DonGuy47’s Pyramids Tips
At long last, here are some exercises!
See also the new Addendum at the bottom of this page.
At first glance, Yahoo’s “Pyramids” game looks like pure luck. Many solitaire games have the property that the outcome of the hand is completely determined at the outset – you just take the plays that are available, and see what happens. But each hand of Pyramids is actually a nifty little logic puzzle. There are many decisions to be made, and making thoughtful choices can increase your average score by thousands of points. Bonus: the higher the probability that you will clear a round, the higher your probability of lucking into a monster high score!
These tips are listed roughly in order, from the most obvious and certain, to the most intricate and speculative. Near the bottom, the ideas are just my guesses at optimal tactics.
First, let’s fix some terminology. The cards you are trying to get rid of are the pyramid cards; the card you play them on is the upcard; and the cards you click on to get new upcards form the upcard pool.
1.
Don’t make mistakes. It’s obvious that screwing up is bad, but it
takes a lot of discipline to avoid it.
How often have you been clicking rapidly through the upcard pool, and
noticed too late that you could have used the upcard you just buried? This happens to me a lot, especially if I’m
feeling tired or impatient. It’s hard
enough to clear rounds without throwing away useful cards! A mistake can easily be the difference
between making the next round and having to start over; it can cost you untold
thousands of points. Force yourself to
scan the pyramid cards fully after every new upcard, and after every newly
exposed pyramid card. If you have just
gleefully removed from the pyramid a run of 4-3-4-5-6-7-8-9-T, it’s easy to
miss the fact that you just uncovered an unexpected 9. Aces and kings require particular vigilance,
since our brains aren’t used to runs of cards wrapping around as they do in
Pyramids.
2.
Leave as many pyramid cards exposed as possible. The more cards you have exposed in the
pyramid, the better the odds that the upcard can help you, the longer the runs
you can plan, the more cards you can remove, the fewer cards you have to use
from the precious upcard pool, etc., etc., etc.
Leaving pyramid cards exposed will be a recurring theme in these
Tips. For now, here are some basic
examples. If the upcard is an 8, and you
have a choice between a 7 whose removal will expose two cards, and a 7 that
will expose only one card, choose the former; if one 7 exposes one card, and
the other exposes no cards, choose the former.
What if neither 7 exposes any cards?
Pick an “interior” 7 over an “edge” 7:
removing an interior card creates two cards whose subsequent
removal will expose a card, whereas removing an edge card creates only one.
3.
Plan ahead.
Suppose your upcard is a 4, and the exposed pyramid cards are 2, 3, 5,
4, 7, 4, 6, and 3. It might take you a
little while to figure out that the longest possible run is
4-3-2-3-4-5-6-7. It’s worth the
time! Sometimes I have to count the
lengths of the various possibilities on my fingers. Good thing none of my colleagues in the math
department is watching.
4.
But be flexible. Suppose, in the previous example, that you’ve
played 4-3-2-3-4, and suppose that this has exposed two 3’s and a 2. Your original plan was to continue with
5.
Aim for nearby cards. Suppose the upcard is a J, and the exposed
pyramid cards are A, 7, T, J, and Q; and suppose that removing the T, J, and Q
from the pyramid will expose at least one card.
Then your options, J-Q-J-T and
J-T-J-Q, are both runs of three, so it appears that you can choose between them
randomly. But in fact, J-T-J-Q is
better, because the last card, Q, is only a K away from the exposed A, and one
of the cards you expose while playing J-T-J-Q may be a K. The other option, J-Q-J-T, ends two
cards away from the exposed 7, so it’s less likely that this option will
produce a 5-card run. The best
card to aim for is the one you’re planning to end with. For example, the upcard
is a 2, and the exposed upcards are 2, 2, 3, 4, and
6. You will play either
6.
The following tips are all related to the idea of
leaving as many pyramid cards exposed as possible (tip #2).
a.
Leave as many different pyramid cards
exposed as possible. Suppose the
upcard is a 3, and the exposed pyramid cards are 2, 4, 4, 8, J. Then – other things being equal – you want to
play 3-4, rather than 3-2, so that an ace upcard will still help you.
b.
Leave as many good upcards as possible. Most generally, try to leave yourself in a
position in which the maximal number of upcards help you. For example, suppose the upcard is a 5, and
the exposed pyramid cards are 4, 6, and 8.
Then (other things equal) play 5-6, rather than 5-4, so that the number
of upcards that help is four (3, 5, 7, 9) instead of three (5, 7, 9).
c.
Order matters. Keep as many pyramid cards exposed as
possible, even in the middle of a run.
To accomplish this, arrange your run so that new cards are exposed as
soon as possible. For example, suppose
it’s the beginning of a round, the upcard is a 3, and the exposed pyramid
cards, in order, are 784954TJQ. Your
plan is to play 3-4-5-4. Do not play
these cards in order, left to right.
Instead, play the 4-5 on the right first, exposing the card beneath them
as soon as possible. If the card
underneath is a 6, you can change your plan, and play 3-4-5-6-7-8-9-T-J-Q! If you play 3-4-5-4 left to right, the 5 is
gone by the time you learn that you have a 6, and you lose thousands of run
points.
d.
Keep piles even. After the first few plays of a round, the
remaining pyramid cards will form three separate stacks. Other things being equal, remove cards from
the biggest stack, rather than the smallest one. The reason for this is that you’re trying to
keep as many pyramid cards exposed as possible; and once a pile is gone, the
number of pyramid cards exposed is permanently diminished.
7.
Gamble, when appropriate. Suppose the upcard is a 4, and the exposed
pyramid cards are A, 2, 3, 5, 6, 8, 9, T, and J. It looks as if you should play 4-3-2-A,
rather than
8.
Avoid the greedy endgame. Keep as many pyramid cards exposed as possible,
even near the end of the game. When you
remove the last pyramid card from one of the three stacks, you get bonus points
(500, 750, and 1000 points in round 1; 750, 1000, and 1250 in round 2; etc.) Avoid taking these easy points, if it might
cost you the chance at another round.
For example, it’s round 1, and the upcard is a 6. There are only three pyramid cards left: a 7 by itself, the last card of its stack;
and X7 (the 7 on top of the mystery card), the remaining two cards of another
stack. The temptation is to play the
isolated 7, to score the 750 bonus points.
But then you’ll have only one exposed pyramid card – the 7 atop the
remaining stack. It’s better to play the
other 7, exposing the X, so that you don’t waste any potentially useful cards
in the upcard pool. To make the example
more specific, suppose X turns out to be a jack, and the upcard pool (in the
order you’ll see its cards) contains T8.
If you take the 750-point 7, you won’t be able to use the T when it
becomes your upcard. You’ll finish the
game in round 1 with a J remaining in the pyramid. If you forgo the 750 points, and expose the J
right away, then you advance to round 2.
(Technical note: The validity of
this piece of advice actually depends on several variables – how much the
“easy” card is worth, your personal average Pyramids score, and the probability
that it is possible to advance to the next round. The more the easy card is worth, or the more
hopeless advancement seems, or the lower your average Pyramids score is,
the more you should consider just taking the points and giving up on making the
next round.)
9.
Keep track.
Suppose the only pyramid cards left are an exposed 9 and J, the upcard
is a T, and there are five cards left in the upcard pool. Do you play T-9 or T-J? It depends, of course, on whether there are
8’s or Q’s left in the pool. If you’re
like me, and cards have been whizzing past for the two minutes of this round,
you have no clue how many 8’s you’ve seen, or how many Q’s. If you guess wrong, play T-9, and it turns
out that the pool contains an 8 but no T or Q, then you’ve just died
needlessly. You can solve this problem
by keeping track of every card you’ve seen, on paper. If you know that you’ve seen four T’s, four
Q’s, and only three 8’s, then you can confidently play T-J, and prepare to
advance to the next round. More
generally, knowing exactly how many of each card you’ve seen at all times can
help you make the statistically correct choice many times throughout the course
of a game – not just right at the end. I
believe that keeping track of every card would probably increase everyone’s
average score by at least a thousand points.
So, theoretically, this tip belongs much higher on the list. But it’s really tedious to keep track of all
the cards on paper. I rarely have the
patience to do it. It’s fun to click
cards at lightning speed and watch ‘em fly!
Addendum, 10-8-06
It’s now been several years since I wrote those tips. Here’s my more mature understanding of the hierarchy of goals.
(1) Don’t waste upcards.
(2) Take the card closer to you.
(3) Keep the piles even.
(4) Uncover as many cards as possible.
(5) Go for long runs.
Given this hierarchy, notice that
it is very rarely the correct play to
go for a long run at the expense of the other goals. It is far more important to finish the current round, than to accrue
points in the current round.