What are the Odds?

I’m sure all of us have heard a friend complaining about losing a game because of their dice (and most of us will be guilty of it ourselves!). Indeed, I have found myself lamenting my dice rolls when I didn't even have a firm grasp on if I was being unlucky or not! As a result this article was born with intent of helping players understand the probability of their choices paying off, both in game and for list writing and wargear choices. Without further ado let's jump into some numbers!

The first topic to be discussed is one of the most important in the entirety of the game of SBG and probably the most complicated in terms of trying to work out the probability in your head; your odds of winning a fight. 

The below graphs show your dice on the top row, your opponents dice down the left hand side, and your chance of winning the duel in the coloured cells. There are three tables, one each for you having a higher fight value than your opponent, a lower fight value, and tied fight values. Let’s illustrate how the tables can be used by taking a character and seeing how he fares in a variety of scenarios. 

1. Boromir of Gondor from the Fellowship army list has F6 and 3 attacks and has charged into a lowly Gundabad Orc Warrior who has F3 and only 1 attack. Using the Higher Fight Table we can see that Boromir has a massive 82.6% chance of defeating the Orc in the duel. 
2. After dispatching this Orc Boromir charges into Fimbul the Hunter who Heroic Strikes to F6, matching Boromir’s fight value! Looking at the middle table, for scenarios with equal fight, Boromir has a 59.5% chance of victory over Fimbul’s 2 attacks. 
3. Once Fimbul lies slain, Boromir looks for his next target only to find Azog bearing down on him. Azog has 3 attacks and F7 so we will need to look at the last table for duels where we have lower fight. Boromir doesn’t look as strong in this duel with only a 35.2% chance to overcome Azog’s superior skill and will likely consider using some of his might points to Heroic Strike or Heroic Defense. (Boromir should feel lucky that Azog isn't on his White Warg as the cavalry charge bonus would bump him up to 4 attacks and give him an even greater edge).

Another example is one I faced myself recently when using my Hunter Orcs against Corsairs of Umbar. When the F3 2A Hunter Orcs engage the F4 1A Corsair Warriors they have a 57.9% chance of victory, but when those warriors gained spear support, upping their attacks in the duel to 2, those odds turned almost on their head and the corsairs now had a 61% chance to win the duel. This left the D4 Hunter Orcs thinking they would rather be somewhere else to avoid getting whittled down. 

Obviously once a duel has been won the need to dispatch with your foe is next on the list, so how likely are you to be able to do that? The below table shows how many wounds are expected with a given number of attacks with different wound rolls required. Drawn Combat’s Dan has recently started bringing his Army of Thror to our games so I’m curious what my Hunter Orcs can be expected to do against his favoured leader, the D9 Thror! The Orcs require a 6+ followed by a 4+ to wound the Dwarf King so if a single 2A Orc manages to win his duel he only has a 16% chance of dealing a wound. Even when 3 Orcs are striking after a duel the chance of a single wound is only 40.7%! They really have an uphill struggle to try and take him down. 

Let's look at another scenario that puts the above table into practice and considers a Hero of Fortitude’s warband filled with 12 archers and the damage output they can be expected to do against a variety of targets. The table below breaks down the expected hits these archers will get depending on their shoot value and the number of expected wounds depending on their opponent’s defence. Simply go to the shoot value of the archers and move right along that row until you meet the column that matches what they need to wound and in that cell will be the expected wounds.

Take for example the difference between 12 rangers from the Rangers of Ithilien Legendary Legion (3+ shoot with S2 bows and a common sight at the 500 pt game level) shooting at a force with a mixture of Osgiliath Veterans and Warriors of Minas Tirith (all equipped with shields). If the Rangers choose to shoot at the Veterans for 3 turns as they make their way across the board they will do an average of 4 wounds. If they instead choose to shoot the Warriors of Minas Tirith, who are D7 because of the Shieldwall special rule, they will average only half of that! 

Another example we can discuss is spending 20 points on a Felbeast to give it armour and upgrade it from D6 to D7. This will give it much more resilience against S2 shooting, but will make no difference against S3 shooting. This means that in a meta game where Rangers of Ithilien and their S2 bows are common the upgrade may well be worth the price, but if Elf bows with S3 are the prevailing form of bowfire the points may be better spent elsewhere.

Finally, let's look at your odds of passing courage checks. This was one of the stats I paid least attention to when starting out, but after playing against a lot of terror causing heroes and monsters I realised it was one of the most important, not to mention the benefits it brings after your force breaks. The below table shows your likelihood of passing a courage check for a given courage value.

At the high end of C7, which you'll find on Uruk Hai Berserkers, you are only ever failing on a roll of a double one. Not much to worry about! Orcs are much more cowardly and often have a courage value of C2, meaning they will be failing their break tests and running 58% of the time. If there a model with Harbinger of Evil nearby this increases massively and almost 3 in 4 of your models will be running away!

Hopefully you have found these numbers useful and they will help you make choices like do I charge into this hero, or do I spend 30 points on a warhorn. If you want a handy place to look at the figures we've prepared a quick cheat sheet that you can find here. Feel free to print it off and use it in your games!