Tuesday, 18 November 2014

Luck Or Strategy?

Graham & I were sat in the pub last Sunday having our regular post game debrief when I asked Graham what turned out to be a key question: did he win by luck or better strategy? As we all know this is the perfect topic for a chat over a pint or two but this time it was different. Firstly because it lead to an second discussion about rolling "good, or bad, dice at crucial moments" and secondly because we'd recorded every dice roll in the game.

That's right, in our 800 point game of Field of Glory Renaissance (FOGR) we recorded over 1,000 dice rolls in a three hour game. That's just the number of spots nothing else. Sad, I know. I don't want to go into the specific reasons why we decided to do this at this point other than to say we've done this before and found it really helpful.

Let's look at the numbers.

In the tables below an ideal distribution would have normalised figures very close to 100 for every score. The significance figure is the variation (standard deviation) from the average and figures over 1.0 are slightly (65%) significantly different from the average and figures over 2.0 are significantly (95%) different from the average.

Before the tables, a word for the general reader: in FOGR rolling 1s usually results in serious adverse consequences just as 5s & 6s usually bring about positive outcomes. This isn't always true but it's close enough for the purposes of this post.

Martin

1

2

3

4

5

6

Sum

Avg

Dev

Raw 94 94 83 91 85 88 535 89.2 4.6
Normalised 105 105 93 102 95 99
Significance 1.2 1.2 -1.5 0.4 -1.0 -0.3

From this distribution you can see I had consistently rolled more than the expected number of 1s & 2s and less than the expected number of 3s & 4s. Overall I was more likely to have rolled 3 or less (303), than 4 or more (232). In FOGR this is often the difference between a hit and a miss, or a pass and a fail.

Graham 1 2 3 4 5 6

Sum

Avg

Dev

Raw 56 83 86 83 94 80 482 80.3 12.8
Normalised 70 103 107 103 117 100
Significance -2.4 0.3 0.5 0.3 1.3 0.0

On the other hand, Graham rolled 10% less dice than I did but rolled a lot less 1s than expected coupled with a lot more 5s than expected. Graham was much more likely to roll 4 or more (340) than 3 or less (280).

All 1 2 3 4 5 6 Sum Avg Dev
Raw 150 177 169 174 179 168 1017 169.5 10.5
Normalised 88 104 100 103 106 99
Significance -1.1 0.4 0.0 0.3 0.5 -0.1

To the relief of statisticians everywhere, the numbers for all 1,017 dice shows a much more even distribution with the exception of significantly (65%) fewer 1s than expected. So even my above average number of 1s did not "compensate" for the low number of 1s rolled by Graham!

If you are still reading this then you are probably about to ask so what? Well I think I can use the data to answer the question in the title of this post. It's quite simple really: whatever strategy I had was "hampered" by my below average dice rolling. Even with my superior troops re-rolling 1s I was still more likely to roll 3 or less second time around. Conversely, Graham's strategy was "enhanced" by the significantly low number of 1s he rolled and the slightly higher than expected number of 5s. So we now know that luck played a big part in this game; it wasn't everything but it was significant.

Hit or myth?

Naturally, the above analysis wasn't available to us straight after the game and as the discussion ranged wider Graham raised the old saw of "what matters most is rolling the right/wrong dice at the right/wrong time". Put another way it's not how many 1s you roll that matters, it's when you roll them that counts. This focuses on luck at a crucial point rather than throughout the whole game.

Now any wargamer will regale you with stories of how such and such a unit of absolute rubbish magically rolled double 6, crushed their opponents and created the opening that won the game. Of course they often have the opposite story too: the elite regiment that rolled double 1, died to a man and allowed the enemy to capture the key position. Interestingly, in my experience the tales are more often hard luck stories.

As the discussion continued I began to question this "received wisdom". I've heard it many times from many different players. Could it be another wargamers' myth? Surely games don't turn on just one or two dice rolls that often?

I'm not saying these exceptional things don't happen, what I am questioning is the importance placed on them by players and the implicit assumption behind it that the many hundreds of other dice rolls played no part in winning (or more usually losing) or in setting up the marvellous breakthrough (or collapse). This can't be right.

For example, in FOG unit cohesion is almost everything. However, if you roll double 1 in combat you drop two cohesion levels. As there are only four cohesion levels (steady, disrupted, fragmented & broken) if you are already disrupted dropping two levels breaks you and you are in trouble. Post-game FOG players will remember, and recount, when they rolled double 1 and broke but they don't always remember the earlier roll that disrupted them and "enabled" the "double drop" and broke the unit. Neither will they remember the failed attempts to rally the disrupted unit before the fateful "double drop".

More generally, if you haven't caused any casualties elsewhere, breaking one unit quickly will not win you a game unless your strategy and luck holds for the remainder of the game. Similarly, if you do breakthrough and cause further losses in short order it's more likely to be a result of poor play by your opponent, further favourable dice rolls or both.

Now pub talk is just that and I don't take it too seriously but there's a deeper point here. After a game you can easily kid yourself that if only you hadn't rolled double 1 at the crucial moment you would have done better (not lost so badly / survived for a draw / rallied to win the game / absolutely annihilated the opposition - you choose). Now we all know the dice favour you sometimes, sometimes they don't, but I don't buy the focus on crucial events at all.

For players, blaming extreme outcomes at crucial moments is just too seductive because it allows the player to absolves themselves from any responsibility. To expose the fallacy you only have to ask who placed the unit in peril, or initiated the successful attack? It can only be you or your opponent. Certainly not the dice. It is also dangerous because, if it's down to pure chance, the player has nothing to learn from the game and therefore won't improve.

If you'd like a non-wargaming analogy think about gambling in a casino. Amateur punters all have "winning strategies", the best being quit whilst winning, but they are all reliant on a run of good luck to do well whilst the house plays the percentages and always makes money. Are you a punter or the house?

Final thoughts

Before any of you comment that the first part says "luck played a large part" and the second part says you shouldn't do that, let me point out that the former conclusion is based on analysis of the whole game whilst the second part is about ascribing the outcome of a game to one isolated random event.

6 comments :

  1. I tried this out a few years ago by just rolling some dice 500 times each and noting the scores. The standard deviation was less than 1% for all five dice. In your game did you use the same dice for all the rolls or did you randomly take dice from a box? If its the former it could be that there's a very slight manufacturing error in some of the dice causing them to be slightly unbalanced. Dice cups and towers help make dice roll more randomly too.The true test of luck is to use professional quality "Poker Dice" which are supposed to be about as fair as it gets. After a particularly poor run of games over a lot of games last year I retired my dice, which had no signs of wear, and purchased a selection of dice from EBay and found my gaming standards seem to return to something more normal rathe than lots and lots of low scores. We are all superstitious creatures when it comes to dice and I know someone who goes mad if you try and use his dice in case you jinx them!
    We always remember the runs of 1's irrespective of the side but rarely remember the runs of 6's.
    At Iceni this year try as I could I just could not roll two up in about 20 combat rolls which would have meant my destroying lots of elements in one particular game.

    ReplyDelete
  2. I use a dice cup and about a stack of 20 dice for combats. Graham rolls his from his hand. Now there's point. ;-)

    Perhaps more seriously we've used these dice for years and not noticed any real bias.

    ReplyDelete
  3. Very interesting and thought provoking. My first year playing FoG, I acquired the reputation as the guy who rolls shite dice. I was running my Gauls and Carthaginians against opponents who ran Romans and Pike armies. In retrospect, it was the matchups that lead to poor results and probably not dicing. Plus I was new. Blaming your dice is pretty common in our field.

    ReplyDelete
  4. Understanding the mathematical model used in a ruleset and using it to one's advantage could be regarded as a prerequisite for a player who wants to be successful. The remarkable thing (for me at least) is that so many players actually frown at that approach and regard it as 'gamey' or downright cheating. I guess that on some subcontious level we have very hard time accepting the fact that all rulesets are just maths. :)

    ReplyDelete
  5. "Luck is just probability taken personally"

    I cannot remember who first said this, but it is certainly a wonderful and appropriate quote for wargamers!

    ReplyDelete
    Replies
    1. A great quote and it's from statistician Chip Denman see http://bit.ly/1AFExf3

      Delete

Comments are always welcome but this blog no longer accept anonymous comments.