Playing the Odds in Ogre/G.E.V.

by Roland Parenteau

From the first time you play Ogre or G.E.V., you know they're games in which you get to throw the dice a lot. A newcomer to wargaming might think any game in which you throw the dice so much is ruled by luck. The judgment is understandable, but not true.

In fact, Ogre and G.E.V. are less ruled by chance than many other games that rely on dice for combat. The law of averages favors the evening-out of die rolls over the course of any game.

This does not mean that bad throws early in a game are likely to be followed by good throws later. It merely indicates that games with a high number of die rolls will have a higher likelihood of giving each player equal treatment than games in which the die is rolled only a few times.

All this means two things for the wargamer: 1) Except in rare cases, the player who plays most skillfully will win; and 2) A player who can use probabilities better than his opponent will have a substantial advantage in the long run.

Ogre and G.E.V. give a player ample opportunity to use his knowledge of probabilities. Take the common problem of how to allocate attacks to inflict the maximum expected damage on an enemy. For example, a player is often faced with the decision whether to attack an enemy unit with one 2-1 attack, or to attack the same target twice (with different units, of course) at 1-1 each. Which is better?

The answer is two 1-1 shots. How do you figure? Let's go over the procedure.

On a sheet of paper, list the 36 combinations in which two dice can be thrown (1/1, 1/2, . . . , 6/6). For each combination, pretend that each number is a die roll resolving a 1-1 attack, and write down the result of two combined 1-1 attacks on the unit. (For the sake of argument, let's suppose the target is an armored, non-Ogre unit.)

The combination 1/1, therefore, would have an effect of NE, while a 3/4 combination would have an X effect. (The 3 would bring a D result, and the 4 would bring another D result to destroy the already disabled unit.)

Follow this procedure for armored units, then repeat it for infantry units and again for Ogres, remembering the different handling of D combat results for each unit type (infantry units are not disabled by D results, but simply lose one step – Ogres ignore D results altogether). When you are finished, add up the number of X, D, and NE results.

What you find may surprise you. While a single 2-1 attack against an armored unit gives a 50% chance of X, a 33% chance of D, and a 17% chance of NE, two 1-1 attacks give a 67% chance of X, a 22% chance of D, and only an 11% chance of an NE result. That means two 1-1 attacks have a better chance of destroying the unit outright than a 2-1 attack, and less chance of missing.

Results with other units are almost as favorable. With infantry as the target, two 1-1 attacks give a 56% chance of X, an 11% chance of two Ds, a 22% chance of obtaining a single D, and an 11% chance of NE. Against an Ogre, two 1-1 attacks have a 55% chance of an X, compared to the 50% chance with the 2-1 attack alone.

Even these numbers do not tell the whole story. Splitting the 2-1 attack into two 1-1s gives the attacker a chance to destroy the target with the first shot, thereby saving some firepower for another target. Against infantry units, there is also the possibility of obtaining two consecutive D results, reducing a target unit from a "3" to a "1."

After obtaining these interesting results I investigated some other possible combinations. The results are shown below.

Percentage Chance of Obtaining Given Result Through Attack Combinations and Single Attacks

Target is:	Armor				Infantry					Ogre
	X	D	NE		X	-2	-1	NE		X	NE
Two 1-1s	67	22	11		56	11	22	11		56	44
vs. one 2-1	50	33	17		50	0	33	17		50	50
Two 1-2s	33	22	44		31	3	22	44		31	69
vs. one 1-1	33	33	33		33	0	33	33		33	67
Two 2-1s	86	11	3		75	11	11	3		75	25
vs. one 4-1	83	17	0		83	0	17	0		83	17
1-2/1-1	50	28	22		44	6	28	22		44	56
vs. one 2-1	50	33	17		50	0	33	17		50	50
2-1/1-1	78	17	6		67	11	16	6		50	50
vs. one 3-1	67	33	0		67	0	33	0		67	33
Three 1-1s	85	11	4		74	11	11	4		65	35
vs. one 3-1	67	33	0		67	0	33	0		67	33
Three 1-2s	48	22	30		43	6	22	30		42	58
vs. one 2-1	50	33	17		50	0	33	17		50	50
	X	D	NE		X	-2	-1	NE		X	NE
Target is:	Armor				Infantry					Ogre

Keep in mind that the percentages given in the table are the chances of obtaining a particular result on a given target for the overall combination of attacks, or for the single attack to which the combination is compared. In conducting several attacks, there is always the possibility that an X result will be obtained on an early shot. This must be considered, along with the urgency of your position, in apportioning the attacks.

It can be shown that, in combinations of attacks involving two different odds (i.e., 2-1 and 1-1 vs. 3-1), the order of attacks makes no difference; the chances of obtaining X, D, and NE results remain exactly the same.

Assessments of the effectiveness of each combination attack in place of the comparable single attack follow.

Two 1-1s vs. one 2-1: Two 1-1 attacks are equal or better in every instance.

Two 1-2s vs. one 1-1: The two 1-2 attacks come close, but are slightly less favorable than the single 1-1 attack.

Two 2-1s vs. one 4-1: Percentages favor the 4-1, but not by much. The big difference is that two 2-1s give you a small chance of missing entirely, whereas the 4-1 gives you none. Two 2-1s would be an intelligent choice where you want to economize firepower.

1-2 and 1-1 vs. 2-1: The 2-1 is better.

2-1 and 1-1 vs. 3-1: If the target is an armored unit, you are better off spreading out the attack. If the target is an infantry or Ogre unit, the 3-1 attack is better.

Three 1-1s vs. one 3-1: If the target is armor or infantry, three 1-1s are definitely better. If the target is an Ogre, the 3-1 is just slightly better – but since two 1-1 shots give nearly a fifty percent chance of destroying the target, with a "free" shot at another target, three 1-1s might still be an attractive option.

Three 1-2s vs. one 2-1: The 2-1 is better.