The origins of the game are unclear. I've seen posts claiming that it dates back before World War II, but have not found any actual citations proving it. One poster reported seeing the Game of Pure Strategy (GOPS) in "Dave Parlett's Dictionary of Card Games", and that Parlett dated it to the 1960s. I've also been told that at least one game theory text also describes the game under this latter name, but again I do not have an actual citation.
Each card has a value from 1 to 13. Aces are low at 1, jacks are 11, queens are 12, kings are 13, and other cards have the obvious values. Players use the cards they start with to bid on the diamonds, with the object being to collect the greatest total value of diamonds.
There are 13 rounds. Each round, the next card is turned up from the shuffled diamond suit. Each player then selects one of their "bid" cards (the suit they were given at the start) and places it face down in front of them. When everyone has selected a bid, the bids are revealed, and the highest bid wins the diamond. The cards that were used to make the bids are then discarded; thus each player will end up using each of his "bid" cards exactly once in the course of the game.
If the bids are tied in a two-player game, the diamond is discarded. If there is a tie for high bid in a three-player game the diamond is placed between the two high bidders and they each get half value for it. (See variants.) If there is a tie for total value at the end, the game is a draw.
Psychological JuJitsu is not intended to be a game of memory, so used bid cards should be left face up in front of the players, making it easy to see what cards each player still has available. Likewise, the diamonds that each player has won, and any that are discarded due to ties, should be kept face up.
The first diamond turned up is the 7. Charles is trying a general strategy of getting diamonds early so he has a lead, forcing Scott to play catch-up. Scott decides to try a strategy of playing mostly low cards at first, hoping that Charles will use up lots of high cards. On the 7, Charles bids 9, and Scott bids 2. (He would have bid 1, but decided to try 2 just in case Charles was also using an "early low bids" strategy and chose to bid 1.) Charles wins the 7. The next diamond is turned up, and the position is as shown below.
Even Charles, with his "early lead" strategy, has trouble getting too excited about a 3, so he bids 3. Scott continues with his plan and bids 1. Charles is pleased. (It's always good when you just barely outbid your opponent, at least in the two-player game.)
The next diamond is the 10. Scott decides to risk a "real" bid, hoping that either Charles will choose to go low this time, or that Charles has noticed Scott's low-bid strategy and will try to steal the 10 with a medium-sized bid. Scott tries his 9, but Charles sticks to his plan and bids his queen (12).
Now the diamond king turns up (see position at right). Scott realises he has to draw the line somewhere, so he bids his king. Charles also bids his king, and the diamond is discarded. Note that Scott is now guaranteed to win whatever he chooses to bid his queen on.
Next comes the diamond 2. Charles lets this one go, bidding 1. Scott likewise bids his smallest remaining card, but in his case that's a 3, so he gets it.
The next card is the diamond 9. Figuring that Scott will save his queen to bid on a larger card (the diamond jack or queen), Charles tries his jack to see if he can grab the 9, or at least get a tie. But Scott outguesses him and plays his queen now. Not only does he win the 9, but Scott also continues to have a "sure bid", since now his jack beats all of Charles's remaining bids.
Up comes the diamond 5 (see above). Charles recovers some ground by bidding 6 against Scott's 4. Scott went low, hoping Charles would bid higher than that.
On the diamond 8, Charles again gains ground by bidding his lowest card, the 2, while Scott bids his 10. Scott wins the card but has used up a powerful bid.
The diamond ace (1) comes up, and each player plays his lowest remaining card. Scott's 5 beats Charles's 4. The diamond queen is next (see below).
Scott can ensure winning the queen by playing his jack, so Charles is tempted to play his 5 and preserve what strength he has left. But he decides it would be disastrous if Scott won the queen using his 8, keeping the jack in reserve. So Charles plays his 8. (He's not willing to risk his 10, which would be totally wasted if Scott does play the jack.) Scott considers his 8, but chooses to play his jack after all.
Scott is now ahead with 32 points of diamonds to Charles's 25. Charles has a very slight edge in remaining bidding strength: 5 + 7 + 10 compared to 6 + 7 + 8. The victor is not yet certain, but Charles will need to do some shrewd guessing in order to win. Basically, (1) he must play his 7 when Scott plays his 6, and (2) he must win the diamond jack. Winning the diamond jack will require playing his 10, unless Scott plays his 6.
As it happens, the diamond jack comes up next. If Scott plays his 6 and Charles his 7, Charles will win. (Charles will use his 10 to win the diamond 6, and Scott will get the diamond 4.) But if Scott does not play his 6, Charles must play his 10 to have any chance. (Charles still has to lose one more diamond when he plays his 5, so if he doesn't win the jack he can't catch up enough.) After some deliberation, Charles plays his 10, and Scott the 6. Charles now leads by 4 points, but Scott has a sure victory.
At this point, Charles has the 5 and 7 remaining, and Scott has 7 and 8. Scott will bid 8 on the diamond 6, and 7 for the diamond 4. He is guaranteed to win the 6, and Charles cannot do better than tie for the 4. So Scott picks up 6 points and wins by 2 (see final position below).
In a three-player game, this gets more complex. If both of your opponents bid about the same, you would like to bid just a little bit higher than both of them. Again, if they are both bidding quite high, you can do well by bidding low. If one bids high and the other low, however, you can't really gain a lot of ground on both of them. You can go high and take the diamond, or go low and save your strength, but the opponent who played low will be pacing you. The result you most want to avoid is making a moderate sized bid and having one opponent bid one higher while the other bids his lowest card.
In the sample game, one player was able to ensure victory after 11 rounds. Sometimes that will happen, but other times the game will come down to a 50-50 guess on the next-to-last round. (Obviously, the bids on the last round are automatic.) Sometimes you may even be able to work out the complete strategy for the last three rounds. In the sample game, when the diamond jack came up in round 11, Scott was a 2-to-1 favorite. He could roll a die and play his 6 one-third of the time, and his 7 the rest of the time. Charles's best play would be to play his 10 two-thirds of the time, and his 7 one-third of the time. You can work it through and see that Charles would win 1/3 of the time and lose 2/3 of the time.
Most of the strategy, however, involves jockeying for position before the last few cards are played. The sample game illustrated two common approaches: grab an early lead, and save your big bids for later. Either of these can work, but the heart of the game lies in adapting your strategy based on what your opponent is doing (or rather, what you think he's going to do!). You also have to pay attention to what diamonds are coming out; the "save your big bids" strategy doesn't do so well if too many big diamonds come out early.
Nor is it sufficient for a strategy to involve a random element, where each bid is randomly determined based on some set of odds. A complete strategy must also take into account, in determining each bid, what bids the opponent has already used, and what diamonds have already gone by (and who won them).
There is a different form of the game, in which the players decide up front how much they are going to bid on each diamond, and cannot change their minds after seeing how the first few bids go. In this case you don't even really need the diamonds: the players simply arrange their bids in a face-down pile, and then start turning up the cards one at a time, and award 1 point to the high bidder on the first pair, 2 points for the second, etc. Though still quite complex, this game is much simpler. It also has a lot in common with a game posted to rec.games.abstract by Colin Bell in 1996, called Colonel Blotto.
One way to study the complexity of the strategies available is to look at games played with smaller decks. If each suit has only 3 cards (valued 1, 2, and 3), then the game is trivial: each player bids N for the N of diamonds. This ensures that the other player cannot do better than draw. (There are several ways to draw, e.g. bidding 2-3-1 and winning the 1 and 2 of diamonds while losing the 3, but you can't do better.) Once you get to 4-card suits, however, the game is already rather complicated, and the analysis of the 4-card game leads to some interesting insights. One point of particular note is that the ability to adjust your bids based on the results of earlier bidding is key to the game.
Another way to score is to award a greater victory if the winner is able to guarantee victory well in advance. On any round, a player can declare that he is going to make this bid and all subsequent bids face-up, showing his bid before the opponent chooses his bid. The score for the game is then equal to the number of rounds in which that player's bids were face up. Obviously, the last round's bids can always be made face up, so this means a game is worth more than 1 point only if someone is willing to start showing his bids on the 12th round or earlier. (In the sample game, Scott could have made his last two bids face up, scoring 2.) Note that, if you make a mistake and realise too late that your face up bids will let the other player win, you can't stop! You must make all your remaining bids face up, and the other player will then get the increased score for the game.
A variant with two players is to pretend there's a third player who selects bids at random. Shuffle the remaining suit and, after the actual players have selected bids, turn up the next card as the dummy player's bid. This variant detracts somewhat from the psychological element, but can lead to more complex endgame positions. That is, it may be less likely that one player will be able to demonstrate a sure victory with several diamonds yet to bid on.
Another variant (with any number of players) is to have only 12 rounds; the last diamond does not get bid on and is discarded. Players won't know until the last round which diamond it is that is being omitted, so someone who has a "sure winner" bid available (because nobody else has as high a card left) won't necessarily know when to use it. Note: Since players will only use 12 bids, they obviously will never use their lowest bidding card, so you should remove all the aces from the bidding suits.
Perhaps the nastiest variant of all (and one which I only recently thought of and haven't actually tried) is to add another player who controls the diamonds. For example, suppose there are four players. Three of them use the clubs, spades, and hearts to make bids as before. The fourth player does not bid, but merely chooses what order the diamonds appear in. Each player pays (say) $1.00 to play the game, and the player with the high score at the end of the hand takes all the money. The player who controls the diamonds cannot possibly win the money (except perhaps if there's a three-way tie bid on every diamond, in which case everyone ends up at zero and they all split the money). What the diamond player does is make deals with the other players in which he accepts money in return for his choice of how to arrange the diamonds.
Initially, of course, all the players are in equivalent positions and there's no advantage to having one diamond or another turn up. But depending on how the bids go on the first diamond, there may be a greater expected payoff to one player depending on which diamond is next. The diamond player would use this difference in value as a bargaining chip. Also, the diamond player should start by choosing a diamond that makes it more likely that such an imbalanced position will be reached.
If you think the preceding variant takes the game to a higher level of headache, consider the next step. The diamond player's position is clearly not equivalent to that of the other players. In particular, the other players could make a deal where they agree to freeze out the diamond player and whoever wins will split the money (leaving out the diamond player). Thus the diamond player's contribution to the payout is split among the other players. So you could imagine letting the diamond player play for free. But that means that any deal he manages to strike with any other player is a guaranteed gain for the diamond player, so perhaps the diamond player should be required to pay some amount, but how much? Well, how about letting the players bid for the right to be the diamond player?
Note that this could also be done without the extra player. For instance, with only two players, each of them could pay $1.00, and then they could bid to see who gets to control the order of the diamond suit. The winner then takes the $2.00 plus the diamond-controlling payment.
High Society, by Reiner Knizia, uses similar equipment but does not feature simultaneous bidding, which of course makes for a tremendous difference in play. Players can add to their bids in a continuing auction, but the amounts they can add are limited to "whole cards" from their starting set; they cannot "make change" by taking back earlier portions of their bid. High Society also adds a clever twist at the end: whoever has the least money left unspent is automatically disqualified; then whoever has purchased the most points wins.
Pico, a 1996 release from Frank Nestel and Doris Matthaus, is similar to Psychological JuJitsu but with a much smaller deck. Players compete with a hand of five cards drawn randomly from an eleven-card deck; unlike the other games described above, the cards one plays are also the cards one hopes to win, rather than a separate deck.
Alan Parr's Dirty Dozen, in addition to having negative and multiplicative payoff items, has a second deck that determines how the winner of each item is determined (highest card, lowest card, second highest, etc.). In each turn, two cards are revealed: a scoring card and a card indicating how the scoring card will be won.
The title Psychological JuJitsu has also been used for a somewhat different two-player board game with some similarity of feel. A token is placed in the middle space of a seven-space track. Each player begins with a store of 50 points. Each turn, the players simultaneously reveal a bid of some portion of their remaining points. The higher bidder moves the token one space towards the opponent. Both players lose the points bid, and the next turn begins. The first player to move the token to the far end of the board wins. Knizia's game Tor is very similar to this, but the bidding units are cards from 1-13, with the special feature that a 13 loses to any card ranked 1-10.
My thanks to Kevin J. Maroney for much of the above information about commercial and historical versions.