Post-Mortem Analysis – Round 5

Link to Round 5 is here

Link to PMA Round 4 is here

This is a critical point of the hand. At the risk of sounding like a broken record, a lot can change when 10 cards are dealt simultaneously instead of sequentially. Moreover, once the stock is empty the effects of a bad draw can be catastrophic, or we could come up golden and reach a position where it’s virtually impossible to lose (unless all three blobs were impostors) – or it could be somewhere in between.

In this case, we got an excellent draw. The main point in these situations is not to panic at the sheer number of cards in the tableau. Careful analysis shows we can indeed remove one full deck of cards (including the Diamonds that have already been removed) regardless of the permutation of unseen cards. It’s not necessarily the best course of action, but at least we have a fallback if analysis reveals nothing better.

All three blobs wanted to “delay” this decision by not turning over any cards – and I believe IM Bartacus and IM Bug chose the wrong plan. They ended up in the following situation:

If we ignore the fact the newly turned over card in column 2 is a K of Spades, then we have three suits removed and two guaranteed turnovers. Now let’s look at Blue’s suggestion: “id,ai,ai,hi,hf,ha,ei,ea,gi,gj (h12=i8)” leading to this position:

This is much better. We can play fe,df,jd,jh,ie,fi,cg,cb,ci,(e7=h7),bi,ei,be,(b1=h6) to reach this position with four suits removed and also two guaranteed turnovers

No wait – in the actual game we get three suits removed and THREE turnovers. We weren’t allowed to count the fact the newly turned over card is a King of Spades (giving a home for the Queen in column 7) but we can count the fact we turned over something in column 2. This means Blue’s suggestion was not clearly superior to the actual continuation, and the team had every right to believe Blue was the impostor. Rot13(SHPX SHPX SHPX SHPX SHPX SHPX SHPX SHPX SHPX!!!!!).

Blue thought he was being clever, by using the Queen of Hearts in column 8 instead of column 6 (indeed using the Q in column 6 would be egregiously bad) but this turned out to be a miscalculation. To be more specific, the actual game continuation achieved one more guaranteed turnover at the expense of one more suit – and this is a good trade-off because the biggest danger of losing this game is if the next 2 or 3 cards are bad. There is little danger of losing because we removed too few suits.

In case you didn’t follow all of the above the TLDR version is rot13(Fcvqre TZ shpxrq hc).

In the endgame, Blue insisted on clearing the mess in column 8 early to avoid column 8 becoming a problem later. This is a good general principle:

KNOWLEDGE BOMB: From a position of strength, it is often wise to identify a “difficult task” and get it out of the way before it becomes a problem later (remember the dangers of one-hole-no-card).

The situation Blue wanted to avoid was this one:

This image is from the back cover of Steve N Brown’s excellent book “Spider Solitaire Winning Strategies”. When I saw this image, I immediately recognised it for what it was – most probably thanks to playing far too many games on a Spider Solitaire server that I am convinced is biased. If Steve played on that server, I would bet my Ph. D. thesis he would not have written the words “this game could have been won if only a little more care had been taken”.

Unfortunately for Blue, this knowledge bomb turned out to be unnecessary – the simple plan of turning over everything outside Column 8 was sufficient, even if the impostor were allowed to call the remaining face-down cards in column 8. My calculations say that ten columns in the tableau is just barely enough to get the job done (and I fully trust IM Bartacus and IM Bug are more than capable of reaching the same conclusion) and the actual cards were nowhere near the worst-case scenario. With winning reduced to a mere formality, Blue had no chance to redeem himself. He tried to inject a little humour by rapping in the Iambic pentameter but it was all in vain.

In summary, a great game with both Team Good and the Impostor having legitimate chances to win until the very end. IM Bartacus and IM Bug navigated most of the traps but let a few bad ones through, and the position looked desperate at one stage. But we managed to pull everything through in the end – until Blue had an absolute brain-fart, miscalculating a critical decision at the start of round 5 and giving IM Bartacus a good reason to believe Blue was the impostor. IM Bug tried to salvage the situation by explaining that “1 impostor” was written in red font and therefore the impostor should be Red. But my Random Number Generator app would have none of that and Blue was declared the impostor anyway on the tie-break. In the end, honours were shared with Team Good winning 100VP out of a possible 200.

3 thoughts on “Post-Mortem Analysis – Round 5

  1. Thanks for the further (and I assume final) explanations. I do understand that when you have lots of spaces is usually the time to pull apart a nasty, complicated column. And I do believe you about blue’s being the best plan at the end, as you are the GM and have proven you deserve your rank many times.

    But here was my thinking: if we use up spaces with two *known* rank breaks, then the chances of bad cards causing us grief are worse than if we take our pot luck with turnovers, where some might be bad cards but on average four of them will be better than just two.

    Here’s the rank frequencies at the end of the blue plan that you favor:

    Remaining: A 2 3 4 5 6 7 8 9 T J Q K
    15 left. 2 1 2 1 2 1 1 2 0 0 2 0 1

    Bad cards: 4, 6, 7, K (4 cards)
    Cards that temporize are A, 2, 5 (5 cards)
    Winning cards: 3s, 8s and Js (6 cards)

    I calculate (not analyzed thoroughly) that if the 2 turnovers are from the set 4, 6, 7 and king then we are stuck. Ace, 2 and 5 “temporize”, and 3s, 8s, or Js win it. If we get 2 bad cards before a good card, we lose. Very unlikely. Computing what possibilities of four bad turnovers there are on my plan is the comparison case and would be more difficult to compute. But one intuition was that our “temporizing” cards are more likely to fit together with four of them and temporize further (and make a bad card or two a temporizing card), even if the winning cards are buried.

    Decision 35 followed the plan of the humble students as best GM could make it out and we uncovered one card but somehow ended up with just 2 more guaranteed turnovers, so I don’t know where the other disappeared to. But it was long ago now and hard to trace. We will need a space for that king no matter how many good cards we have gotten.

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    1. Hi Bart, I have edited the Post-Mortem Analysis posts so they have been blockchained i.e. one can follow the links starting from Round 5. Let me know if you find this useful.

      Once again, congrats to you and Bug on a very well played game throughout 🙂

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  2. I can’t actually see what you’re referring to regarding blockchain. I don’t see anything new at the end of “Round 5” except “Victory”. I’ve never found the links between posts very helpful. The idea of a list of the titles of all the base posts (or all relevant to particular project, like this Among Us Lite) with a hot link would be nice. I think I can always fish the text URL out of the hot link if I need to. Older systems like blogger.com had that feature… list of base posts by date. “View all posts by spidergm” sounds promising but just seems to list the texts of them in one huge list.

    I realize now that the analysis I gave yesterday was in a level of detail that has gone by. You recognized that the two plans were close and didn’t said that blue’s plan would guarantee success, and didn’t say that ours was terrible, and recognized some small mistake in your presentation — and that’s good enough for a post mortem.

    For the third year now I’m having fun with “Advent of Code”, https://adventofcode.com/2021. I’ve forgotten how central programming is to your job, if I ever knew. But I’m doing this with basically a 1998 version of C++.

    I’ll be interested in what plans you’re considering for the next project.

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