Continuing from last week

Recall that we can remove a full set of Diamonds. There is a hidden catch I didn’t mention from last week. Removing Diamonds would imply we uncover no less than three Aces. There are exposed Aces in columns d,g,j. Any experienced player knows that too many exposed Aces can kill a game (perhaps even quicker than Kings) because nothing can play onto an Ace. Too many Aces exposed means a restricted set of legal moves at every stage of the game and the only way to fix this is removing a complete suit or dealing a new row of cards. One of these is usually not desirable and the other is difficult to achieve. I’ll let you guess which is which 😊 In any case we know that there will always be a full set of Diamonds exposed no matter what turns up on the next deal of cards. I decided to gamble by turning over a card column c even though I am no longer certain to remove Diamonds. I exposed a Two of Spades.

Next is the Five of Diamonds. We shift that onto a Six and reveal the Eight of Hearts. We are forced to deal another row of cards:

Well that was awkward. We have three Fours and no Fives. Perhaps I should have removed Diamonds while I had the chance, but on the other hand chances are I would not have liked those ten cards no matter what I did.

This raises an interesting point: if you were paying attention you might have noticed I am playing “Spider Master” instead of “Spider Random”. Since Master is the “intermediate level” of all Four-Suit games (the levels are Expert/Master/GrandMaster) we do not expect an easy ride. We started with some good luck in the beginning and therefore we were due for some bad luck. Under normal circumstances, this reeks of “Gambler’s Fallacy”. But given that I did not choose “Spider Expert” or “Spider Random” I will stand by this judgment. Needless to say, Whinging About The Injustice Of It All is not a recognised strategy by the experts, so how would you continue?

Continuing from last week

This is a reasonable set of 10 cards. We can obtain no less than three empty columns – if we so choose. But what do we do for an encore? Recall that an action ends when we expose at least one more card, so getting an empty column doesn’t cut it for an advanced player. Column ‘b’ sounds like the best source of new turnovers since any other column requires us to spend at least two empty columns. So we have three guaranteed turnovers since there are three empty columns and at least three face-down cards in column ‘b’.

We should also start thinking about removing suits. There is no suit with all 13 cards visible, but we can “threaten” to remove a suit or two. The Six of Spades is a nice card since it enables us to complete a run from King to Three. We can also guarantee a run from King to Five in Diamonds. With the 3-2-A in sight we have a “twelve-suit” with only the Four missing. With 30 cards in the stock and 15 in the tableau it is heavy odds on the Four of Diamonds will be found in the stock (recall there are two decks so the odds are better than 2:1). Unfortunately, building these partial runs will imply a reduction in our minimum guaranteed turnovers. I guess one could compromise, e.g. turn over one card and still retain options of building partial runs. So there is plenty to think about and it is difficult for even an expert to find a “definitive best play”.

Another consideration is that we have had a relatively easy run so far, so we might expect some “bad luck” given the hand is not random (we chose Master level). The initial row had 5 turnovers, and both rounds 1 and 2 have at least 4 turnovers (pretending they are the start of a new hand). So I won’t be surprised if something unpleasant happens on the next round of 10 cards. I guess if the next round is e.g. all odd cards then we probably can’t do much about it anyway. So we will cross that bridge when we come to it, if you pardon the terrible cliché.

At this stage of the game I will not give a sequence of moves but simply give the resulting diagram and leave it as an exercise for the reader to verify this diagram can indeed be obtained from the initial position.

The Jack of Hearts is a good card giving us an easy move that even my Dad can’t 70,85,67,75 up.

<bc> 8c

That’s a nice card. Shifting the 5s onto the 6s gives us a suited build, an empty column (Q of Hearts onto K of Diamonds) and a turnover (8c onto 9s). Nice!

<bi> 4d

Note the use of procrastination. We can always get our empty column back.

<bg> 9h

Aha! We drew a Nine so we retrieve our empty column without having to commit to <ed>. We might choose to empty column ‘j’ – this allows us to connect the 32A in Diamonds and recall that we have a twelve-suit in Diamonds with only the Four missing – no wait up, we just turned a Four of Diamonds two moves ago. Things are looking good!

Exercise for the reader:

• Can we complete a full suit of Diamonds?
• If yes can we procrastinate? i.e. can we turnover a new card (not necessarily column ‘b’) and still retain the option of removing the Diamonds?

Continuing from last week, we had the following position

We have only one guaranteed turnover. Let’s hope its a good one.

< gc, ab, jb, ef, if, hf, dj> As

Note that I deliberately broke the 7-6 of Clubs in column ‘i’. This is because if we expose an Eight then we get an empty column. The down-side is of course if we don’t draw an Eight then we are stuck with one less in-suit build then we “deserve”. This type of trade-off is typical in the middlegame. It would be nice if we could ensure (1) any Eight wins back an empty column and (2) we don’t lose any in-suit builds. Unfortunately I can’t see any way to achieve this.

Another reason for breaking the 7-6 of Clubs is I can arrange ten out of thirteen cards in Spades in a single column. From experience I find this increases the chances of completing Spades when the missing cards finally do come out. This type of “advanced” consideration can easily outweigh “basic statistics” such as the number of in-suit builds.

Finally we have to decide which of the four left-most columns to turn-over. I chose column ‘d’. I turn over an Ace of Spades and must deal a new row.

As usual, whenever a new row is dealt it is wise to study the game state in some detail before making any moves.

• Do you think this is a good set of 10 cards under the circumstances?
• How many guaranteed turnovers do we have?
• Can we complete any full suits? Yes, No or Not Even Close?
• How would you continue?

Continuing from last week

I hope you understand the notation by now; if not please refer to previous posts.

<ch,ic,hc,bf, cb> Ks

<jc> Jc

<ba, bi, gb> 9c

<be,gb > 6h

<ai,ga> Qs

<jg> Ad

<fa, cf> Qc

Now is a good time to take stock and assess the position. Clearly we are doing very well with only 16 cards face-down in the tableau and four rounds left in the stock. We have one “implied” empty column since the Ace of Diamonds can play onto the Two of Hearts on the left. This is worth one turnover in any of the four left-most columns. We also note that:

• There are only four columns containing at least one face-down card. This is good news when playing for empty columns, but there is a new danger: the possibility of one-hole-no-card. It’s not an immediate problem since the cards in columns b-c-d are “clean”, but it’s still something to bear in mind.
• We are not close to completing a full suit. This can be “blamed” on having so many unseen cards in the stock, but it sure beats having so many unseen cards in the tableau! Spades and Clubs do look promising with only three cards missing.

So it seems our strategy should be to keep trying to tidy in-suit builds and expose as many face down cards as possible. I generally find once all cards in the tableau are exposed, the complete suits will take care of themselves (barring a series of major accidents). But if you can’t expose all face-down cards then you have to “earn” your suits. How would you continue?

Continuing from last week

We have two guaranteed turnovers and there are no tricks to improve that. At least we get some in-suit builds. We also have the ability to connect the K-Q-J-0 of clubs (an action we considered last week, but rejected)

<be,bc,eb,hc,ij,bi,be,fb>  Js

<je,fj> Ac

<fc,ib,ij,ih> 6d

<ig> 0s

<e2=h1, ih> 4s

<gh,gh> 7s

Our position has improved considerably. We have turned over 6 more cards and we still have two empty column and two turnovers.

You may be wondering why I shifted the King of Diamonds onto an empty column. This is an example of long-term planning: We have to shift the king sooner or later and it’s easy to do so when there are plenty of empty columns to go around. Note also the column contained an off-suit K-Q combination so if we only had one empty column then it would be difficult to shift it later. For the same reason I chose not to shift the K-Q of clubs in column ‘b’. I am essentially trying to guard against the dreaded “one-hole-no-card” scenario in the future.

I also took care to swap columns ‘e’ and ‘h’. This is because an in-suit Q-J of Hearts will be easier to shift if a King later appears at the right moment.

The question of when to dump a King onto an empty column is difficult to answer (let alone explain to someone like Captain oBVIOUS). Until you gain more experience (or epiphanies!) a good general guideline is the following:

• If you find yourself unable to turn over a new card despite having one or more empty columns then chances are you are not taking maximum advantage from a position of strength.

Yes, there will be occasions when you have a rough start and have to fight tooth and nail just for an empty column. Then you find there is no real opportunity to avoid one-hole-no-card. But that means you never had a position of strength to begin with.

The above guideline does not refer to Kings specifically. Consider dumping a King onto an empty column when:

• You are afraid of one-hole-no-card, or
• You still have reasonable chances of recovering an empty column (a different empty column unless you can complete a full suit!)

Anyways back to the game. What would be your next action? (Hint: tidy up in-suit builds using reversible moves first!)

Here is the position from last week

The first order of business is to shift the J-0-9 in Column ‘c’ onto the Q of Clubs. This illustrates the concept of “duplication vs diversification”. We already have three exposed Queens so can easily afford to use up one of them. But we don’t have an exposed Four. By diversifying we give ourselves more opportunities to reveal cards since any exposed Three can later play onto the Four of clubs. Even if we don’t expose a Three we also get the option of shifting some junk in Column ‘a’ (one empty column is not enough to shift the 8-7-6-5-4-3-2 without some “stepping stones”).

Note also that procrastination is not possible. Any legal action must spend our only empty column, so we must make the choice now: shift the J-0-9 or leave it – and all the signs point to the former.

We next shift the Jh-0s-9s-8s onto the Q of Hearts using much the same reasoning: procrastination is impossible, we build in-suit with Q-J of Hearts and again diversify, exposing a Ten. This Ten is especially useful since it gives us an option of shifting the 9h-8d-7d even if a bad card turned up.

The next order of business is to look for opportunities to “tidy up”. We have 8d-7c and 8s-7d in the first two columns which suggests it may be possible to build in-suit with 8-7 of Diamonds. It turns out this is possible, using “stepping stones” in columns ‘c’ and ‘g’. Note that we have to temporarily break up the 7-6 of Clubs to achieve this. Also observe that we can now procrastinate in column ‘a’ since it is possible to shift 8d-7d onto the Nine of Spades after using up the empty column.

At this stage the obvious choice is to shift the Two of Clubs onto the empty column, since that takes care of the last hidden card in Column ‘e’. This would improve our chances of winning back an empty column on the next round.

An advanced player might consider filling the empty column with the Q-J-0 of clubs. The reason is we already have a King of Clubs exposed, so if things go well it might be possible to exchange the Q-J-0 of Clubs with the Q of Hearts in Column ‘b’ without fear of losing the empty column. Unfortunately it is not possible to connect the K-Q-J-0 of Clubs immediately without compromising our position – no wait up, it is possible! We can shift the J-0 of Diamonds onto the Queen of Spades, then shift the Jack of Hearts plus 0-9-8-7-6-5-4-3-2 of various suits onto the other Queen of Hearts, which means we are not losing an in-suit build after all. Then we dump the Queen of Hearts onto the empty column and move the Q-J-0 of Clubs onto the King.

This is a far-sighted play but does not have the advantage of clearing the last face-down card in any column. It’s close, but I vote for the simple option of dumping the Two of Clubs. We are nowhere near completing a full suit of Clubs and our immediate concern is turnovers and empty columns. The K-Q-J-0 of Clubs can wait.

Finally we should also consider shifting the Two of Hearts into the empty column and then building 3s-2c. It’s always good practice to consider every legal option and search for any edge, no matter how small. In this case, I’m not seeing it. Two of Clubs it is.

Our final action is <hi,cf,ib,a6=b1,eh>. That’s quite a lot of work for one card. And we get a … drumroll dlrdlrdlrldrdlrdlrdlr … THREE OF HEARTS, 70,85,67,75 YEAH!!!!

This is clearly one of the best cards we could hope for. Of course the game is far from winning but two empty columns puts us in a strong position. How would you continue?

We start with the following moves

<ae> 0d

<aj> 5h

<ia> Kd

<fi> 0s

<ef> 2h

<ji> 0c

<hf> 4c

<hc> 8d

<fh, deal = 85J6AQ99J7>

 

Not much thought required here. We start with three in-suit builds, then look for other “safe” moves such as moving a Queen onto either of two Kings. We managed to turn over eight cards in round 0, perhaps a disappointment after such a promising start – but this is probably not too surprising for a Master-level hand. Of course we are careful to build in-suit with 8-7 of diamonds before dealing another round.

We deal a row of 10 fresh cards and now the fun begins. There are many possibilities to consider: what would be your action here? (remember an action is a sequence of moves that ends as soon as one or more cards are exposed).