ec2-54-92-201-232.compute-1.amazonaws.com | ToothyWiki | DouglasReay | RecentChanges | Login | Advent calendar | Webcomic

A collection of links to things I find interesting in the areas of teaching, learning and how the mind works.

  1. [Jaeggi, Susanne M. & Buschkuehl, Martin et al {2008} 'Improving fluid intelligence with training on working memory' PNAS]
  2. [Wired Article]
  3. [N-back task]
  4. [computerised version]
  5. [free computer version]
  6. [associated google group]

See: /SnapBackGameRules

If the research is right, and regularly spending 20 minutes practicing something similar to the N-back task can boost your working memory long term and improve your effective intelligence in a transferrable manner, that would be fun.  I thought of doing some sort of program to run the task but, thinking about it, the real challenge is probably to make it interesting enough that people do it regularly.  Ie, make it a game!

The closest I've come across is the pairs game, where 16 cards (8 pairs) are dealt face down, and you have to find matching pairs, having only two face up at the same time.  But a) that's pretty boring - low replayability  and b) it is more positional memory - there is no failure point if you fail to remember all the previous ones to identify exactly what was 3 previous, so it isn't really testing working memory.

So, here's my proposal for a two player game Racing Snap Back (it could fairly easily be generalised to one person or multi player):
1. Take one or more packs of cards.  Shuffle and split it more or less evenly between the players. (Or just give each player a deck, which should allow reaching N=8.  Two decks per player would allow a longer game with more multiple tricks of lower orders.) When both players are ready, count down "3 2 1 go"
2. On the word "go", each player starts placing down their cards.  The player looks at a card, then places it face down, looks at the next card, places it face down beside the first card, and keeps going forming a row of face down cards.  For convenience this can snake back and forwards or go in left to right rows, just as long as it is clear which cards are next to which. {I'm not sure - would just transferring single cards from a face up deck onto a face down deck, one handed, be easier logistically?}
3. If a player thinks they have had two cards in a row that are the same number, the player puts down that card then say "Snap One Back".  At the word "snap" both players stop.  The claim of "One back" is then checked, the first two cards being revealed.
4. If the claim is correct, the revealed sequence gets put as a trick face up to one side by the player, and they are then looking for the next higher type of sequence (so from 1 back to 2 back.  From 7 back to 8 back.).  They may still collect lower order tricks, but the scoring system will encourage going for higher numbers.
5. If the claim is incorrect, the trick gets put face down, as a penalty trick
6. Once the claim has been settled, and the trick placed in the correct pile, the winning player counts down "3 2 1 go" and play restarts.  A new card can be looked at, but not placed down until the word "go".
7. If a player runs out of cards, they pick up all but the last N cards in front of them, shuffle, and then continue. (Where N is the order of their highest sequence)
8. The game ends by surrender, mutual agreement or some pre-arranged condition such as 20 minutes passing, first to reach N=9, first to get 10 tricks (excluding penalty trick) or running out of cards
9. The players lay out their tricks in front of them, in two rows.  The further away row is the positive tricks, going from "1 back" tricks on the right, numerically upwards to the left.  The closer row is the penalty tricks, placed under the appropriate positive position.
10. Scoring is binary.  Treat the rows as binary numbers and take the negative away from the positive.  IE each "1 Back" trick scores 1.  Each "2 Back" trick scores 2.  Each "3 Back" trick scores 4.  Each "4 Back" trick scores 8.  Each "5 Back" trick scores 16.  Each "6 Back" trick scores 32. etc.  (A less harsh scoring variant would be to halve the negative cost of penalty tricks.)

As described, there's no way of remembering what order a trick is - making the scoring tricky. Also, since advancing to the higher levels means you get fewer cards back-and-shuffled when you run out of deck, I think that would be a slight disincentive to advance. --CH
The order of the trick (N) is one less than the number of cards in the trick.  However, you might well keep your side collection of tricks sorted by order to save faff. --DR
Ah, sorry. I'd missed it was the entire sequence, and not just those two cards. --CH
No problem.  All feedback is useful, including lack of rule clarity.  I'm not sure running out of cards is a disincentive to raise order in multiplayer as when the game ends, it ends at the same time for all players. --DR

I considered emulating the dual N-back task by taking advantage of it being multi player, having all cards remain face up, and allowing challenges on the other player for missing a trick.  This would allow more interaction and make it more competitive (and so perhaps more fun?) but I'm not so sure the task would remain working memory, with the cards face up.  Perhaps do open deck to open deck card transfer for both players, synchronised maybe, so players transfer cards at the same rate? --DR

This game would completely break my brain.  --Vitenka
The idea is that, with practice, it EXPANDS your brain. :)  --DR

Further thought: for an adult playing with a child, some sort of handicapping or ranking system would be useful.  I'm thinking that an N'th level Dan would be one whose score is shifted N places to the right (ie divided by 2, N times).  To compensate for this, they start the game with it being assumed that they have already found (but not actually gotten score for) tricks up to and including size N (so they can immediately start looking for tricks of size N+1).  If you wanted to be nasty, penalty tricks of size N or less would not have their negative score shifted, as the player shouldn't be dealing in such fiddling small change, or perhaps they would be forbidden from taking that size trick at all (thus avoiding non-integer scores). --DR



Feedback - dealing one handed from deck to deck does work, but the second deck must be face down, because it is too easy to see what cards are below the last placed one even if you are trying not to cheat.

Speed up - remove the court cards (and jokers).  This increases the frequency of repeats.  Also, shuffle well.  Short sequences such as 4,5,6,7 left by a rough shuffle are annoying.

Idea for simplified scoring system: each time you get a penalty, reduce your N by 1.  (You can't go lower than N=1.  The aim is to get the highest N.)

2008-05-31 (Morag's Birthday BBQ)

The one handed turning of cards from a face up deck to a face down one, while initially counter intuitive to some people, was adapted to after the first few games.

Tactics that ruleset needs to be not susceptible to
Remembering first 3 cards, then counting until a match is found.
remember 3, look for matches in next 3, remember 3, look for matches in next 3

It was felt that just competing on speed, the first to reach a target or the one to get the highest score, was not interactive enough - a feeling of playing solitaire in company - there being nothing you could do to aid or hinder the other players.

The variant of only one deck having its cards turned over and everyone being able to call on it was tried.

This had something of the feeling of SET, however if you use the cards being turned as score counters (tricks) it disrupts memorised chains, which favours short over long ones.  If you don't, then either you need a clear way to indicate which order each player has achieved, or you fall foul of Vitenka-like counting strategies.


Use a single deck for multiple players.  Each player gets a D6, starting off showing "1".

A call of "snap" can be made by any played as soon as the card is placed on the sequence pile (the one being delt to).

On the call of snap, everyone (on a count of 3) does a rock-paper-scissors like motion, holding up a number of fingers (possibly using two hands).

Everyone who holds up the correct number of fingers (eg 4 fingers for a 4-back) AND who is elligible for that order of call, increments their dice by one if the call matches their dice.
It needs to be allowable to hold up no fingers, indicating that you don't think there's an n-back for any n. Well, it doesn't need to be, since holding up 10 fingers will never penalise you, but that's not exactly intuitive. --CH

Everyone who holds up an incorrect number of fingers AND who is elligible, decrements their dice.

If you are not elligible you don't increment or decrement your die, unless you made the original "snap" call and get it wrong.


Alice, Bill and Charles are playing.  Alice is currently on 4, Bill on 4 and Charles is on 5.

The sequence goes 1, 9, 7, 9,
At this point, Charles says "snap"
Charles counts "3, 2, 1, reveal"
On "reveal", Alice reveals 2 fingers, Bill 3 fingers and Charles 2 fingers.
Bill got it wrong and reduces his order die from "4" to "3" and play continues.
6, 3, 9
Bill says "snap" and counts down.
Bill reveals 3 fingers, Charles 5 fingers, and Alice 5 fingers.
They are all correct (both 3-back and 5-back are valid calls in this position)
Alice doesn't change her order die.  She's not elligable for a 5-Back yet - she needs a 4 to improve.
Bill increases his order die from "3" to "4" again, and has now redemed his mistake.
Charles increases his order die from "5" to "6".  He just needs a valid 6-Back call to win.

2008-06-03 (Tuesday Games Evening)

Vitenka suggested that when someone calls "snap" it disrupts the memory.  Therefore it might be an idea, after a "snap" call has been resolved, to do a 'run in', displaying the last N cards (where N is the highest number shown on a die) before letting play continue with new cards from the draw deck.
I think this is a very important idea, and addresses what seems the greatest "theoretical" issue with the game as it stands. The rest of my issues are practical ones. --AC

Rachael suggested that the speed is important, and dealing is best done by a third party who is not playing.  I'm not sure how well this would work in 2 player, but I agree that it would be preferable for multi player games when possible.  Having a computer version where people could sit in front of the same screen (it would just need to page forwards or back along a string of randomly generated numbers), or even play as a real time distributed game.

Vitenka asked why it would not be advantageous for someone who is behind on "1" just to call "SNAP" on every card (which would be disruptive). I'm not sure the best way to penalise or discourage this.  Three strikes and you're out seems possible, but would require extra counters of some form.
Having the 're-reveal them to refresh memory' thing going helps cope with the disruption of this.  --Vitenka

Edwin mentioned that for 3-back he was memorising 3, then trying matching for 3, but that this tactic was harder for 4.

Discussion with Alex brought out that it is necessary to allow calling of orders less than currently showing on your own die, else a safe tactic to stay in lockstep is just to show the number of fingers on the caller's die.

The other issues I think are practical - getting through the deck too quickly, and the deck sliding around to reveal future numbers. I suggest using two or three decks shuffled together to address the first issue - that'll also make snaps a little more likely. Ideally for the second issue would I think be something like a [casino shoe], or failing that just keeping the deck face down. Then you reveal one, leave it face up on the table for a second, then put it on the face-down stack before revealing the next. --AC
I agree about doing face down to facedown, though that does risk people forgetting which way it goes.  I'd like to avoid the need for boards or specialist equipment like dealing shoes - Ideally this will be a ruleset I can publish, then have other people play with equipment they already have. --DR

Working out how much 2 decks would improve the probability is not as simple as seems.  You have to look at the balance of low-order-Ns to high-order-Ns as well as at the mean-time-to-next-snap.  The other issue is which cards are in the deck (we played with 9 different cards: 2,3,4,5,6,7,8,9).  If one played with infinite decks, the chances of the initial 7 cards being a 6-Back AND NOT containing any 5-backs, 4-backs, etc. are 9/9 * 8/9 * 7/9 * 6/9 * 5/9 * 4/9 * 1/9.  If you play with 1 deck, the odds are 36/36 * 32/35 * 28/34 * 24/33 * 20/32 * 16/31 * 3/30.  If you have already dealt 6 cards (which may or may not have themselves been snaps), then the ongoing chance of any individual cards being a snap is 1 - (8/9)^6, with infinite decks.--DR

What do people think about the counting down 3, 2, 1 then reveal your guess?  Does counting from three give long enough for people to work out, from their stored memory of previous cards, how many back the snap is? --DR

2008-06-24 (Tuesday Games Evening)

Long play test, with JacquelineWalpole and Vitenka both kindly dealing.

Popular suggested amendments:

1. Start with the dice showing "3".

2. Allow correctly guessing a number higher than the one on your dice (to a maximum of 6-back) to increment your die.

The combination of these two alterations should speed the game up considerably (the desired play time is about 10 mins)

  1. [Memory system - japanese kanji]
  2. [How working memory works]

ec2-54-92-201-232.compute-1.amazonaws.com | ToothyWiki | DouglasReay | RecentChanges | Login | Advent calendar | Webcomic
Edit this page | View other revisions | Recently used referrers
Last edited November 23, 2008 1:43 pm (viewing revision 18, which is the newest) (diff)