# Game On (30 May 2021)

We continue our game from last week. Last time I asked what is the minimum number of face-up cards we are guaranteed if undo is allowed and we don’t care about losing 1 point for every move or undo?

Not surprisingly Bart and George found the correct answer of six cards (it wasn’t meant to be difficult). With the help of undo we can see what’s beneath the Queen of Hearts, the two Jacks and the three Tens. One can also argue the correct answer is 56 because we get to deal all cards in the stock and then undo – or perhaps even 66 cards if we count the ten cards that are already showing.

Nitpicking aside, our card-tracking now looks like this:

It should be pretty clear we can improve on our 66 exposed cards. But given we know so much information it might be possible to complete a suit by force! Here are some questions to ponder:

• Which suits have all 13 cards appearing at least once?
• Assuming you answered “more than zero”, can we actually remove a suit (regardless of identity of face-down cards)?

## 2 thoughts on “Game On (30 May 2021)”

1. Master T, I have just pulled an all-nighter working on this so I do not feel very witty right now. Perhaps I will just post my findings without going into the digress mode.

I only hope that I correctly copied the present position into my AncientExcel CheeterSheeter. But the truth is that even if I have the Data wrong, this was, for me, a good solve.

There is a run in Diamonds available:

Deal – Do Nothing

1st Draw – ed

2nd Draw – hj, hf, dh, da, eb

3rd Draw – fb, hf, cg, eg, ig

4th Draw – ja, ji, ji, jd, fj, eg, fg, ei, gi, ga, ch

5th Draw – da, ad, ab, ib, ab, jb, af, aj, aj, ij, fj, hd, hj

It looks so simple and neat when printed out, only 35 moves. But it was a long trial and error happening. About 5 hours. Use of the Z-Key numbered in the thousands.

Forgive my boldness for asking, but, Master T, can you see this far ahead and work out this solution in your mind? You must have known there was a successful suit build or you would not have given us this task. I could never ever ever hope to carry this in my mind.

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2. Bart Wright says:

5/30/2021

“But given we know so much information it might be possible to complete a suit by force!”

What is the alternative to completing a suit by force? By finesse? I think perhaps you mean that we’re investigating whether we can build a suit given what we see even if it would be a really bad idea for winning the game overall to do repeated deals without even trying to expose more cards.

Yes, we have all the blues. It does look promising. After the first deal we can build JT in column 3, and 7654 in column 1. After the third deal we can build KQ in column 10, and add JT from column 1. The remaining cards we need are 9832A. A copy of all of those except 2 is available in the 4th deal, and the 2 has been lurking since deal 2. I don’t have the stamina to map out in my head exactly how to put it all together. I don’t think we will have to do the 5th deal.

As for one feasibility check (heuristic), the counts of ranks through the 4th deal are:

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

There are no dramatic excesses or shortages of any given rank. We’re 2 short on homes for wandering 2s, but the ones in column 4 and 5 do not have to be moved once they come up. We’re not more than 1 short for any other rank.

So if I was a middle manager, I would tell upper management I am confident my underling can get the job done, lol. Not that I could prove it.

As the underling, thinking about a few more details… Build that JT in column 5 instead of 3. Columns 3 and 4 will rapidly become unusable because of the pair of 2s that will show up in each. After the 2nd deal, in columns 9 and 10, get the queen of spades into column 9, so in deal 3 the blue queen falls onto its king. There are plenty of homes for the 4/5/5/ that will fall in column 5 so we can dig out the JT from there. Similarly enough homes for the 5/2/6 in column 1 to dig out the 7654 we built. We need to clear the blue 2 in column 3 before the 4th deal. Plenty of homes for the 6, then the ace falls right on the 2. Then at the 4th deal, easy to expose the queen in column 10, bring in the JT from column 5, pick the 9 and 8 right off the top of their piles, take the 7654 from column 1, then the 3 and 2A are in plain view. Presto! Suit removed. The underling is to some extent mumbling to himself as he explains this, which is one reason he’s still an underling, but when the cards show up he can actually do it.

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