Math Mayhem: Scrabble Endgame Edition!
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- Опубликовано: 3 окт 2024
- I always talk about how math is such a huge part of top-level Scrabble strategy, and today I have just the perfect position to prove my point. In today's video, I'll be attempting to dissect a fiendishly complicated situation I encountered at a recent tournament game against my good friend and fellow expert, Andy Hoang.
To navigate the maze of possibilities, we'll need to get through some combinatorics and probability and -- a fan favorite -- the amazingly counterintuitive idea of passing your turn. Did I make the right play? Did Andy? You're not gonna want to miss this one, so watch to find out! 
Игры
Re: the odds of Andy having the J being 7/9. You don't need to compute the combinations of 9C7 or 9C2.
Think of it like this: there are 9 places the J could be. 7 of those places are on Andy's rack, and 2 of them aren't. Each place is equally likely.
Came to the comments to make this exact same point. It's amazing how often combinatorics can be much easier or harder depending on the direction you approach from...
This would never work against a human, but I played a funny game the other day where I swindled a bot by passing in the endgame. I was down by 75 with AILERON/ALIENOR on my rack but no playable bingos, but after I passed, it handed me A(C)ROLEIN as a 149-point out-triple-triple. The best part is that according to Woogles's analyzer bot, the two best moves after my pass both lose the game in this way, and the third-best gives me O(V)ERLAIN for 158 instead.
Haha that's awesome! Exploiting HastyBot can be oddly satisfying :D
If there’s one thing I’ve learned from tournament Scrabble, NEVER take a triple digit lead for granted. I’ve lost a 200+ point lead before. It’s devastating.
Also: Andy is a beast.
Less than a week ago I won a tournament game after being down 150 at the start of the pre-endgame. It's crazy when it happens, you just have to play to your outs
@@itchy7879Congratulations! It seems insurmountable but when you hear your opponent exchange tiles and then you bingo the adrenaline returns!
@@itchy7879 That's awesome! If it was a super creative or notable play email it to me, maybe I'll make a video of it :)
100%. Obviously you'd always rather be up 100 than down 100, but it's never over til it's over!
I'd like to think I would've played BE in that situation -- at least if I wasn't short on time. PRISTINE isn't that challenging to spot with that pool after all. However, I wouldn't've been able to calculate all of the odds per potential play, and I would never have had a lot of confidence in it being one of my best options available.
My logic would just have been "plz plz I need a triple-triple... ohh crap he might block.. omg I need to fish while preventing his blocking play". My thinking would not have gone any further than that, and I would probably have tunnel-visioned on that 3x3 being my only chance of grasping victory from the jaws of defeat.
To be honest that's about as far as I got during the game! I didn't generate PI as an option, so I never bothered to calculate the odds as I didn't have anything to compare BE against. I did see ZAP but was able to determine it was going to fall short, and I understood that BE won when I drew the N and Andy had the J, so I went for it.
I love positions where its best to pass, theyre always so interesting to me. Great video!
Me too, they're rar\e but super fun when they come up. Thanks for watching!
great play by andy and great analysis! cool to see you share this -- there are so many beautifully calculated fishes that we don't hear about because the RNG didn't work out. glad to see this one make the channel!
Thanks Ben, glad you enjoyed it and appreciate your support!
This is so cool. I love when you explain your thought process in extreme detail. It is so interesting
Thanks so much, really glad you enjoyed it!
Mack is ridiculously smart lol I'm curious what your thoughts were during the actual game. I'm assuming you did all of these crazy analysis postgame? All of this math is great, but if it's not practical, it's not actually useful.
He's ex quant, not surprised he's cracked at math!
Yeah pretty much all the ramifications of BE I understood during the game (i.e. that I needed an N and that Andy could pass if the J were in the bag), I didn't calculate the odds though as PI didn't occur to me in the game. I saw ZAP but quickly realized my bingos were going to fall short and dismissed it.
Since math is scary to a lot of people, you can get away with math phonies sometimes. I once played ARCSINED* and my opponent said "I know you're a mathematician, so I guess I can't risk this one."
People also sometimes don't know their greek alphabet. They may know EPSILON is a real word, but not the less-used-in-math-and-stuff UPSILON, and maybe challenge the latter thinking you're making stuff up...
Thanks for showing this game. You mentioned it on a comment of mine in an earlier video, so it's nice to see how it played out.
Thanks for reminding me of it!!
Super interesting position! I love these ones where the only winning move is to pass.
Same!
Would you say you are better with words or math
Good question, I'd have to go words if you made me pick (after all, I've learned every word 2-9 letters, which maybe a handful of other people in the world can say). There are waaaaaaaaay more than a handful of people in this world better than me at math haha
@@mackmeller thanks
I have a silly question. I watch a lot of scrabble videos, but I haven't played since I have memory.
If you play BE and Andy has the J... can't he exchange the J for whatever is left in the bag and win?
Thanks for watching! He can't since exchanging isn't allowed with fewer than 7 tiles left in the bag.
What happens if Andy trades 1?
He can’t trade since fewer than 7 in the bag!
And the odds of losing on time are......
Your difference of two squares formula in the thumbnail is wrong 😭😭😭😭😭
Haha yep, admittedly I stole the thumbnail from an images search and didn't bother to check every formula 😂
ok but what actually happened?
It's at the end of the video! I drew the J and Andy smartly passed and won the game
Scrath
Correct me if I'm wrong but it's not just the probability that opponent draws J, it's the probability he draws J AND he didn't draw both Ns. So it should be 1 - 9/36 = 3/4.
That's covered in the chance of Mack drawing an N, because it's 2/9 and not 1/2 or 2/2.
It's maths btw ;) and JA is legal in SOWPODS, +1 to the uk :) Obviously it's maths unless you want to argue you study "stat". Not sure it's combinatorics you mean either, it's probability? Combinatorics is about counting permutations and arrangements not probabilities?
math vs maths is just a regional thing, neither is definitively correct
@@Mr.D.C. Both are legal in SOWPODS of course. I bow to your superior knowledge of stat anyway.
The process of counting winning draws definitely falls under combinatorics.
@@almightyhydra no it's just probability? Combinatorics is like how many tree graphs you can draw with N nodes and stuffs. And colouring in theorems etc. and graphs/networks etc. What would I know though with just my degree in maths including 1 year of combinatorics (which was the easiest 3rd year course I admit)
Combinatorics = counting how many things exist
Probability - how likely is a thing that exists (may exist I suppose) to happen
more like MATH Meller 😂🤣😛
hahaha