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A&A Chess

Axis and Allies, in short: A&A, is a board game, played with a number of players (two to five), simulating the second world war. The game contains a large element of luck, as battles are decided by throwing dices. July 1995, David Albert Harrell invented a diceless variant of this game, which he called A&A Chess. I wouldn't actually classify this game as a chess variant, as it has only little resemblances to chess, I think; but as opinions of others may be different, it is included here on these WWW pages.

A&A Chess (NO dice)

by David Albert Harrell

If you play a lot of A&A, you will experience some wild fluctuations in the dice. When this happens, I usually feel cheated, whether the dice have fallen in my favor, or against me. When the dice severely enhance my position, I don't feel deserving of the subsequent victory, and when they roll against me, I'm not too happy either.

Several years ago, in the course of my artificial intelligence experiments within the A&A environment, I was disposed to find a method of resolving "battles" which did not allow severe fluctuations in the random factor of the "dice decisions". This necessity fostered a most elegant and interesting modification, which has transformed a frequently frustrating game of luck, into a new and reliable competitive encounter, based entirely on skill. I call this new game hybrid "A&A Chess".

Many A&A players have expressed serious objections to the notion of some "diceless" method of resolving battles. Many say that "this" would not be the same game, and they are correct. A&A and A&A Chess are as different as Backgammon and conventional Chess. However, the difference is more difficult to appreciate, because the pieces and board, for these two games, are identical (except for dice). A&A Chess is a completely different challenge, and it will inevitably attract its own type of player.

People who like A&A the way it is now, should certainly continue to play A&A in this fashion, but I am certain no one really objects if new people, who may perhaps have never taken an interest in conventional A&A, find the uniquely competitive environment of A&A Chess to be of some interest.

I, for instance, am a serious chess player. I have never been interested in games such as Parcheesi, backgammon, or craps; if you can understand why, then I suspect you will like A&A Chess, and I sincerely recommend that you try it.

Here is an opportunity to become part of the opening evolution of this new game. Serious players may now begin establishing play records that will accurately reflect their individual abilities. The game is evolving into the unique class of the totally cognitive. Such competition is the most severe kind, among gaming entities, because these purely cognitive gaming environments leave no escaped route for the ego. Only a handful of such games exist, such as "Go" and "Chess".

Some of you may never have heard of the ancient Oriental game "Go". Over the centuries, the simple 2D environment of "Go" has come to be considered (perhaps unjustly) a game of limited parameters, when compared to chess; just as chess may someday be considered a game of limited parameters, when compared to "diceless A&A".

I invite you to experience the purely cognitive A&A Chess environment. If you already play A&A, the metamorphosis takes only minutes; merely substitute the following simple modification for the traditional casting of the notoriously inequitable bones of fate.

David Albert Harrell

A&A Chess Official Rules
International A&A Chess Federation

When deciding the results of an assault within a "battle", add the separate totals of the "attack" and "Defense" capabilities for both groups, and then divide each of these sums by 6. The respective products of these divisions represent the number of units "destroyed" in the given single assault. (As always, the attacker retains the option to continue the attack by launching another assault.)

Example 1:
If 6 men attack a group of 3 men: the results of the first single assault is a loss of 1 defender, and 1 attacker.

Attacking Force: 6 men. (total attack capability = 6)
Defending Force 3 men. (total defense capability = 6)
Defender loss = 1 unit (man).
Attacker loss = 1 unit (man).

Example 2:
If 4 tanks attack a group comprised of 3 tanks and 6 men: the results of this single assault are a loss of 2 defenders, and 3 attackers.

Attacking Force: 4 tanks.
Defending Force 3 tanks and 6 men.
Defender loss = 2 units.
Attacker loss = 3 units.

FRACTIONS: (the remainder of the division by 6)
The fraction, in the case of the attacker, if less than five, is ignored. If the fraction is equal to 5, than it is considered a "hit".

In the case of the defender, the fraction is considered a hit if equal to 4 or 5. If the fraction is less than 4, it is ignored.

Examples 3:
Attacking Force: 4 tanks and 5 men.
(total attack value = 17) (the fraction 5 is considered a hit)

Defending Force 3 tanks and 5 men.
(total defense value = 16) (the fraction 4 is considered a hit)
Defender loss = 3 units.
Attacker loss = 3 units.

Examples 4:
Attacking Force: 4 tanks and 4 men.
(total attack value = 16) (the fraction 4, or less, is ignored)

Defending Force 3 tanks, 4 men, and 1 bomber.
(total defense value = 15) (the fraction 3, or less, is ignored)
Defender loss = 2 units.
Attacker loss = 2 units.

Anti-aircraft fire is handled as follows:

Total the number of planes used within a given entire move, and divide this total by 5; the product of this division indicates the number of planes lost , and the fraction (4 or less) is ignored. In cases where the planes involved in a move are disbursed among two or more territories, and the total number of planes exceeds 4, then the commander of said aircraft may choose which plane (or planes, in the case of more than 9 planes) will be considered lost by anti-aircraft fire.

Examples 5:
If Germany sends 3 aircraft to the UK and 2 (up to 6) aircraft to Russia (assuming both territories [being attacked] are defended with anti-aircraft), 1 aircraft is lost before the attack totals are computed. (Flying over multiple anti-aircraft, in a single move, increases these totals accordingly. For example if 3 planes fly over two territories with AA, then 1 plane is lost at the point where the total equals or exceeds 5.)
In the case of economic bomber runs, the same anti-aircraft rule modifications are used, and the attacker is awarded a 2.5 production unit deficit (on the enemy treasury) for each bomber that survives the "anti-aircraft fire". If the total has a fraction, it is ignored.

Attacking submarines are handled normally, except their attack strength is totalled separately and divided by 6; the product of this division indicates the number of defending units which will be removed from the board, WITHOUT opportunity to return fire. The fraction is added to the normal remaining attack total of the given assault.

Example 6:
Attacking Force: 2 battleship, 1 fully loaded (2 fighters) carrier, and 5 submarines.
(total attack value = 25)
Defending Force: 1 battleship, 1 fully loaded (2 fighters) carrier, and 1 transport.
(total retaliatory defense value = 15)
(16 - 1 : assuming the transport is selected as the casualty of the 3 submarine's first strike hit)
Defender loss = 4 units. (the remainder or fraction of "1" is ignored)
Attacker loss = 2 units. (the remainder or fraction of "3" is ignored)

Units having had their attack values augmented by weapons development are treated according to their given increase. Dice rolls representing "rocket attacks" are always considered to be a value of 3.

There are five variations of A&A Chess. The first, described above, is the "orthodox" method, known simply as "A&A Chess".

A&A Chess (RYOF) "Roll Your Own Fraction".
If you wish to retain a slight random element in your contest, simply roll a single die to resolve fractions which would normally (using the orthodox variation of A&A Chess) be ignored, i.e., remainders of 4 or less for the attacker, and 3 or less for the defender. (For example, if the fraction [remainder] was 3, then a die roll of 3 or less would be considered a hit.)

A&A Chess (RYOF<6) "Roll Your Own Fraction less the 6".
If you desire even more uncertainty in your game, you can roll a die to decide all fractions less than 6, including such values as AA fire, rockets, and bomber E-run depletions on the enemy treasury.

A&A Chess (COF) "Carry Over the Fraction"
All fractions (< 5 for the attacker, or < 4 for the defender) of single a "battle" (an attack on a single territory or sea zone) are "carried over" to the respective totals of subsequent assaults within the same battle (in the event there are multiple assaults). When the attacker withdraws, or one side is destroyed, the final remaining relevant fraction or fractions (if any) are ignored if < 5 for the attacker, or < 4 for the defender; otherwise the given fraction is considered a hit.

Notice that when dealing with fractions (representing a hit: > 4 for the attacker, or > 3 for the defender) the enemy casualties are remove from the battle board simultaneously as they occur (during the assault in which said fraction qualifies). Such qualifying fractions are not added again to the next attack assault totals. In contrast, a barely qualify fraction actually creates a deficit in the running total, which will effect any subsequent assault; this is necessary to maintain equity when using the "Carry Over the Fraction" method. For example, if the attacker's last assault minimally qualified with a fraction of 5, he would have some slight degree of incentive to withdraw, knowing he must now total another full 6 points to gain his next hit.

A&A Chess (COF+R) "Carry Over the Fraction + Roll"
Same as COF except a single die may be cast to resolve any remaining relevant fraction or fractions (< 5 for the attacker, or < 4 for the defender) in final assault of a given battle.

This last variation, A&A Chess (COF+R) offers maximum equity, lightly seasoned with a "minimal dash of luck" on the end. However, I believe the totally diceless (COF) variation will inevitably became the most popular. Luck clearly plays a large role in the game of A&A, but I am convinced that dice will eventually have "no roll" in A&A Chess.

Any one of these modifications will provide a more meaningful contest than the conventional "all dice" approach. Another advantage is that these new methods virtually (orthodox and COF, completely) solve the email-play problems of dice rolling. (The single dice roll offer very little temptation, nor even opportunity, for indiscretions of honor). Respective moves are simply made by each player in turn. The final configuration, after a move, is merely sent to the opponent, along with perhaps an explanation of anything one has done, which can not obviously be resolved. If the receiving player cannot justify the move, then he may challenge the move; calling for a full explanation of the issue he questions. This has the effect of reducing the time, correspondence, and confusing normally associated with email-play.
Copyright 1995. All Rights Reserved.

Any private non-profit entity may use these modifications without charge. However, profit oriented entities, such as the Milton Bradley Company, may NOT incorporate this modification (nor any derivative and/or variation thereof) into their rules or game documentation, without written permission from David Albert Harrell.

International A&A Chess Federation
San Diego, California

Announcement of an International competition

In 1995, a competition in diceless A&A was held. Below, you find the announcement.

From: D.Albert Harrell
International A&A Chess Federation
San Diego, California

The first official International competition in diceless A&A will take place (via email) in September 1995. The winner, and first IA&ACF World Champion, will be recorded and announced following the final round of this match. All other participants will be officially rated according to their final standings.

There are no entrance fees or payments of any kind involved in this tournament. However, judging from the initial response to the recent publication of the A&A Chess format, there will certainly be a great deal of notoriety for the winner.

A&A Chess Federation 1995 Tournament.
1. All Tournament games will be played using the totally diceless COF variation of A&A Chess. (Carry Over the Fraction). Anyone who needs a copy of the Official IA&ACF Tournament Rules should email a request.

2. If you wish to be entered as a contestant in the Sept. 95 International Championship Tournament, you must officially register by requesting a starting game assignment from D. Albert Harrell on or before Aug. 26. You will receive the Rules and email move formats within a few days, and your game starting assignment on Aug. 28.

Written by: David Albert Harrell.
WWW page created: 1995 or 1996. Last modified: April 9, 1998.