An Odd Call


Hollow Earth Expedition (HEX) is a game based around one of the truly classic pulp settings, a hollow Earth inhabited by dinosaurs and lost civilizations. Exile Games has a short teaser/ introduction to the game in an example of play on their website.

As such examples go, it does a very nice job of giving a little flavor of the setting and showing how combat and some combat options work. In the example a Great White Hunter character decides to go off alone to track down and kill a T Rex. He tracks the T Rex but fails to gain surprise. The hunter then makes a Called Shot trying to at least stun the animal so that he can get a second shot in before it tears him apart, but he rolls just a little too low. So the T Rex rushes him and mangles him into unconsciousness. However, in this example certain things seemed a bit off. Off enough to warrant a closer look at how good a call Called Shot is in HEX.


Dice in HEX are effectively d2’s. While pretty much any die, or even coins, can be used, every die has a 50% of scoring a success and a 50% chance of scoring nothing. To attempt a task the player rolls the appropriate number of dice determined by skill and circumstance and counts the number of successes.

The basic combat attack involves the attacker rolling their attack dice, which will be determined by skill, with bonuses for things like a powerful weapon and penalties for things like cover or range. The defender then rolls their defense dice pool and counts their successes, subtracting these from the attacker’s successes. The attacker’s remaining successes are the resulting damage from the attack. For example, if the attacker rolled 6 successes and the defender 3 successes the defender would take 6 – 3 = 3 points of damage. Depending on how much the damage exceeds the target’s Stun rating the target may be stunned or knocked unconscious by the attack. This is actually a rather D&D like system in that being really hard to hit or heavily armor are both represented by the same thing, a high defense rating.

The combat option being addressed here is the Called Shot. In order to make a Called Shot a character takes a penalty on their number of attack dice equal to the defense rating of their target. The target then does not get to roll their defense dice against the attack. For example, if the attacker had a dice pool of 14 dice for the attack and the defender had a defense of 5 the attacker could ignore the defense by taking a penalty of 5 to their attack, leaving them rolling 9 dice. The defender would then not get to roll any defense.

In the example of play the hunter has a special talent giving him a bonus for Called Shots. His accuracy talent reduces the normal penalty by 2. So if a target has a defense of 5 he can make a Called Shot against them and only suffer a -3 die penalty rather than the normal -5 die penalty.

HEX’s equivalent of hero points/ bennies/ FATE points are called Style Points. They can be spent for various temporary bonuses. For 2 Style Points a character can increase the effectiveness of a talent. So in the example the hunter spends 6 Style Points to increase his accuracy talent by three levels to four. As each level reduces the Called Shot penalty by 2, the result is that he reduces the penalty by 8, instead of his normal 2. Style Points can also be spent to increase a dice pool by one die per point spent. So a character rolling 5 dice to try to climb a cliff could spend 3 Style Points and roll 8 dice, 5 + 3, for the attempt.

Increasing the accuracy talent versus increasing the dice pool

In the example the hunter has a total dice pool for his attack of 14 dice. He has pumped up his talent so that he will reduce the Called Shot penalty by 8, a maneuver that cost him 6 Style Points. It turns out that the T Rex has a defense of 8. So the Called Shot penalty for our mighty hunter is reduced from 8 to 0, 8 – 8. He rolls 14 dice and manages to roll 8 successes and the T Rex doesn’t get to roll defense.

What would happen to the roll if he had not pumped his talent but instead just burned the Style Points getting extra dice? His attack pool of 14 would be increased by 6 for a total of 20. However, the Called Shot would give him an 8 penalty, reduced by 2 thanks to his accuracy talent, for a 6 die penalty. This would give him a grand total of 20 – 6 = 14. The exact same number as he got pumping his talent.

What would happen if the T Rex had a higher defense, say 10? If he pumped his accuracy talent he would suffer a penalty of 10 – 8 = 2 to his attack pool. This would give him 14 – 2 = 12 dice. If he simply increased his pool he would get 14 + 6 = 20 dice. However, the Called Shot penalty would be 10 – 2, from his base accuracy talent, = 8, for a final total of 20 – 8 = 12. Once again, the exact same number of dice.

But what if he has misjudged how tough a T Rex is and the dinosaur only has a defense of 5? If he pumps his accuracy talent, he has 14 dice reduced by a Called Shot penalty of 5 – 8 = -3. However, the penalty can’t be reduced below zero so the penalty is 0. He would roll a total of 14 – 0 = 14 dice. On the other hand, if he just adds dice to the pool he gets 14 + 6 = 20 dice. The Called Shot penalty would be 5 reduced by 2 for his accuracy talent to 3. This gives him 20 – 3 = 17 dice, a significant improvement over pumping his accuracy talent!

So pumping his accuracy talent is often just as good as increasing his dice pool. However, it is never better than increasing his pool and is sometimes worse. Therefore, he should never pump his talent, just add dice to his pool. Apparently he is not as experienced a Great White Hunter as we thought.

Called shot versus a regular attack

In comparing a Called Shot against a regular attack we should start by assuming that our hunter does not have an accuracy talent. After all, it would be misleading to compare the two for a character with a special bonus to Called Shots.

Without the talent the hunter would roll 12 dice for his Called Shot. He starts with 14 dice and adds 6 using Style Points. As shown above, adding dice via Style Points is as good or better than using them to decrease the Called Shot penalty. Without the accuracy talent he would suffer the full 8 die penalty for a total of 14 + 6 – 8 = 12 dice. Given that each die has a 50% chance of scoring a success and the T Rex can’t defend against a Called Shot, his average damage would be 6, 12/ 2.

A regular attack would use his 14 plus 6 from Style Points for a total of 20 attack dice. He would not suffer any Called Shot penalty because he wouldn’t be making a Called Shot. However, the T Rex would then get to roll its 8 dice in defense. The average success on 20 dice are 10 and on 8 dice are 4 giving an average damage from the attack of 10 – 4 = 6! The exact same average damage.

It should be noted that just because the averages are the same does not mean that the attacks are statistically identical. It is possible for all 20 attack dice to roll successes and all 8 defense dice to fail, ok the chance is about 4 in a billion but it is possible, yielding 20 damage. No matter what he rolled for the Called Shot he could never do more than 12 damage. Because so many more dice are being rolled for the regular attack it is less likely to roll completely average and more likely to roll above or below average than the Called Shot. For those of you following this series, its variance is higher. This is displayed in Figure 1.

This leads to an interesting result. If average damage or lower is good enough then a Called Shot is probably a character’s best bet. However, in the T Rex example our intrepid hunter gets munched because he needed to do 9 damage to the T Rex to stun it, and only did 8. The likelihood of rolling 9 or more damage actually goes down in this example using a Called Shot rather than a regular attack as can be seen in Figure 2.

The difference is significant, with the regular attack scoring 9 or better 17% of the time while the Called Shot only scores that 7% of the time.

Called Shots are useful when average or lower damage is good enough, while regular attacks are the best bet for hitting a tough opponent for high amounts of damage.

Accuracy talent

Our intrepid hunter isn’t a complete fool, however. His accuracy talent gives him a bonus for making Called Shots. As mentioned above, thanks to his talent he rolls 14 dice to make a Called Shot on the T Rex, average damage 7. However, he gets no bonus on a regular attack and so would roll 20 dice minus 8 dice from the T Rex’s defense for an average of 6 damage. Does this bonus make the Called Shot a good call? Yes. His chance of doing 9 or better damage with his Called Shot is 21% as opposed to 17%. He made the right choice but just didn’t roll well enough, and so may end his days as T Rex chow.


Why look at Called Shots in HEX? They are a good example of a specific type of combat option. Called Shots pass the big test for a viable combat option, sometimes they are better than a regular attack, and sometimes they are not. However, the actual effect of the maneuver is the exact opposite of what you would expect it to be.

When someone hears the term Called Shot they are thinking of attacking a very specific part of the target in an effort to strike at a weakness. Hitting a specific target should be more difficult than firing at the center of mass just trying to hit the target at all. So, one would expect that a Called Shot would be more likely to fail completely than a regular shot. However, as the Called Shot is specifically targeting a critical spot on the target, should the Called Shot work, it would be expected to generally be more effective than a regular shot.

Called Shots in HEX do the opposite. They produce more consistent results than normal shots. They are more likely to do some damage but less likely to do large amounts of damage. It is this kind of combat option that really throws people for a loop. Unless they have run all the numbers, they will be using the option when it is least effective and not using the option when it’s most effective.


6 Responses

  1. Another great analysis article, Erik. I’ve never even heard of the game, and yet it was still enjoyable to read on a geeky, OCD, math and puzzle level.

    Especially love the conclusion section. Why do game designers do this sort of nonsense? There’s so many games where the flavor text of the special actions are completely disconnected from the mathematical reality of the action, like the called shots in the system under the spotlight here. As you pointed out, it results in players picking options based on the flavor text, and often getting an effect that does something other than what they were hoping for. Looking at this, one has to conclude that the designers didn’t have a fuzzy clue what their special move did to the probability. And considering how simple their core mechanic is, they should have been able to figure the probabilities out themselves. Very sloppy and amateurish game design.

  2. Thanks Rolfe, though in certain respects their called shot mechanic is actually extremely clever. Almost every game under the sun does called shots by decreasing accuracy and increasing damage. But here accuracy and damage are the same, so they simply can’t do that. Instead they came up with a method that changes the variance. Yes, they should have looked at the results more closely, but on the scale of rules blunders I’ve seen it’s a pretty moderate mistake.

  3. While they may have come up with a clever mechanic, the choice of conceptual flavor-text they awkwardly grafted on to it was an ill-considered and sloppy decision. The name they chose will no doubt mislead players about it’s intent, purpose, and effects.

  4. Obviously I think that it is an error. I just wrote a long winded article on why I think that it’s an error:) However, I think that it is a very subtle error. On the surface their called shot mechanic does what you would think a called shot mechanic would do, it allows you to ignore armor. It seems likely that that is how they came up with it, looking for a way to ignore armor. The problem is that if you understand variance this mechanic that seems to do the right thing actually does the opposite. Compared with something like the feinting rules from seven skies this requires real attention to the statistics to catch. Given the trouble most designers seem to have with addition I’m not surprised by this kind of mistake at all. The point of these articles is in fact that Nobody seems to check stuff like this. In my OCD I just think that they should.

  5. I think they should, too. In fact, I think it’s high time the industry stepped it up a little. Just sayin’.

  6. […] to gain an advantage, it should actually be a way that a sneaky fighter can gain an advantage. If called shots are supposed to help deal with tough, armored opponents, then they should be good against tough, […]

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