# Game on (14 Jan)

This is the position from last time

The bad news is pretty clear: we got two much-needed Tens but it’s only enough to temporarily recover the empty column before needing to use it immediately. On the plus side, I now have a new reader (George) following my blog. George readily admits to not being the best player on this planet, but he writes in an engaging style and seems like one of the Awesome People.

Bart identified several options. To save space I will use the letters a-j to denote columns

• <fj,fj,bf,df,bf,eb> to maximise the chances of getting an empty column next time. The problem is exposing an Ace, which is not what we need. Also, we need to think about turning over cards, not recovering the empty column and ending up where we started
• <fj,fj,bf,gb,dg,dg,bg,eb,cd>
• <fj,fj,db,db,cd,cf> turning over a card.

It is interesting to note that despite having only one guaranteed turnover, there are still a large number of reasonable options to consider.

My preference was  <fj,fj,db,gd,gh, bh, dg, df>. Note the use of two supermoves and breaking off-suit hoping to clear up stuff in column 2.

The Two of Diamonds in column 4 is especially useful since it enables us to shift the Ace of Spades in column 3 if need be. If the next card is a Three or Seven then we might have a real chance.

We turn the Four of Clubs. Not the best card, but at least the Two of Diamonds allows us to shift the Ace in column 3, uncovering the Five of Clubs, and hence an in-suit build. Of course, a Three would no longer allow us to get back an empty column.

We get a Ten and Queen in column 4, but unfortunately in the wrong order. Here I avoid shifting the J-T-9-8 of Spades onto the Queen. We need to get back an empty column and exposing an Ace won’t help our cause here. It would be different if there was the prospect of eliminating the Spade suit, but we’re not even close. Time to deal another round.

Clearly this is a good deal. We have two easy empty columns available. But we also should start thinking about clearing suits. Just because no suit has all 13 cards visible doesn’t imply we shouldn’t worry about completing a suit. Also note that the tableau has 19 face-down cards, but only three of them are not buried by at least one King.

At this stage of the game, being able to visualise many moves ahead is a must for the serious player. Here are some useful practice questions:

• What is the longest “straight-flush” we can obtain if we weren’t allowed to turn over any more face-down cards? (for instance 7-6-5-4-3-2 of Hearts would be of length six).
• Can we guarantee three empty columns if we weren’t allowed to turn over any more face-down cards? Obviously these would be columns 2,4,6.
• What is the minimum number of guaranteed turnovers?
• What is the minimum number of guaranteed in-suit builds? Of course, if we get enough in-suit builds then completed suits might suddenly materialise by weight of sheer numbers 😉 More often than not, players have to earn them especially at the Four-suit level.

## 4 thoughts on “Game on (14 Jan)”

1. Bart Wright says:

Something has gone wrong in terms of the pictures matching the text. Quite possibly it is in my version of things, but in either case I can’t go further without resolving it one way or the other.

It looks like your picture in this post repeating the situation left at the end of last time is correct. That’s not the problem.

However, in your preferred sequence this time,

fj,fj,db,gd,gh, bh, dg, df

I don’t see how you can do your 5th move “gh”. G at that point has KQJ, with the Q and J different suits (hearts and diamonds). “h” has a king of hearts. You can’t move the Q and J together. Trying to salvage this, the next move would work if the J of diamonds wasn’t there so you would have a queen showing in h to put the jack of clubs onto and then the rest of your plan would work — but the jack of diamonds is there, fouling up the works.

At least that’s how it looks to me. Quite possibly I missed something.

My plan for now is to ignore the past and look at the new problem you pose on its own terms, because the present is what it is…

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2. Bart Wright says:

I think I see my problem now. You have an empty space so you can move the J/Q in two steps. The jack of diamonds is in fact on column h and when you move from column b you are just moving a 10, and not the 10 and Jack together. At least that’s the way it looks now. Sorry for misunderstanding before. 🙂 So you could zap this post and the previous one with no harm to the dialog…

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3. Bart Wright says:

Agreed this is a very good deal. Good enough to allow a win? I’d still say odds against.

In answer to your question about getting a third space, the answer is yes, you can. With “gi” we free up a queen. Column b simplifies to a j-8 sequence (using our 2 spaces) on the queen.

As for the straight flush, this problem stretches my thinking ahead abilities. I do not think we can get Jack of clubs down through 2 of clubs, for a 10-card straight flush. If I haven’t made a mistake, we can get a 7-card one. In sketch form, you first make your 3 spaces — one critical detail is to move the 3 of clubs from c to h before moving the two. Then you need to put the 2 and 8 from the long column into spaces, leaving you with one left. Now we are trying to do housekeeping with 1 space, which is often tricky. We then use the 6 of spades as a steppingstone (Ace of hearts wiggling back and forth as needed), to shift the 5 of clubs from c to e. So now we have 8 of clubs through 2 — a 7-card sequence.

It is close that you might be able to use your single space to assemble the J, 10 and 9 of clubs into a sequence on column g and then move the 8-2 sequence onto it, creating a 10-card suit. My think-ahead powers don’t go that far out reliably. But doing it just now, I find a 89 of diamonds on one pile and a 8 of hearts/9 of clubs on the other, and no way to swap them with one space. Steppingstones are long gone. You can’t even start on this before the 2-8 club thing because that 6 of spades is a vital steppingstone, and you can’t move the 5 of spades onto it until the long club run is formed, so the ten of clubs is stuck and we have to do all the JT9 of clubs work afterwards with a single space.

If I could do this 10-card flush on balance I probably would, though there’s a decent case to be made against. (I wouldn’t do the 7-card flush if we can’t get to 10.) We have a king of clubs free, so if either queen of clubs AND either ace of clubs came up on the deal we could remove a suit. What would that get us? The rightmost king of clubs disappears, covering a nice spade sequence and potentially letting us get at 4 unturned cards.

Back to the “what longest flush can you make?”, if the 10-card club flush is not doable, we still have a 7-card one, which is better than any alternatives (there’s 8-K of spades (6)).

As for minimum cards to turn, I say the answer is “3”. We have 3 spaces. We need to use one for the 6 in column c. We can put whatever comes up in the 2nd free space, and whatever comes up there in the third.

Number of guaranteed in-suit builds — meaning joining 2 in-suit sequences (of length possibly one) that were not joined before? Not an intuitive statistic to me, but I’ll try listing the lower card of a 2-card fusion I think we can create. I am NOT considering what you can get if you put things in spaces, because I don’t think it’s worth it for any of them in this situation.

Hearts 9, 8,
Diamonds 8, 7,
Clubs: T, 9,

That’s 8 total.

As for what I would actually do in this situation, if we can’t do the 10-card clubs (and I don’t think we can), it is to make the 3 spaces — the process of making them improves order in general. I’d do a couple other tweaks to remove suit breaks. But then I would start uncovering cards from column c by putting them in spaces, one after another unless a new card gives me a new option. We’re hoping those extra 3 cards can let us keep going now, but if not together with the 10 coming up we hope they will allow some good things to happen.

We still need some good cards to help us out of this mess, so aggressive play is better than trying to make our spaces easy to recapture next time.

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4. Master T I thank you for the kind words kind Sir.

Can I just stick to the homework answers today and not let my thoughts roam to such things as trying to not think of elephants? Perhaps, but I think not. I would refer you to Mikhail Nejémievich Tal and his hippopotamus problem.

What is the longest “straight-flush”….?
6 and I think I can do it in three suits. Clubs thwarted my grand slam.

Can we guarantee three empty columns…?
Yes

What is the minimum number of guaranteed turnovers?
2

What is the minimum number of guaranteed in-suit builds?
If indeed I can do a six card diamond straight flush in Col 8 like I think I can that would give us 7. But I’m thinking that when you have the three open columns in route to the diamond jamboree you should be able to seize the opportunity and hook up the J, 10, 9 of clubs and then still do the six diamond run. If so that would be 9. But that apple is just out of my reach.
So my answer is “I don’t know” but I would not be surprised if some folks reached double digits.

Now to post this and read what the adults have to say.

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