of two rare live performances by Count Binface. Oh, dang. Yes. Yeah. Managed to squeeze into one of those.

Great. Which was delightful, very, very fun. I hope that he does more. Yes. Live appearances. Both as Count Binface and as a human. As the close human associate to Count Binface, John Harvey. Yes, yeah.

We'll be at an evening of necessary detail of the Cambridge Theatre. Yay. If people want to come and see a binless, John. And I did a work in progress, which it's so, much more and so much different from what I had when I did it in Adelaide. So I've got a lot more to work with. I was hoping by the end of the run, I would have a much clearer idea about what the next show is. Got it, yep.

And I sort of do, but there are now infinite possibilities about how I go about doing it. So it's both been incredibly useful. And the problem is there's just too many options. You're still at the generating clay point, not the sculpting it back point. Yeah, yeah, that's it. Or like I'm sort of at the sculpting it back, but working out like what shape do I want it to be? Oh, okay. Yeah, yeah, I've got lots of clay, but yeah.

Clay for days. Too much clay. That's how we describe you. Yeah, yeah. Oh, too much Clay Hill. Who left this pile of clay here? Yeah, checks out. So I'm pretty happy with how it went, but so I didn't do any real promotion for the show.

I didn't have any posters or flyers. I barely mentioned it online. Because to quote Glenn Moore, who was also doing a work in progress, which he did not promote very much. Yep. That way you get the real comedy perverts in. Okay. And like, they're the sweet spot if you're trying out new stuff.

Yeah. You know that they're going to be patient and they're less inclined to never give you a chance again if you flop. You want the people who understand what a work in progress is. Yes. And are happy to just kind of see it happen. Yeah. Yeah, yeah.

And as the copy for the show said, because sometimes seeing how the sausage is made is much more interesting than seeing a sausage. Yeah. And so that was how I sort of sold it. And so many, it was only a 40-seater, but it sold really well, considering I hadn't promoted it. And so I had such lovely always. audiences, like the last night was maybe the quietest one. And even then, it felt really lovely. And a lot of them were listeners. So thank you to all of you who came along. My only problem with the run actually is everyone was so nice that I had to keep reminding myself that I would not

be able to get away with a lot of them. Like a lot of the jokes still don't have proper punchlines. And I do want to write those. I don't want to be like, well, they were fine with me just moving on. Every audience will be that forgiving. No, no. So that's the only thing. It's like, oh, yeah, yeah, yeah, I should probably keep trying. Yes. But everyone was so lovely.

Oh, also in the copy, I said if anybody has. Like on your flyer. Yeah, yeah. In the, well, I didn't have a flight, but it was in the website when you buy a ticket. Yeah. And it said, in case of emergency, please bring a show and tell item. And I've forgotten that I put that on there. That's the most back sentence I've heard in a while.

Yeah. And then halfway through the first show, a hand went up and they went, are you doing show and tell? And I was like, oh. And so then I had to start putting a post-it up to remind me to check in for show-and-tel items. And in fact, every night except for the last night, people brought show and tell because that's the type of people. That's the audience you attract. And I love them for it. And there was some really, really lovely, interesting things.

two highlights. One of them was someone who genuinely has the longest tongue in America, or at least did at the time they were on Ripley's, believe it or not. Wow. And obviously you haven't got favourites, but what was the other one you'd like to mention? Someone brought an antique ear trumpet. An antique ear trumpet. Yeah, you know, in like cartoons.

That is one of the funniest things to bring to a comedy gig. Yeah. So they sit in the front row and then like, hey? Great. That's me. That's the sound of me, my being holding a trumpet up to my ear. And the thing is, is, The show started yet? When they said they brought an antique ear trumpet, they held it up for me to take.

And I misheard them, which definitely means I need one. So yeah, that's my sort of audience that they were like, we've got you. Even if you forget that you asked for backup, we're here for backup, which is really nice. So in conclusion, thank you everybody who came. lots of folks who stuck around afterwards. Oh, and in fact, one of our listeners, Emil, who wrote in about listening to the podcast while working on Six-Axas robotic arms, came along to the show. Oh, great. Emil was in, so Amil was in town to work on the robotic arms at a bottling factory.

Great. Didn't know that there was a fringe on. Oh, that must have come as a real shock. got to Edinburgh and was like, Why can't I walk down the street? Yeah, is everyone here for the cure? Because they were doing a concert. And then someone was like, oh no, it's Edinburgh fringe.

And Emil was like, oh, I wonder if either Matt or Beck are doing a show and saw that I was listed. So basically got into Edinburgh three hours prior and I was the only show that they're still up. Because they had to go and work at the factory the next day. So that was a delight. But quite a few folks, someone, there was a couple. on the last night that had driven up from Newcastle specifically to see me. Oh, thanks everyone. And then they were going, oh my goodness, we didn't realize how big.

Big everything else is. And I explained that actually it was very quiet because it was the last Sunday and everything was kind of like settling back down again. So that was really nice to see them. I said they definitely should come up and see more shows sometime. It's very sweet of everyone to go and see your show that I couldn't be bothered getting to. To be fair. You were in London and doing a lot.

That is true. In fact, that's what I want to talk about today. Yes. How have you been? I've been good. So I did not make it up to the fringe. I'm attempting to recover from a busy period. I'm like you but two weeks in the future.

Yeah. Where I've hit the end of my crazy travel and all shows and everything. And now I'm just trying to recuperate. And so I was like, you know what? I'm not going to go. Instead, well, actually, it would have been and, but I realised it was kind of one or the other. I went to Big Feastable.

Oh, yes. The festival that you and I have been to. We've recorded an episode from a tent there once. Yes. And it's a matter of public record. I'm close personal friends with Alex James, base player from below. Yes.

It's involved in the festival. You barely mention it at a real. I don't bring it up that often. And previously, I've, like, installed geometric mirror balls above the DJ booth there. We've done a sundial. I had a robot

that DJs, which is in my current show. And a little while ago, Alex reached out and said, hey, what they really wanted to do this year was get some kind of big reflector. They were thinking of a parabolic reflector, like a paraboloid, which I've done stuff with previously. Yes. And they were like, hey, wouldn't it be amazing if we could, like, install a big geometric reflector so we can make cheese on toast using the power of the sun?

And I was like, that's amazing. What a great idea. Yeah. And then, as I think a sign of growth, I said, I'm sorry, I don't have the capacity. I'm so proud of you. To do what is objectively a great project idea. Yeah, yeah. With people I love working with.

And I was just, I just, this was like a while back, I just looked at my 2026 and knew I did not have the space of my life before August. to do that. Yeah. And so I said no. I'm very proud of you. And so I thought I'm just sharing the null story. Oh, you and I are both very privileged to have lots of great opportunities. Yes.

And we tell stories about our wonderful hijinks. Mm-hmm. And I just thought occasionally it's worth sharing the stories that don't happen. So there, didn't do it. Yeah. I mean, well, this is why my chat isn't about doing a month-long run. And it's about doing a week of work in progress so that I can take my sweet time coming up with the next show.

Exactly. Oh, and happy ending. Some physicists at Oxford uni ended up helping out Alex and they found this big parabolic cooker that you can buy and they had one on site. So I didn't get involved

but I got to watch the result and I got to just hang out at a festival. Yeah, that's nice. Didn't have to do any prep. Didn't have to do anything there? It's great. Yeah, I'm really proud of you. I don't mean to sound like I'm patronising

but honestly, I think it's just as important knowing when to say, because it's hard when you want to do it. Yes, it's hard when you want to do it. And it's a difficult thing to acknowledge when you've got to say no to things that would be great. Yeah. But you've already got enough other things you're doing that you opted into that you can't

squeeze in one more. Yeah. And it can be painful sometimes when you're like, oh, I wish I'd done that. But I have found more often than not, I've been so grateful for what I got instead. whether that's rest. Yeah, yeah. Or just being able to enjoy myself and not have to stress about something. There's a little bit of FOMO, but there's a lot more.

I'm trying to think of the opposite of FOMO. Oh, there is an opposite of FOMO. Is it? Glad you missed out. GOMO? Glad of missing out. Gamo, glad at missing out. It's Jomo.

Jomo. Joy of missing out. Well, I'm glad you've been having. Sure. And I will say, by the way, like, one of my mottoes in life is they can't all be winners. And that's just a way that I encapsulate. You're never going to make the right decision all the time. And so sometimes you'll say no to a good thing. And afterwards, you're like, oh, actually, I should have done that. Yeah. But you can't, you'll never be 100% accurate. So you've just got to acknowledge, sometimes you'll turn things down that you wish you had done and vice versa. As long as on average, you're doing a right. That's what you could ask for.

Our first problem was sent in by Joel, who went to the problem posing page, and typed, Hi, Matt and Beck, big fan of the cast. And then they clarify, meaning both the podcast and the group of performers involved. Good work, Joel. My problem, this is Joel speaking now. Oh, yes, yeah. We know yours. Joel's problem is that there is no word for doing something more than three times.

repetitive good point joel over the top over the top unnecessary eventually funny joel continues we have once twice and thrice times a lady times a lady but as far as i know there is nothing more as you guys did such great work with tweakly and twakley yes meaning every two weeks, I thought this would be a great opportunity to invent more words. Beck. This feels like a Beck problem. Oh, yeah. Have you discovered and or invented what comes after twice?

I discovered that there are no English words for post thrice. Is thrice a real word or is that just? Yes. Oh, okay. If I had spent less time inventing subsequent words and more time researching, maybe I could have told you what thrice comes from. Because it feels like people have just taken twice and just extended that to thrice.

Like it's an artificial... It's got real Shakespearean vibes to me. That is true. But I'm sure producer Laura has already been looking at up. He's on the case for thrice. What is the first documented use of thrice? The first documented use, according to etymorline, which I can never say.

Etimonlein. Like etymology. Etim online. Etim online. That's the terrible name. Etymonline. Anyway, it's from the old English. First used circa 1200.

Oh. And it means three times over on three occasions, similar to twice. So thrice is legit. It is very legit. Right. If legit means old. That's how I take it to me. So basically, if you wait 800 years, anything becomes legit.

Yeah, yeah. But that's, it survived a pretty long time. Yeah. Okay. So, okay. I'm on board up to thrice. And next we have. Okay.

So these are the ones you want to remember for the next 800 years. Oh, these are all new from herein. This is. Yeah. Wow. There's been a couple of, from what I've found, people being like, oh, maybe the, it goes into like quarters and quintet, that kind of thing. So I've taken that and I've run with it.

Would you like to hear the first nine? Oh, my good. Goodness, the fact he said first nine means there's more after. Tell it, just give me the one for four. If I did something four times, I've done it. Horse. Course. Yeah.

Coarse. Like quarter. I did that twice. Whereas that. I did coarse. Got it. Five times. Quince.

Quince? Yeah. Like the jelly. Like the jelly. Quince. I got to keep, I think is, because these are like all new words. to me, I need to go back to a sentence that has twice in it and then swap in quince. Yeah.

You've got to say it quince. Yeah. Yeah. Once you've said it quince, it starts to settle in. Yeah. Yeah. Six is since. Since.

If I've told you quince, I've told you since. Since I did it since, it's a cinch. That's my new sentence. See? Look how much fun we're having already. We really have fun. Fun with words. Yeah.

Seven is sense. Sense. That makes sense. Eight is ens. Ence. Yeah. For eight. Yeah.

How'd you get that? Once twice thrice, course, quince, since, sense, ands. So, ends. Is eight? Yep. Which is spelled with an E. Yep. That's kind of where that came from.

Eight with an E, ants with an E. Yeah. Okay. Yeah, cool. Fine. And nine is nice. Nice. Phew.

Once twice thrice, course, quince, since, sense, sense, It's nice. Nice. That ends nice. Yeah. Great. Well done. I assume you got to nice.

Mm-hmm. And you're like, that's rounded out nicely. Oh, no. Just you dusting off your hands for a job well done. No. And you're finished. You did 10 as well. I've gone up to 100.

I feel like if you've done something over 100 times, then you don't need a word for it. Okay. All right. You ready? Yeah. Yep. Okay. Stop me if you need me too. So, shall I go from the beginning again? Yes, please.

Once twice, thrice, coarse, quince, since, sense, ands, nice, tense, elevenths, or I will accept, eleuson. For the next one is a dozen. Yep. Threisans, coarsence, quincense, since, since, and since nicence. It's got a little Dr. Susie there, but... And then 20 is twents. Twents. Yeah. I thought, told you once.

Told you twins. All right. You ready for me to continue? Yeah, yeah, yeah. So we got Twentz, Twece, Twis, Twas, or two dozen. Twins. Twins. Twins.

Twins. That were 29. Got it. Thrance, trance, thrice, thrice, thrince, or three dozen. Threcentz, threence, threence, threence, threence, threence. Then we're, then we. We've got quants, quence, quarets, ques, quarras, qurence, quesens. Some of these might sound similar, but I assure you the spelling is different.

That's fine. They've got nuances. Corsents, quorants, or four dozen, and quonants. Then quince, quince, ques, queries, quay ars, quinquis, quis, quis, quis. Quisance, quesence, quence and quinints. Keep going. Sintense, or five dozen. This has been sentence.

Yeah. Seance, senis, senis, sequare, sequins, sissence, sience, sience, sience, sience, sience, sience, seester. No, that's ridiculous. Sentence, seance, senis. She's just like sentence, seance. Yeah. Senise, senise, so nice, so quass, or six dozen, so quince, so since, seence, seence, senance, so nints, intents, enonce, enise, enise, neace, and quass, and quince, and quince, and since, or seven dozen, ensence, andence, and nints. And then finally we're up to

Nynce, nience, nis, nonce, nints, nince, and then we get to hunts. Hunts. I've told you hunts. I've told you a hundred times. I've told you once, I've told you hunts. Yeah. Yeah, yeah, yeah. That's great.

Yeah. I was very tempted to put in, like, Dennis as an option. Your temptation to joke around. No. I'm impressed. You managed to suppress that. I will pass this list onto producer Laura to decide the best way to disseminate. Of imparting it with the masses.

Now, my favorite, 60. Can you give a 60 again? 60 was sentence. Sentence. Sintense. Funny word. New word. Sintense.

And the fact that you encoded 60 as five dozens is really nice. Thank you. And if you did something once a minute, it's been a sentence hour. Yes. Yeah. That's very good. That's my favorite. They were all great.

I hate to choose one of your word children. But syntax. Pence was nice. Thank you. Well, do you have anything else to add? Or is this? I mean, I could. No, no, no.

That's enough. Anyway, I'm just suggesting that we use this for the next ants hunts years. I think we'll use it up to hunts. Thank you. And then we're done. And then we're never using it again. Look, I don't know what to add, mate. Joel thought that would be a great opportunity to invent more words.

and you've done that a hunts. So, good work. Joel, I guess, report back. Let's know. This next problem comes from Tristan, who wrote into the problem posing page and says, The Coffee Shop Below Our Office offers coffee roulette every afternoon. They say you place your order and then you guess red or black. They've got a pack of playing cards and the next card that they reveal if it matches red or

you get the coffee for free. Assuming it is a standard pack of cards randomly shuffled and the guess is random, how many free coffees would they give away on average? Tristan also wants to know what is the chance that you would get a free coffee. And Tristan finally adds a follow-up. If you saw the last one or two cards of the people in front of you, what should you guess to increase your chance? Okay.

Yes. You saw this. And I was like, I'm intrigued. Yeah, what intrigued you? I think I've always found it interesting when you do the sort of chance or game show type questions. There's an element of feeling like we're rigging something and that excites me. Okay, you're right, we can. And I love freebies.

I'm obsessed with freebies. I've never come across this deal before, but in case I do, I'd like to think I'm ready. And I don't want to spoil it where we're going to go here, but we can give Tristan an advantage. Oh. So, so it's going to end. end well in that regard. You know what? When you sent this to me, I was like, oh, that's pretty straightforward. It's because the first two steps I didn't find particularly exciting because it's on the level of we're approximating this, you shuffle the deck and someone guesses red or black

naively every time, 50-50, just randomly guesses. They'll be right half the time. Yes. So if the person's guessing randomly red or black and the cards are randomly red or black, 50% of the time it'll happen to match. Yeah. Which means half. the time the person's not paying for their coffee. Right. So that answers one of the questions. Oh yeah, of course. The probability you don't pay for your coffee is 50%.

Oh yeah. That's quite a big. It's a big discount. It means if you went there every afternoon, you on average would pay half the standard price of the coffee because you'd pay half the time and not pay half the time. It'll average out to 50% discount. Good deal. It's interesting.

They've done a 50% off discount probably at the time of day when fewer people are coming in for coffee because it's the afternoon. You won't get to sleep. Exactly. And they're going to be. doing a discount in such a way that you only really get it if you go there often enough. So they're encouraged repeat customers. Yeah.

Yeah. So it's all very clever. Also, if you win, you're more inclined to go back there because you're like, we. Yeah, exactly. People find gambling addictive. Yeah. And caffeine. Oh my gosh.

These guys are exploiting. Yeah. Addictions in humans. And you do have to order the coffee first. Oh, you got to commit to your spend. Yes. Yes. Yeah.

Now, in terms of how many coffees the cafe is giving away, depends how long they do it for, I guess. If they do it for a standard deck of 52 cards, on average, they'll give away 26 coffees a day. Yeah. I don't know, though. If they're doing 52 people. If they're doing all 52 cards.

The big thing this hinges on, so actually, Tristan, do get in touch if you've got an answer for this. Do they ever reshuffle the cards? Because everything I'm going to talk about now is strategies. Like, if you see other people play, can that give you an advantage? Yeah. And that all of that, it's basically it's card counting. We've worked out a card counting system for coffee roulette.

And the same ways can see-nows can stop card counting. Obviously, coffee roulette could as well. So if they shuffled the deck every time, card counting is useless. Okay. If they had like 10 decks all shuffled together, then they've basically mitigated any advantage you're going to get, I'm counting coffees. You have to count a lot.

Bingo, yes. Whereas a single deck, and if they go through from top to bottom and then stop once the deck has run out, that gives you an advantage. So we'll take Tristan's suggestion here. They say that what if you can see the one or two people in front of you? Let's go for the best case scenario. You see both the people in front of you. They order their coffee. They choose red or black.

They turn the card over. You pay attention. Now, there's four options here Because there's two people in front of you It could have gone red black, could have gone black red Which is kind of the same thing, one of each Or it could have been red red, red or it could have been black black If it's one of each, that doesn't help you at all

If they're both the same It's evened out Yeah, evened out If they're both the same You've, instead of having a 50-50 chance of being correct You've now got a 52% chance of being correct Yeah Because and I'm

averaging over wherever you may be in the deck. So let's say you don't know where you are on the deck, or you go so often you're going to be like, you might be there at the beginning of coffee roulette or near the end. This is averaged across the entire deck. If you sat there on a nearby table, watching the entire afternoon of coffee roulette and wrote down every single card,

at the very end, you would know what the last card is. So in fact, you'd have 100% success. But you probably bought so much coffee to wait there all the whole time. It'll cancel out the advantage. So this is on average. So given we don't know where we are on the deck, you've seen two cards, which means there's 50 cards you've not seen. Yeah.

And let's say you see two reds. There are now 26 blacks somewhere in that 50. Versus 24 reds. Exactly. Yeah. So if you guess the opposite color, you have a 52% chance of being correct. So if you can just look ahead two places, that gives you a very small advantage. Yes.

You can get a bigger advantage the more cards you see, but something very interesting happens. If you're only seeing one card, so you've got half the information if you saw two, you've still got exactly the same advantage of winning. Wait, what? I know. Okay, hold on. Let me see if I can figure this out. Yeah.

So I see that they've chosen red. Yep. The card turns out red. It doesn't matter what they chose. The card is red. Yeah, let's say you see red. Which means that there are now 26. six black and 25 red.

Correct. Right. So I don't have like a tiny, tiny more chance? You do. So in that case, there are 51 cards you have not seen. Yeah. 26 of which are the opposite colour. Uh-huh.

And if you work the odds out, that gives you a 51% advantage. Yeah. And you're like, well, hang on. It's, I had a 52% chance when there were two cards. But half the time, if there's two cards, you don't get any information. And so, every single. time to see one card, it gives you a 51% advantage. Yes.

Half the time when you see two cards, you get a 52% and the other half you get no advantage, you're 50. Because if it's a red or a black, a red and a black or a black or a rich. On average, you get a 51% advantage to two cards, which is the same advantage you get for one card because half the time two cards doesn't work. Huh. And in fact, if you work it out for any number of cards you see, the evens are always the same advantage is the odd that just happened. So seeing four cards gives you the same advantage as seeing

three on average. On average. Yep. Got it. Because half the time with four, no advantage. Whereas every time with three advantage, because you either see three of one color or you see two to one, that's going to be an advantage. So the odds always give you an advantage. Evens give you a bigger advantage some of the time and no advantage the rest of the time. Yeah. It all neatly cancels that. That's very nice. So even if you happen to see the cards in front of you, that in itself is a bit of a Russian roulette as to whether it's any use. Yes, agreed.

Now, this is, again, I'd be very little careful here. This is on average, like if you had a system where you always saw three, you'd have the same advantage of if you had a system where you always see four. But in general, the more cards you can see, the better. Yeah, yeah, yeah. Because you can always add more information. Yes. And so this is just in very general, hilarious average terms.

Yeah, yeah. But it doesn't mean you should stop looking. Yeah. Because if all we don't see the fourth one, I've got a better, no. Yeah, yeah, yeah. Yeah, yeah. You should see as many cards as possible. Yeah, so it's like a statistical version of the saying it all works out in the wash.

Yeah, yeah, kind of. Yeah, yeah, yeah. Yeah, it's great if you can see as many as possible. It won't always be helpful. but when it is helpful, that's great. Yeah. Yeah. Now, in terms of my advice for Tristan, they kind of got two options.

One option, and this is the least helpful one, is to not be in the queue and somehow shove in when the hand is hot. Oh, when you've had several cards of the same color. If you see a couple in a row, actually, I ran the numbers. Let me just grab them here. I got a little distracted. Yeah, at what point should, if you saw all reds showing up? Very neatly, you get roughly one extra percentage point advantage per card in a run. So if you see one card, you're going into 51% advantage.

If you see two in a row that are the same colour, and you guess the opposite, 52% advantage. If you see three in a row that are all the same colour, and you guess the opposite, 53% advantage. And actually, it goes up faster than one at a time. So four in a row is a 54.17% advantage. And then if you see five in a row, it's about a 55% advantage. And so it's not going, you're getting an extra percentage point. If you saw eight in a row, that would give you a 59% advantage. Okay, so here's the thing, because eventually it's going to start evening itself out, right?

Unless you get, like if you get 26 reds in a row, great. Oh, yeah. Oh, yeah, eventually it's going to be 100%. Yeah. Because if you see all the reds, they don't even have to all be in order. If you see 26 of any one color, the rest must be all the other color. Yeah. On average, that's only going to happen on the last card.

It gets very unlikely you'll see like eight in a row or something like that. Yeah. Let's say you saw five reds in a row. Yeah. And then the sixth one was black. Yep. The seventh one was red. Yeah.

Then you've still got... Yeah, he's still got advantage. Another way of thinking out it is the ratio between how many reds and blacks have seen. Yeah. And that is how card counting works. You're not actually memorizing all the cards or doing a complex calculation because you want to just keep a track of are there more big cards than small cards left in the deck? Yeah.

And so every time you see a small card come out, you add one to your running total. If you see a medium card, you do nothing. And if you see a big card, you subtract one from your total. So all you're doing is just kind of keep this running measure of, have there been more bigs or smalls? Yeah, yeah, yeah. And this is a simplified version of that. Had there been more of one color than the other, you guessed the opposite one.

So the Italian card game Scorpa, which is about SCOPA, if anyone's playing along at home. Which you were obsessed with. I do love it. I think if I tried to teach. Yeah, yeah, yeah, yeah. That's a deck of 40. So you've got four suits. 10.

Yeah, 10. 10 each. It's really nice. And what's nice is it's sort of a simple maths game, basically. There's different ways you can score points and you're sort of trying to, you're sort of trying to, get like the best number or best card in each hand type of thing. It's one of those ones that's harder to explain it is to play. You know, classic.

Like when I'm playing it, I always have in mind in each round, when each hand is dealt because you have several rounds in a game, I'm always aware of like, oh, hang on, we've used up all of the nine cards. Exactly, yeah. This would only be bad if they have a nine, but statistically they can't have a nine, and so I can play this card safely. I assume that's how most people play cards. But what you're telling me is this is also technically a form of card counting.

Card counting covers a lot of different strategies. What you're really doing is keeping track of what cards have been used. So you know the probabilities of what might or can't come up in the future. In terms of poker, it's generally true that the more complicated your card can, counting system, the more likely you are to make a mistake. Yeah. And that rules out any advantage you got from the more nuanced system. Oh.

So the standard add one or subtract one card counting system, it's the easiest one possible. Mm-hmm. I mean, technically it's one, zero negative ones. There's kind of three, you're looking for three categories of cards. But that's something you can keep a running total in your head and that will give you a mild advantage. Yeah. A sufficient advantage.

Yeah, I've come to realize that if I try and play poker, like, just statistically. It's not. I think I do Texas Holden as the version. Yeah. And that is not useful. You don't see enough cars. No, and you shuffle every hand, so it's not.

And some of those people really know how to rinse me. They rinse the cars and they rinse you. Yeah, yeah. Here's my final advice for Tristan. Look, Tristan, if you can stand around, watch as many as you can in front of you, and pick the opposite color to whichever. they were more of.

Yeah. You could start doing what they do in poker where if all the cards in front of you were all the same, so you have no advantage, order a cheap drink. And if there's a hot run of one color, order a more expensive drink. Yep, yep. Because then when you're more likely to win. But even if you see five in front of you on average, that's a 52% advantage. So it's not a big margin.

Like it's worth doing. It's fun. Yeah. And if you're a cafe running this, you're advice. your advice is either shuffle between each coffee purchaser or mix multiple decks together or I guess you could just be like you're guessing the suit. Or you could change what you have to guess. I personally would stick with one deck, red or black, straight through the deck and end

because you will encourage people to come in to try and card count and actually it's giving them such a small advantage. Yeah. Your increasing custom will more than cover. Like if you have a system people think they can try and get an advantage in, you'll get more customers, then you're going to lose giving everyone a 52% edge as opposed to a 50-50. If I was near a cafe where I got to play a, did you win? I get so excited when I go into a shop and they've got one of those spinning wheels and I'm always sad when they're not like, do you want to use the spinny wheel?

So I'm like, oh, do I not get to use it? Yeah. I see in places where you roll a dice and if you roll a sticks, you get your whatever free. Like, there's other ways of doing it. But I quite like coffee roulette with a deck of cards. There's a lot of fun. Now I just need to find a way of making this votemate emails. And then I might do them more.

Every email, just pick a colour and turn a card over and you reply or not. Ooh, oh my God, I'm actually going to do that. Yeah. I will report back in... Yeah, gamify it. In a few weeks. Yeah, you do that. Okay, done.

Now it's time for any other bufferingness? Yes. I'm speaking to your... You couldn't think of a better... I couldn't think of it. I don't know. This is normally the section in the show where we go through just updates, bits of information, other things, just little things we want to talk about. Yeah.

Very rarely do we have a theme. Yeah. For A.O.B. But previously, when I was talking about the 2A. Morse, Abba Fair Share sequence. Yeah. You put a call-out. Could you just recap the request you threw out for the listeners? So in that problem, it was about 40.

14 people choosing players for a team and what order they should choose in so that nobody has like a huge advantage over the others. And you clarified how best the method would be chosen, jumping from like the first person who chose to the last of all this sort of thing. And I said, as that is a pattern of a sort, it'd be interesting to know how that could be experienced via music or visuals. And the listeners heard you? Yeah. And they have sent us many, many options. Yeah, more like any other beatness, am I right? Aobabellness.

So, what do we go first? Back? We heard from Chris on Patreon. This was discussed in episode 140, which came out on the 10th of August. On the 10th of August. The same day. Chris responded to us on Patreon. They said, just to be the first, please suffer this completely artless rendition of the sequence.

Fill the speed, not the art. For 14 times 16 picks, which was for the teams, for the fantasy football teams, in D. Freigian using Mingus and Fluid synth. I don't know what these things mean. I bet they're like libraries for...

But I'm happy already. Making audio with Python. Okay, hear it out. That was pretty good. Do you see my face? That was the happiest I've seen you look in a while. That was so cool. I mean, you could hear the patterns in that.

Yeah. That's an interesting tonification. I really like that. That's great. I know you said it's artless, but that was, I mean, we've got, we've got like another 20 or 30 of these, so I don't know how they're going to do better than that. Okay, next one. Also on Patreon, pirate numbers is the name.

They say, if they're to like to be first, oh, you were second, you're so close. Here's 60 seconds of the 14 player sequence as piano notes, starting with C3. Oh, mate with certifiably terrible Python code. Yeah. This one's going to take longer. Okay, so it's slower. Yes, yeah, yeah. It's a different key.

That's nice. I don't know if a sample pack is the right description, but they're nicer tones, maybe. Yeah? Yeah. But it's interesting how people have created this using totally different techniques. I mean, I think of both cases with terrible Python code. I mean, I would like for more things to be made using Mingus and Fluentz.

Which I think you can get a cream for. Should we push on? We've got one from John has done theirs manually. Actually played it. Okay. This is our first non-co-generated entry. It's the same but less precise. I like being able to hear their fingers hitting the keyboard keys.

Yeah, yeah. There's something very endearing about this. Yes. And also, that's a lot of effort. to go to. Yeah. Good work, John. Yeah.

I mean, you're still going. Keep it up. Oh, what a flourish. Good work, John. Okay, Damien says as an engineer slash muso, they love the episode. So they threw together a quick demo that takes the sequence and maps it to different scales. So this was a collaboration between Damien and Claude. And then they did a bunch of tweaks for the final output.

So I'm guessing the way they mentioned in Claude, it's another AI. Yeah, Claude is like the, I mean, people will argue about this. It's probably the most common one used by programmers. Okay. Yeah. For code assistance. Which they said, it means it touches on both topics in the episode because we did talk about AI and the episode. Yeah, yeah, yeah.

That's a good point. Thank you, Damien. And they've made a website where you can pick your scale and the tempo and then it will play it. I will say as someone who made it very clear on that episode that I don't like AI. But also this has been used in a different way. I suspect it's not taking anyone's job. Let's just say the conversation about coding AI and generative AI are very different conversations. And I have a whole problem with the fact that we can't have one conversation without the other one showing up.

But anyway. Okay. Okay. Okay. Okay. This is a really good use of Claude to put together. Okay. That's all I need.

I'm convinced. Yeah. Clawed on the heavy lifting and you can see Damien's intention like they came up with this concept and made it happen. It's really nice. So I can set a tempo. It's set to 300 beats per minute. Let's go up to 360.

Why not? And you can choose a scale. Ooh, blues. Heck yeah. Let's do that. All right. Let's hear it. Okay.

And now I'm going to. going to click to a more sequence for 14 players. Oh, that's bluesy. The visualisation's a nice touch. Yeah, I really like it. Oh. They're so good. The visualization adds a lot to seeing the pattern.

So much. It's really good. And now I want 14 people to get together and do this as a dance. Yeah, yeah, yeah. If there's any choreographers listening, that is excellent. Check this link in the show notes used with what. Matt has announced as being totally ethically fine. I'm on the record. I'm okay with that.

Yeah, this is great. And I wish that it was being used for more stuff like this. Next one was done by Seta Laias, I think it's pronounced. That's their Reddit username. So on our subreddit, they have put together visuals, which is, oh, it's really nice. It's like a keyboard. We'll link to this below. but we'll play in now just the audio. And here it is. Okay, that's fun. Not only is the 8-bit thing like really nostalgic.

They do. There's noises, I think, they say. I love that. And I like the fact that's like, you can see them falling down as a visualization. That's lovely. It's got a real like 16-bit computer game vibe. Ah, good work. Finally, we heard from Theo, which came in to,

the problem posing page and Reddit because Theo wanted to make sure we saw this since Beck was annoyed by my problem travel ABC from episode 106 ah thank you Theo I decided to both try

to make up with her an annoying match for a change thank you wait a minute so I created the two a Morse track featuring Matt's excellent lyrics yes I was so I think so I would do it Matt sang Ababa bab Barb Abba Bab Abba Bab Bab bath. Thank you for talking pretty much in exactly 100 beats per minute. That's my policy.

It was a lot easier that way, though I think the danceability highly depends on the context and condition of the listener. It's mathematically correct. I beats per minute, hunch. Hunts. Hunts. Hunts. Hey. All right, there's a new mix for you. Theo does apologise for the low production quality. That's our policy around it. Theo, um, all, yeah. Producer Laura did just. I got a real offended look for producer Laura. Basically flip the bird to Matt.

Oh, and she's left. Theo says after a while I couldn't listen to it anymore, so I just kept it that way. Nope, fair. Great. And then Theo added, after listening to it the next day, it sounds really wonky, but I think that's because of the weird rhythm starting on the second 16th note. Look, Theo, you don't need to justify this. I apologize. Theo did say it could just capture the real Parker feeling of it not being quite right, which...

Well, well done. Theo, you're achieving your mission. All right, let's have a listen. Abba, bar, bar, barb, barb, aba, barb, abab, abab. Abba, abab, abab. Barb, ever, abe. You're enjoying this too much. He doesn't even begin to describe it.

I think it's beautiful. Sounds like the artist lemon jelly. Okay. Oh, what a finish. Theo, that was sensational. Two things. One, producer Laura, can that play us out for today's episode? Of course.

And now I think an excellent use of Claude would be to add a visual to that where your head is the little circles that dance in and out of the circle. The way that most coders use Claude is exactly the way you use our listeners. ship. You just voice prompt them. Make this for me. I know. And then I have the audacity to be like, nobody does their own work.

No one does their own work these days. Yeah. Yeah, yeah, yeah. Yep. I see it now. I see it now. Yeah, okay. Consider me humbled.

Well, thank you, everyone. I think we can ding the listeners for once. Heck yes. Incredible. Well, I'm afraid the Problem Squared program has Finally halted, and that's all the output you're getting from it this episode. We'll be back in the future, but thank you for listening to this one. Huge thanks to everyone who just joins in.

And an even bigger thank you for a lot of you who don't. Thanks for just listening. No, bigger thank you to the ones. And we like to thank our fantastic Patreon supporters, who, as well as getting access to exclusive content, also get the smug satisfaction of knowing that they make this whole podcast enterprise continue crunching. And we like to thank them by mispronouncing three names every episode, which this time shall include...

Junk. Junk. Rews. D. Y. Likers. A.I. Exandra. M and I. And finally, thank you to the pseudo. That's the command you use when you're like the top level authorized admin to install something.

You pseudo install or pseudo run. Oh. Producer Laura Grimshaw. That was the theme. I get it. From before the music. Ababa bar. That's wiped everyone's brain.

Dig us away. Matt. Abba barb, barb, aba. Barb, Abba, Abba, Bab. Have a barb, barb. He's so catchy. All right, back. We're in the room together.

Laura's handing over the Connect 4. Wow. It's been a while since we were able to physically put one in ourselves. And Matt's last go was the top metal. Right, the top there. Yes. And you're green. Yes.

I... I'm trying not to count them because this is what I would normally do at this stage. That feels like cheating. That could be card counting. But I am going to go for 3B. You've got to do it yourself. You're holding it. Oh, yeah.

Over there, huh? Yeah. Interesting. Ababaaba. You diggers.