Wednesday 14 November 2012

The 'psychology' of numbers and game mechanisms … and misunderstanding chance

One of the most common comments I have had about my PORTABLE WARGAME rules is the fact that the Close Combat mechanism seems counter-intuitive to some players. The reason for this lies in the fact that players dice to see the effect of close combat on their Unit and NOT the effect their attack has had on the enemy Unit. In itself this is not a difficult problem to solve, and I hope to provide players with an alternative mechanism that achieves the same results in due course.

In my eyes the existing mechanism is not that different from the combat mechanism that Tim Gow incorporated into MEGABLIZ. This works as follows:
  • Each player counts the number of Strength Points that their units have.
  • They then pass one dice for each of these Strength Points to their opponent in a Combat Box (a small box with a lid that can be fixed so that opposing players can not see the scores on the rolled dice).
  • The players then shut their Combat Boxes, shake them to roll the dice inside, and then open the boxes to see the dice scores.
  • The results are then read off the Combat Matrix that is fixed to the inside of the Combat Box lid. The Combat Matrix shows the dice score required to inflict a casualty (i.e. remove a Strength Point).
  • Each player then adjusts their units' Strength Points accordingly.
Using this method the results of a combat are concealed from the opposing player … but each player has – in fact – rolled the dice that determine the effect of combat on their troops and not on their opponent’s troops.

Thinking about this ‘problem’ reminded me of a conversation (or was it correspondence?) that I had many years ago with Andy Callan. He pointed out to me that there was a ‘psychology’* behind the way we use (and perceive) the numbers generated by dice throws and the mechanisms we use to determine results using those numbers, and that if a game designer was not aware of this ‘psychology’ players might feel that a mechanism was counter-intuitive. In other words, if the mechanism or the results it generated did not conform to the ingrained expectations players had, it would not feel ‘right’.

For example players inherently expect higher numbers to produce positive results and lower numbers to produce negative results. Likewise they expect additions to dice scores to reflect some benefit and reductions to reflect a disadvantage. Since Andy Callan pointed this out to me I have always tried to bear this in mind … and as far as I can remember this holds true for the mechanisms I have used in my PORTABLE WARGAME rules.

Interestingly this ‘psychology’ also tends to cloud some people’s understanding of chance. When I was looking at ways of using an ordinary D6 die to replace the special dice used in Richard Borg’s MEMOIR ’44 rules, I was taken to task by one reader when I suggested:
  • Using 6 on a D6 die to replace the Grenade symbol on a MEMOIR ’44 die;
  • Using 5 on a D6 die to replace the Tank symbol on a MEMOIR ’44 die;
  • Using 4 or 5 on a D6 die to replace the Infantry symbols on a MEMOIR ’44 die;
  • Using 1 on a D6 die to replace the Flag symbol on a MEMOIR ’44 die.
I pointed out that the chance of a particular symbol coming up when a MEMOIR ’44 die was thrown was the same as the chance of a particular number or combination of numbers being thrown on a D6 die … but the person was adamant that I was wrong because:
  • The symbols appeared once (or in the case of the Infantry symbol, twice) on a MEMOIR '44 die, and each face of the MEMOIR '44 die had a symbol on it:
  • I had ignored the Miss symbol out altogether;
  • I had not allocated a value to the numbers 2 or 3 on the D6 die.
In actual fact the chance of throwing a MEMOIR '44 die and getting a result that will 'hit' an Infantry Unit is 1 in 2 (a Grenade symbol or one of the two Infantry symbols) ... which is exactly the same chance of throwing a 4, 5, or 6 on a D6 die; Likewise the chance of throwing a MEMOIR '44 die and getting a result that will 'hit' an Tank Unit is 1 in 3 (a Grenade symbol or a Tank symbol) ... which is the same chance of throwing a 5 or 6 on a D6 die; ... and so on.

The mathematics does not lie … but the perception we have of what we ‘see’ when the die is thrown engenders a feeling that the results that are generated are not ‘right’. In other words, the ‘psychology’ is tending to cloud our understanding of chance and making us feel uncomfortable with the mechanisms used and the results they produce.

Game designers (like me) should beware! Failure to understand this 'psychology' could be fatal to our wargames rules!

* When using the term 'psychology' in this blog entry I am using it in the sense that it concerns 'the understanding of mental processes and behaviour'.


  1. Interesting post as so often. I think there are actually 3 different aspects to some of these, habit, understanding and emotional connection.

    By habit I mean when a gamer is used to doing something one way and a set of rules does it differently. Even if they agree with a mechanism it can cause issues. A good example was with the fire and move in the BBPW we both were looking for the same result:4,5,6 if stationary, 5,6 if moving but my habit was to have a 4,5,6 base and a -1 penalty and your approach was a 5,6, base with a +1 bonus. Same scores, same reason and equally valid from a fresh start but when playing my habit would often over rule my understanding and I would make an error at least once a turn. The sort of thing that one swiftly overcomes if playing 1 set of rules as news habits eventually form but become something to keep an eye on when switching back and forth.

    The emotional connection is how I express my view of the psychological phenomena you mention. In war one attempts to do harm to one's enemy and rolling dice against him is the game equivalent.

    Understanding is a tricky one, especially when it collides with the others. For example, again using myself. I don't mind rolling for my unit in combat although emotionally I prefer the other way. But if I feel that cavalry are more likely to be shot apart if attacking a machine gun frontally than if they are charging some natives armed with obsolete weapons, then I want to see an unfavourable modifier when attacking the more dangerous enemy. To some extent the roster provides this because the machinegun is less likely to be destroyed and so the melee will be more protracted giving my unit more likely to make a roll that will indicate a hit. Its not really the same thing though unless multiple rounds are fought immediately as in Morschauser since it introduces an element of delay and the chance of outside intervention but its close enough to work.

    I decided once that since elite troops were actually more likely to fight on despite enemy action rather than actually doing more damage then I would give troops a -1 when fighting them as opposed to giving the elites a +1. After a couple of test games, it just "felt" wrong and I kept getting it wrong and having to redo the fights or shooting. I gave up eventually since the difference wasn't worth it too me.

    Its these sorts of things that makes design challenging!

  2. It all comes down to a realisation that any particular face of the cube is as likely to show as any other particular face. It is when you throw fistsful of dice things get tricky. Sort of.

    The psychology associated with dice games is an important factor. I recall years ago when playing a game, my opponent, about to make a roll, proposed a particular interpretation of the result. It doesn't matter what he proposed except to say that [a] it was a non-standard reading, but [b] the outcomes odds were precisely the same as the standard reading.

    As the odds were exactly the same, he thought I ought to have agreed to his proposal. He certainly was put out at my blunt refusal. My attitude was 'not on your bally life!' Reason? I could not for the life of me figure out why he made the suggestion at all (and it didn't help that it was a distraction). We argued the point for a while, and his case that the outcomes and odds were the same was correct. Quite correct - and entirely beside the point. He wanted to change. I saw no reason for change. I certainly saw no reason why he wanted to change. Probably the aroma of rat that surrounded his suggestion was simply a product of my imagination. That I felt I was being hustled into an agreement didn't make me feel easier about it. The sneer that I got didn't make me any happier (and up until then I had a good opinion of this guy), but persuaded myself that it was his problem and got on with the game.

    Have to say, though, I didn't like the sour taste in my mouth, and was glad enough to see the back of that game.


  3. Ross Mac,

    Habit, understanding, and emotional connection are probably a better ways of expressing what I was trying to explain in my blog entry, and are probably one of the results of playing dice-driven board games when we are young … which is something that I did not mention.

    I suppose that when it comes down to it we have become ‘conditioned’ to certain ways of looking at chance. For example:
    6 = Good result; 1 = Bad result
    +1 = Bonus; -1 = Negative
    Our experience builds on that. Hence the slightly different methods of achieving the same result that you mention in your comment. I suspect that they are the result of our different experiences.

    The emotional connection – and the example you give – is something that I had not really thought about, probably because I came at the solution from a different perspective … but what you say makes a lot of sense. In future I will try to remember that ‘In war one attempts to do harm to one's enemy and rolling dice against him is the game equivalent’ so that my choice of mechanism will be more likely to ‘gel’ with the players.

    Game design – and the thought processes that designers go through – is something that I try to understand in order to improve my own designs. I always look for ‘designer’s notes’ when picking up a set of rules as they will usually give you an insight into what they are trying to achieve and how they are trying to achieve it.

    All the best,


  4. Archduke Piccolo (Ion),

    I must admit that I might have had a similar reaction had another player suggested such a change in the way the results of dice throws were interpreted during a game … even if the chances of any particular result were going to be the same. Why change? And why suggest the change after the game has started?

    If the situation had arisen during a play-test, I might have considered the suggestion and asked why … but not during a ‘normal’ game. That just does not fit in with what I consider to be the ‘spirit of the wargame’.

    Some years ago I adapted one of the opening paragraphs from the RULES OF GOLF, as set down by the Royal and Ancient Golf Club, to describe how to play wargames. The amended paragraph read as follows:
    Wargames are played, for the most part, without the supervision of an umpire. The game relies on the integrity of the individual players to show consideration for other players and to abide by the rules. All players should conduct themselves in a disciplined manner, demonstrating courtesy and sportsmanship at all times, irrespective of how competitive they may be. This is the spirit of the wargame.’ I used to use this – and Fred Janes’ ‘Nothing can be done contrary or what could or would be done in actual war’ – at the beginning of every set of wargames rules that I wrote. Perhaps I ought to get back into the habit of doing so?

    All the best,


  5. Bob,
    An interesting topic. I agree with most of the points made, but have come round to the idea that rolling to discover the degree of damage - whether that be casualties or morale - suffered by one's own troops is a simple, but effective way of introducing some uncertainty/'fog of war' to an open, face to face game.

    Provided one has a trustworthy opponent who plays in the gentlemanly spirit you describe, of course! The opponent can still have the satisfaction of rolling 'to hit' the enemy.

    One could combine this with some simple rule that when a unit was reduced to the point that another successful 'hit' would cause it to break, this should be signalled on the tabletop display, perhaps by moving a command stand or placing a casualty marker, sine the opposing commander would then be able to deduce the unit's state from its appearance - I appreciate this is more applicable to close range, blackpowder warfare than the later eras when troops conceal themselves...


  6. if you call it the equivalent of a saving throw then in a players' mind it becomes more intuitive (i.e. if I throw a 5 or 6 my unit doesn't get hit). As you say, its all about interpretation.

  7. Arthur1815,

    One of the reasons why Tim Gow decided to have a 'hidden' combat result in MEGABLITZ was to produce that degree of uncertainty in the mind of the players. For example, talking to two opposing players during one game where I was umpiring I got feedback that went something like this:
    I just mounted an all-out attack but it does not seem to have had any effect on the enemy, even though my own casualties were quite light.’
    My troops only just held on that time. Another attack like that will decimate them.’
    You can guess the result; the attacker held off and brought up more troops to mount another attack and the defender used the break in the fighting to pull back to a better position.

    Finding an ‘honourable’ opponent is not always as easy it could or should be, which is a great pity … although I know a great many wargamers who would certainly deserve that epithet, yourself included!

    I like the idea you suggest for black-powder-era battles, as it is much more likely that your opponent would have a better idea of the effect combat is having on your units than during latter periods … although I can image that there might be arguments about visibility being obscured by powder smoke and generals ordering units to lie down to confuse the enemy!

    All the best,


  8. Phil Broeders,

    I had not thought of explaining it that way ... but it makes perfect sense!

    I know game designers do not like the idea of 'saving throws', but they are one way of ironing out some of the anomalies generated when one used a simple D6 die to generate results.

    All the best,


  9. Bob,
    I don't know if you are familiar with Acadamey Games' Conflict of Heroes series, but for those of your readers who aren't, I will explain how they handle secret combat results. When you score a hit against an enemy unit, the enemy player draws a counter from a bag (or bowl or box or whatever), looks at it, and places it face down on the affected unit - unless it indicates destruction, in which case the unit is removed. These results can range from no effect to completely pinned, with various shades in between. Their system is a trifle complex because each unit has fire points, movement points, and points required to activate, which can all be affected to some degree by the various hit counters.

    I always thought that would be a good system for minis, with only 2 - 4 results possible: unaffected, destroyed, and whatever other states apply in those rules; perhaps pinned, or a penalty against morale or activation or firepower. That way the opponent doesn't know the exact effect his fire has had until the unit activates again -- or fails to.

    Even in solo play, you could place these counters without looking at them until it is that unit's turn.

    And for those of us with dice luck issues, it would average out the results by having a finite, even if very large, set of counters from which to draw.


  10. The Ferryman (John),

    It is not a game that I have every heard of before, but the mechanism sounds interesting and somewhat akin to the 'chip' system that John Sandars used in his World War II rules, although in his case the results were not hidden as his rules were developed for solo use.

    All the best,



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