An Interesting Decision in Round 3

In this post, I wanna discuss a very interesting decision taken by Bart in Round 3.

In the diagram below Bart’s last move was “cb” deliberately breaking an in-suit build on the basis it was impossible to turnover any cards. Ergo, he played to maximise the chances of getting back the empty column after dealing the next 10 cards. Before reading on, what do you think of this play?

Although I am not particularly fond of this play, I can see where Bart is coming from. From experience I know that once you achieve some lofty goal such as clearing a space or removing a full suit, the in-suit builds tend to take care of themselves. If you have sacrificed an in-suit build or two for some obscure reason and the card-gods are kind, you essentially win them back without really trying. No doubt Bart has figured out the same from his own experience at the Royal game. The main risk is after dealing 10 fresh cards you can’t do any of the wonderful things you intended because you need an empty column to procure an empty column. Bart calls this the “can’t-get-started problem”. Ironically, Bart did suffer this problem despite his best efforts to avoid it.

Knowing when to break in-suit builds is an essential skill for the improving player. The simplest explanation is “weight of sheer numbers”. Consider the diagram above. Suppose that, for sake of argument, there are 2,000 legal positions you can reach before dealing a new row of cards – but that number goes down to 100 if you add the restriction of never breaking in-suit builds. With a Suit-Break (S) versus No-Suit-Break (N) Ratio (R) of 20:1 it is at least plausible that our optimal play will involve breaking at least one in-suit build. I have discovered a truly marvellous list of many different reasons why breaking suit is sometimes useful, which however, this blog post is not large enough to contain. Fortunately, there is enough room for a picture, which is well known to be worth a thousand words.

However, I think Bart goofed despite his noble intentions. Ideally, I would like to simulate a large number of iterations of this position with an Artificial Intelligence, so I can be reasonably certain Bart’s play did (or did not) cost a sizable chunk of winning chances. Alas, Ninja Monkey only has the status of Artificial Stupidity so I have to rely on heuristics instead.

Lame attempts at humour aside, my instinct says Bart’s play is suboptimal for two reasons:

• Assuming we make a routine play such as “bc, fb” in the diagram position we have no less than five (5) clean columns with no face-down cards and a single sequential run of cards: a straight flush in poker lingo or “atomic” in Bart lingo. We don’t have to do anything drastic to have reasonable hopes of getting at least one space on the next deal.
• Bart’s play does not address what happens after we get back the empty column. The simplest play is “bc, gb,cg”. This gives us a “twelve-suit” in Hearts – every card minus the Ten – in two columns. If the Ten of Hearts appears in the next round we can entertain hopes of clearing the Hearts. Moreover, “bc,gb,cg” exposes a King when no other column is also headed by a King. This may be exactly what we need if any Queens turn up on the next round. We might be able to improve this plan further by tidying up column 8, which contains the K-Q-J of Hearts.

My recommended play from the diagram position would therefore be “bc, e3=i5, h5=i2, gb, cg” with an outside chance of completing the Heart suit. The chances of clearing Hearts on the next round aren’t exactly great, but at least I’ve made a start.

From experience I find that putting all eggs in one basket (e.g. maximising our chances of winning back a space in column 2) is almost never worth it. When 10 fresh cards appear simultaneously instead of sequentially a lot can change. We’ve all had games where we believed Nines were the worst card in the world and no rational sentient being could find a reason to like Nines and then we suddenly changed our mind when all the Eights and Tens appear in a single round. Reminds me of that Dr Seuss character who is suddenly enlightened and thanks Sam I Am for such a splendid meal. If I do get one-hole-no-card then I play on general considerations and let the cards fall where they may: if I cannot turnover a card then perhaps I can settle for freeing a Jack because no other column is headed by a Jack and there are several Tens unseen. Ergo, I still gain some value from a space, even if it is less than one turnover. I might make an exception if the game state were really bad and getting a space in column 2 was the only reasonable game plan (but in this case we are probably headed for defeat anyway). Or perhaps if the game state were really good you can justify going all-out to prevent an unlikely parlay (or “reverse Hail Mary”, pandering to Bart’s love of all things American Football).

Overall, Bart’s decision in round 3 was my only real criticism throughout the game and everything else was played at an extremely high level. Well done team!