Karl Reiner, suite. Apr�s avoir expliqu� pourquoi l\’argent est si rare dans Age Of Steam la semaine derni�re, Karl �voque cette semaine ce que font r�ellement les actions individuelles dans Age Of Steam. Tout un programme.

Ce qui peut �tre l\’occasion de lire (ou relire en cas de d�soeuvrement extr�me) ma tentative sur le m�me sujet, notamment en contradiction compl�te sur l\’action Turn Order.

Un de nous deux se plante, c\’est sur, mais qui ?

First, let�s look at what happens to turn order in bidding sequences where Turn Order is not chosen at all, using a 5 player game as an example. I have seven scenarios, all of which assume that all players� maximum bid is $3.

a) You are the first player. You pass. Now you are the last player in the new turn order. There is of course no cost to you, but you have descended -4 positions on the order.

b) You are the first player. You bid your maximum value, let us say $3. No one else bids, and therefore you retain your positioning in first place. The financial penalty you pay is $3, with no drop or gain in turn order.

c) You are the first player. You bid a minimum amount, let us say $1. There are two overcall bids, of $2 and $3 respectively, from the next two players. The final two players pass. Now you decide to pass, as you cannot exceed your maximum. You are now in 3rd position, and have expended $1 for a net drop of -2 positions.

d) You are the last player. All players in front of you pass. You are now the first player in the new turn order, at no cost, for a net gain of +4 positions.

e) You are the last player. The first player has made his maximum bid of $3. All other players have passed. You decide to pass, as your maximum is also Three dollars. You are now second on turn order, at no cost, for a net gain of +3 positions.

f) You are the last player. The first player has made a minimum bid of $1, followed by $2 and $3 from the next two players. The person ahead of you passes. You also pass, moving you up from fifth to fourth spot, at no cost, for a gain of +1 positions.

g) You are the last player. Two players ahead of you pass and two players ahead of you bid $1 and $2 respectively. You now bid your maximum $3. All other players pass, and you are now first in turn order, at a cost of $3, and a net gain of +4 positions.

Note that I have chosen to omit a scenario where the first 3 players pass and the fourth one bids his maximum. That scenario is damaging to the first 3 players, who drop the maximum amount, and damaging to the fourth player, who is probably overpaying to move up from second place to first. Even should this occur, the last place player will move to second place for a cost of nothing

As can be seen in the first three scenarios, the natural tendency is to fall in turn order, from first to last, or to require a fairly hefty bid to retain your position. In contrast, the last bidder has a natural and overwhelming tendency to rise in the turn order regardless of whether he is making a bid. The last player will especially benefeit when players early in the turn order exert the greatest pressure on other bidders by bidding close to their own maximum dollar value. This is important to note: again, when other players are using best-play practices, the last player will move sharply forward in turn order at no cost, whereas players earlier in the turn order will move downwards.

Note that I have chosen to omit a scenario where the first 3 players pass and the fourth one bids his maximum. That scenario is damaging to the first 3 players, who drop the maximum amount, and damaging to the fourth player, who is probably overpaying to move up from second place to first. Even should this occur, the last place player will move to second place for no cost, as per the �buoyancy� factor illustrated in cases d), e), f) and g).

Now consider all seven cases again, this time using Turn Order.

a) You are the first player. You pass, using the power of Turn Order to stay in the auction. All other players pass. You are now first in the new turn order, at 0 cost. Turn Order has gained you +4 positions. Even if the second player bids $3, and all other players pass, you gain +3 positions, at zero cost. Remember, it is in the interest of early players to bid something, otherwise they naturally move down in the turn order, so if other players use optimal strategy, your benefeit is maximized.
b) You are the first player. You bid your maximum $3. No one else bids, and therefore you retain your positioning in first place. Turn Order has not gained or cost you anything.

c) You are the first player. You bid a minimum $1. There are two overcall bids, of $2 and $3 respectively, from the next two players. The final two players pass. Now you pass using Turn Order. The second player also passes, and you finally pass, gaining second place. Turn Order has gained you +1 positions.

Compare scenarios b) and c). If you have Turn Order, you can now choose to aim for second place in turn order at a savings of $2, so Turn Order has allowed you greater freedom of Choice for relatively equal outcomes. If other players bid or raise, it essentially predisposes you about second place, at a significant cost savings.

d) You are the last player. All players in front of you pass. You are now the first player in the new turn order, at no cost. Turn Order has gained nothing, since you would have been first regardless.

e) You are the last player. The first player has made his maximum bid of $3. All other players have passed. You decide to pass, as your maximum is also $3. The first player is not required to raise his bid, so you must pass again, leaving you in second place. Turn Order has gained nothing, since you would have been second regardless.

f) You are the last player. The first player has made a minimum bid of $1, followed by $2 and $3 from the next two players. The person ahead of you passes. You also pass, using Turn Order. Now the first two players pass, and so do you, leaving you in second position. Turn Order has gained you +2 positions.

g) You are the last player. Two players ahead of you pass and two players ahead of you bid $1 and $2 respectively. You now pass, using Turn Order. One player ahead of you bids $3, and all other players pass, including you since your maximum is also $3. Turn Order has saved you $3, but cost you �1 position.

Sum up the savings for the early versus the late turn order scenarios. The overwhelming advantages in both cost and position occur in scenarios a), b) and c), when you are the player using Turn Order and bidding early. I grant that in scenario g), Turn Order, although a mixed blessing, but does allow a certain amount of flexibility. It still does not compare to the flexibility afforded to the first player by the choice between scenario b) or c).

This does not mean that one should pick Turn Order when you are first in the bidding: especially when Locomotive, Urbanisation, and Engineer can gain you both higher income and scoring opportunities. Turn Order is not inherently as valuable as these actions in my opinion. It does mean, however, that the value of Turn Order decreases the longer it is left unchosen, and conversely, that it is more powerful if chosen by someone early in the turn order.

Karl Reiner

Cet article a été publié le Mercredi 16 mars 2005 à 23:19 et est classé dans Géneral. Vous pouvez suivre les réponses reçues par cet article grâce au fil RSS 2.0. Commentaires et trackbacks sont tous deux fermés pour le moment.