Among Us Lite – Round 5

Link to previous round can be found here

Previous Moves

Round 5 initial position:

Ts9s8s7s6s5s4s3s2sAsJs/xxxx9c8s7c6c5d4h3d2hAs7s/xxxxxTc2cAh6s9s/xxKdQd3s/Qs6d/Ts4dQhJhTh9h8h7h6h5h4h3hKc/Ac5s/xxxxKcQhJhTh9h8d7c6h5c4c3c2cAcKhQcJcTd9d7d/KhQcjcTc9c8cKsQs2h/4c2s

Stock = 0, Suits removed = 1

Checksum: 11 + 14 + 10 + 5 + 2 + 13 + 2 + 23 + 9 + 2 + 0 + (1*13) = 104

Red: I propose we simply clear Spades with “id, ai, ai”, study the resulting position for a few more days, then choose the best way to remove suits and/or turnover our next card. If we still can’t decide where the next turnover is, there is always the option of clearing Hearts next.

Green: Yikes, this is too complex even for me. I like the idea of not turning over a card and minimising the chance of rot13(shpxvat hc) by trying to do too much in one day. “id, ai, ai” it is.

Blue: I wanna start thinking about Spades, Hearts and Clubs. Therefore “id,ai,ai,hi,hf,ha,ei,ea,gi,gj (h12=i8)”, study the resulting position for a few days then choose whether to clear Hearts or turnover a card. Of course If Bart/Bug insist on a turnover today then I won’t stop them.

Actual play (Decision 35, 22 Nov): id,ai,ai, if,bf,bj, eh,ei,bg,bh, (b2=f1), bc, gh, ca,ca,ga,cd,gc,ha,fe,ig,df,fi,fh,ah,af,cd,bc → King of Spades

Green: I’m voting “ca”. The missing cards are AA2334556788JJ. We can’t claim a lock but one or two more good cards should see us home. At least this decision is relatively straightforward.

Red: I prefer “ba” working on a column with only three face-down cards. The alternative “ca” duplicates Tens in columns 3 and 6 so the usual advantages of not shifting a King to an empty column doesn’t apply. Removing the Clubs costs an empty column – that’s too suspicious even by my standards … uhhh just kidding 😊

Blue: I like “ca”. We have plenty of empties, so our main concern is avoiding “one-hole-no-card” traps – and the best way to achieve that is to focus on columns with the most face-down cards.

Actual play (Decision 36, 25 Nov): ca → Four of Spades (Bart + Bug + Blue/Green)

Actual play (Decision 37): fi, cf → Eight of Clubs (Trivial)

Actual play (Decision 38): ca → Ace of Diamonds (Trivial)

Green: Be careful, with only one empty column the obvious “ch” would be embarrassing if we turned over an Eight. Better to sacrifice an in-suit build with “gb, he, ce” so we are well placed if the next card is a Seven or Eight.

Blue: Another alternative is “gb, (d2=h1), cd” which doesn’t lose an in-suit build. We can afford to bury the Q of diamonds since a Jack wouldn’t embarrass anybody – except the impostor.

Red: rot13(OYHR VF FHF). We are very close to completing the second Spade suit so we don’t want the 3 of Spades buried under an off-suit 2-A. I support Green’s “gb, he, ce”

Actual play (Decision 39, Nov 27): gb,he,ce → Five of Clubs (Green + Red + Bart + Bug)

Actual play (decision 40): ic, ei, ce (trivial) → Three of Clubs

Blue: Everything is lookin’ really great/except for one thing that I really hate/we might not be able to navigate/ to the face-down cards in column Eight/sort it out before it is too late/My final plan is now ready to state – “cf, ha, hc, (e1=h4), (c4=h9) he”

Green: I like Blue’s plan a lot, although his rapping in the iambic pentameter leaves much to be desired. The missing cards are A235678JJ. The flexibility in Column 10 means either Two or Five is a good card. I don’t see any way to lose even if Red were allowed to call the next three cards.

Red: Green is waffling too much and “ce,bc” looks simplest. Either we revert to Blue’s plan or we can remove the Club suit using the Four of Clubs in Column 10. That’s four in the corner. Four in the spotlight, losing its religion. Note that we were lucky because the last two cards gave us exactly what we need to complete clubs without shifting that pile of rot13(fuvg) in Column 8.

Actual play (decision 41): dc,jd,cj,ec,je,df (no card)

Green: Bart’s intentions are clear. Turn over all cards in columns 2&4 then trust that the game is won even if the impostor were allowed to call the remaining cards. I vote “be,bg,bi” regardless of what the next three cards are.

Red: I also vote “be,bg,bi”, but if we have N guaranteed empty columns regardless of unseen cards then we also turnover min(2,N-1) cards in column 4.

Blue: Interesting that Bart refused to turn over a card even though we were criticised for the same on Decision 35. In any case, let’s get this rot13(fuvg) over and done with. I also vote the same as Red.

Actual play (Decision 41b, 29 Nov): irrelevant

The final Moves

We have no trouble turning over the last cards in columns 2 & 4.

It is trivially easy to turn over all the cards in column 8 and the impostor has conceded “defeat” 😊

Among Us Lite – Round 4 Summary

Final position of Round 4

We’ve managed to clean up the Spade suit and are only one Jack away from shifting it onto the foundations. Hearts aren’t too shabby either. We have also turned over every face-down card in columns 1 and 10. On the minus side, we still 15 face-down cards in the tableau – and only one deal left. The game is not totally hopeless, but we would need some luck right now. I should point out Bart and Bug have done well to reach this position. For obvious reasons, I can’t discuss the specifics of where they went right or wrong at every non-trivial decision.

The other important issue of course is this one:

It is possible that neither Bug or Bart has any clue what’s going on. It’s also possible that both readers have every clue who the impostor is, but are not letting on – hoping to make my job tougher (it’s hard enough playing the role of all three Kolourfull Kibitzers). Or the truth may be somewhere in between. We shall find out in due course!

Google Docs – this is a test only. What could possibly go wrong? :)

Bart suggested I can use a google-doc so anyone can edit it. I s’pose I had better go with the flow to avoid howls of “Spider GM is SUS”.

Here is an embed link for a word document. Please bear in mind I am learning Google Docs for the first time, on top of attempting to mash up Among Us (App Store, not BoardGameGeek) with Spider Solitaire for the first time. At the risk of quoting someone else’s famous last words, what could possibly go wrong? 😊

https://docs.google.com/document/d/e/2PACX-1vRMTrc5RJAONMd64JyNbES_W1Lv9HlrT4LVMjTf6cZv6hSkDQw9V-3_CWKsDLaszkHNuqwzpwPKjQZg/pub?embedded=true

While I’m here, I may as well test if I can successfully repeat this for an Excel spreadsheet:

Please let me know if this test is successful, i.e. (1) Can you access these documents (2) Can you edit these successfully.

And we digress …

Here’s a video of someone claiming it’s the smartest he has been in Among Us.

I have no idea what’s going on, but for some reason I did find it amusing. I suspect I would be absolutely terrible at games involving social deduction, and Jack would be equally terrible at Solitaire card games.

WARNING: contains coarse language

Hopefully we can return to some actual Spider Solitaire content soon …

The six-point rating scale for evaluating other players

Hitherto we have focussed on improving our own game. Now is the time to turn the concept on its head and critique the play of others. Bwahhahahahahahaahahah 😊

If you’ve ever tried to improve at Spider Solitaire, no doubt at some point in your life you attempted to google search videos of other players plying their wares and (preferably) winning at the end. You probably also noticed that not everyone can reach the lofty heights of GM Jan Gustafsson killing it in Banter Blitz, crushing various chess players online while simultaneously trash-talking about irrelevant TV shows and what-not. I’m sure there are decent Spider Solitaire players out there, but that obviously doesn’t imply they know how to make high-quality videos.

Here is an example video of someone beating 4-suit Spider without rot13(haqb):

HOMEWORK:

For the following questions we will use the following six-point scale:

Part I

On a scale of 1 to rot13(ohyyfuvg) how would you rate

  • The difficulty of the hand (1 = hardest)
  • The strength of the player (1 = strongest)
  • The quality of presentation (1 = best)
  • Overall score (1 = best)

IMPORTANT: Do not attempt to justify your answers. This is intended as material for future blog posts. In other words, Now Me doesn’t wanna steal the thunder from Future Me.

Part II

Search for other videos of someone winning at the four-suit level without rot13(haqb). To avoid confusion the following requirements are specified:

  • Must be four suits
  • No rot13(haqb) – except for correcting obvious mouse-slips that don’t reveal face-down cards by accident.
  • Must win – no glory for a near miss, even if the hand is ridic difficult 😊
  • The complete game-play must be shown (e.g. no skipping the boring bits)
  • Do not play more than one hand.
  • A video is not DQ’ed for lame music, terrible jokes, swearing at every bad card or clumsy attempts at rick-rolling.

Answer the same four questions in Part I. If you found multiple videos, answer these questions for at most two videos with highest overall score only. Again, do not attempt to justify your answers.

FUN FACT: a bonne is a French term for nursemaid or housemaid.

Something different

In a previous post, I’ve had (legitimate) complaints about someone not being able to see images clearly.

It’s easy enough when I’m typing in the comfort of my own home, with my own PC that is yay wide and yay high (insert corresponding hand motions here). But my readers could be reading on mobile phone. The other issue is suits of the same colour can be hard to distinguish.

I’ve seen poker cards with four different colours, so Clubs become green instead of black and Diamonds are blue instead of red. I am not aware of something similar in Spider Solitaire programs (online or otherwise). Perhaps this is a chance for one of my readers to teach me something instead of the other way round!

Absent the possibility of four-colour suits, the next-best option is for me to transcribe a text version of the current game state – which you no doubt will have noticed in my previous post. Transcribing images seems to be the Done Thing in Puzzling Stack Exchange, which I have also contributed to.

Another problem I noticed over the years is if I type a string of numbers separated by hyphens then some devices may treat it as a phone number. This was back in the day when I was liberally using ASCII to encode rude words. But if I use commas instead of hyphens then things are OK. Similar considerations may apply to move sequences such as <ab,bd,gb> where each letter corresponds to one of the ten columns in Spider Solitaire.

TLDR version: the noble Spider GM is aware that he has goofed and is trying to make every effort to un-goof in future posts. Let me know if you have any other thoughts.

Easy Difficulty (Alternative version)

“I think that’s enough Peak Stupid for now.”

I am about to lead my students down the mountain, but Ninja Monkey does a quick head-count and confirms one is missing. Through my peripheral vision I spot one of the Bad Idea Bears standing in front of a magic mirror (which nobody has noticed before). Wait a minute, he seems to be poking his finger through the glass. This would violate the laws of physics, even by Peak Stupid standards – unless Peak Stupid was stupider than I had previously thought.

“Don’t do it!” I yell. “Don’t –“

Dweet

Not even Ninja Monkey’s extremely fast metabolism is enough to stop BIB1 from walking through the magic mirror. He is gone forever, unless I have the courage to walk through the same mirror myself. But with BIB2 reduced to tears it seems we have no choice. I hope it’s not like that stupid veil thing from the Harry Potter movies.

There’s only one way to find out if you pardon the terrible cliché – I tell the rest of the gang we’re not descending Peak Stupid after all.

“Okay Bad Idea Bear Two, I want you to stand approximately nine and three quarters metres from the mirror. On the count of nine and three quarters I want you to run at full speed towards the mirror and then jump into it. Don’t be scared, you can do it.”

BIB2 reluctantly agrees.

“One two three four five six seven eight nine NINEANDTHREEQUARTERS!!!!”

Dweet

I am the next person to go through the mirror.

Dweet

BIB1 is looking at some more board games, unaware of the gravity of the situation.

“It’s safe!” I shout. “You can come – ”

Hang on, I’m not sure if my fellow students can hear me.

Dweet.

BIB2 materialises in front of the other side of the Magic Mirror.

Dweet … dweet …. dweet dweet dweet … dweet (etc).

Several of my other students appear one by one, and I breathe a huge sigh of relief.

“Head count,” I tell Ninja Monkey.

“No need for that,” he responds. I counted exactly 50 dweets.”

Despite the Ninja Monkey having Asperger syndrome, the Animal Kingdom still values his contributions to society. I’m more concerned about the Bad Idea Bears. Uh oh, something is weird. We seem to be in exactly the same place (or pretty close to it) after passing through the magic mirror. There are board and card games galore, and BIB1 is studying Snakes and Ladders. Of course, it takes me less than 3 nanoseconds to spot my favourite card game in the centre of the hall. The cards are already dealt.

“This is strange,” says BIB1.  –“It’s the same layout as before except every snake and ladder has been swapped. Once you get past square 88 it’s all ladders to the top”

“This is also strange,” says the Stockfish. “Black has the 16 chess pieces and White has the 12 checkers.”

“But White has the first move,” says the Dumb Bunny. “Does that give him enough compensation?”

A rare lapse of character sees the Eagle accidentally knock a brown die (with numbers 2,2,3,4,5,6) onto the floor. He quickly replaces it on the Backgammon table.

Connect Four is even weirder,” says the sloth as he hangs upside-down from a chair. “For some reason the pieces float upwards instead of down.”

Minnie Mouse soon discoveres Texas Holdem is again rigged – except the Magic Eye trick only works on cards 5 or lower. If you hold any other cards then you’re good – unless of course the flop comes something like 2-4-4 rainbow.

Dweet

“Monkey, did you count correctly?”

“Actually, that dweet was a semitone lower than all previous dweets,” replies Ninja Monkey. “My best guess is somebody passed the magic mirror in the other direction”

And sure enough, BIB2 is missing.

Dweet

Before I literally know it, BIB2 is standing in front of the magic mirror again.

“Bad Idea Bear Two,” I say. “We need to talk.”

The Eagle is seated in front of the Spider Solitaire table.

“Before you play, I should warn you Spider Solitaire is rigged – but in a good way.”

“87,72,65,84,84,72,69,70,85,67,75?” says the Eagle.

“I expect the game would be significantly easier than usual – for instance the probability of three cards of the same rank appearing in any row of 10 cards will be significantly less than usual.”

“There’s a better way to test your hypothesis,” says the Eagle. “Can I win this hand without any supervision from you? If I win, then there’s a good chance your hunch is correct.”

I give my best student the thumbs up.

The Eagle proceeds wins, but not without a struggle (I would have beaten the 67,82,65,60 out of that hand much faster, but at least his play is fundamentally sound). The cards magically arrange themselves into a new starting layout. The Eagle proceeds to win four games in a row. Only on the fifth hand does he finally lose a game, perhaps due to a lapse in concentration.

All my other students take turns experimenting with the Spider Solitaire cards, and I am happy to let the eagle supervise events. Meanwhile I rest myself on the floor in front of the Magic Mirror, to prevent any more shenanigans from the Bad Idea bears.

THE END

 

Game over, we win!

Continuing from the previous post, the recommended action is

  • Clear the Spade suit
  • Exchange the 6-5-4-3-2-A of Hearts in Column 5 with the 6-5-4-3 of Clubs in Column 6.
  • Dump the 9-8 of Clubs in Column 3 into the empty column
  • Clear the Heart suit, winning back the empty column
  • Shift the Qh-Jd onto the Kh in Column 1, turning over a face-down card in Column 6 (and keeping an empty column)

Note that I went to the extra effort to clear a card in Column 6 rather than Column 5. This is because clearing cards in Column 6 is harder than Column 5 (especially since the Q-J are offsuit). As a general principle it is often wise to save an easy task for later and get the “difficult task” over and done with whenever possible – this helps avoid the embarrassing situation of “One Hole No Card” as alluded to in a previous post.

The resulting position is shown below, with the newly-exposed card redacted.

This is a lock

The astute reader may have noticed I violated the principle of procrastination by removing the Spade suit unnecessarily. This is because the game is in fact mathematically won.

To see this, let us consider all possible face-down cards (which we identified from last week):

  • Queen of Clubs: this can go “underneath” the Jack of Clubs (Jack onto Queen, winning an empty column, Q-J to Column 8, losing an empty column)
  • Queen of Diamonds: this goes onto the King of Clubs
  • Ten of Clubs: this goes onto the Jack of Clubs
  • Ten of Diamonds: this goes onto the Jack of diamonds
  • Ten of Hearts: this goes onto the Jack of Hearts
  • Nine of Diamonds: this goes underneath the 8-7 of Diamonds
  • Seven of Clubs: this goes onto the Eight of Clubs
  • Six of Hearts: we will count this as a “bad card” since the 7 of Diamonds is offsuit (and will counterfeit the Nine of Diamonds). This goes into the empty column
  • Five of Hearts: This is a bad card and goes into the empty column.

Note that the first seven cards are good, and we don’t even require an empty column to achieve the corresponding action. The only possible snag is there are two bad cards and only one empty column. But wait! If we draw both the Five and Six of Hearts then we can immediately place the Five on top of the Six. The net effect is to condense two bad cards into one – hence there is no snag after all.

Finally we also check that there is no issue with one-hole-no-card. Assuming we turnover all cards in Column Six first we will eventually get an empty column in Column Six and then we can choose randomly between shifting the Jh in Column 2 or the 9-8-7 of Hearts in Column 5 into the new empty column. Essentially we are “pretending” that all nine face-down cards are in Column 6.

It turns out the redacted card is the Seven of Clubs. The rest of the face-down cards in Column 6 are: Ten of Diamonds, Queen of Clubs, Queen of Diamonds.

The starting layout is shown below

Summary

This was a difficult game. The first ten cards were average, a minimum of three guaranteed turnovers, but two in-suit builds and no Aces or Kings. I only turned Four cards in round 0, but had an excellent Round 1 with several turnovers thanks to an empty column, but then got a catastrophic middle game with four Kings appearing on the same deal. Just when a loss seemed certain, I managed to find chances by clearing a complete set of Spades. I procrastinated by waiting until both Spade Kings were exposed so then I could decide which was the better King to remove. On the last round, I had three guaranteed turn-overs and realised all hope was not lost. I survived kadoban in the endgame and managed to win. I worked out victory was mathematically certain with only nine face-down cards remaining.

I hope you enjoyed playing through this game as much as I did.

Merry Christmas and Silly New Year!

Spider GM, Ninja Monkey, Ninja Mouse, Bad Idea Bears, all the other animals in the Animal Kingdom, individual playing cards, the two project managers, their team players, and anybody else who appeared in at least one silly story that I have forgotten would like to wish all Spider Solitaire players a merry Christmas and silly new year 😊

Coming soon in 2020 to a place near you: More Of The Same

Artificial Stupidity in Chess

You may remember some time ago I discussed an algorithm for Spider Solitaire that is not very good: it simply outputs random moves. It turns out somebody did a much better job in the game of chess. Some dude designed no less than 30 Artificial Stupidities and organised a Tournament of Fools, and published a number of papers in SIGBOVIK. Ideas for weird algorithms include color preference (e.g. White prefers to play pieces onto light squares), random moves, blindfold algorithms (simulating a novice trying to play blindfold), algorithms based on mathematical constants like π and e, single player (pretending opponent will pass) and linear interpolation between Stockfish and some other lousy algorithm (e.g. choose Stockfish’s best move with probability p, lousy move with probability 1-p. But my favourite algorithm was the Mechanical 68,79,82,75 that proved a forced win for Black after 1 d2-d4?? a7xd4!! checkmate 🙂

You can watch all the fun in the video below:

I’m not sure if these ideas will be applicable to Spider Solitaire. Color Preference is easy since we can prefer to move red cards or black cards, and single-player is even easier given the nature of the game, but I am not aware of any equivalent of Stockfish. Mathematical constants should be easy but probably not very interesting. It may be possible to simulate a blindfold (human) player who struggles to remember every card, but I’m, not sure how to do that yet. And I don’t know of a (sensible) variant of Spider Solitaire where all the red cards are replaced with chess pieces. Since Western chess has Black vs White, it may be more appropriate to use Xiangqi, which has Red vs Black pieces. Perhaps something to think about for next time.

Thanks to my good friend Tristrom Cooke for the heads up.