Probability in Oathmark - Magic

Early on, when I started writing this blog, I wrote a several articles on probability in Warhammer Underworlds. Since then, I have discovered Oathmark. Oathmark uses D10 for all its dice rolls and I am interested to see how easy (or hard) it is to cast a particular spell.  

To begin with I need to explain how magic work in Oathmark. Each race has access to spellcasters. Each spellcaster has a level. The level dictates two aspects of the spellcaster: 1. How many spells they know, 2. How many dice they roll when attempting to cast a spell. It is this second component that I want to consider. 

My questions are:  

1. What is the best spellcaster level to take in my army? 
2. What are the best spells for each level of spellcaster? 

Casting a spell

When a spellcaster attempts to cast a spell, they roll a number of D10 equal to their spellcaster level. 

Example. A spellcaster (2) would roll 2D10 when attempting to cast a spell. Whereas a spellcaster (5) would roll 5D10.  

To successfully cast a spell only one of the D10 needs to equal or exceed the casting number (CN). Therefore, the higher the spellcaster's level the easier it is to cast a spell. Why is this? 

Understanding probability

Let us consider a D10. This is a die with 10 sides. If, I need to roll a 7 or more on this die to be successful, four out of the ten sides (7,8,9,10) will give me success 4/10 = 40%. Another way, I could put this is to say I would be unsuccessful 6/10=60% of the time. When calculating probability, understanding the chances of failure is important to calculate the chances of success with multiple dice. 

If I roll two D10, I obviously increase my chance of rolling the desired number. So, let us consider the casting roll of 7 again. If I have one die, I have a 60% chance of failure and a 40% chance of success. If I roll two dice, I have 6/10 x 6/10 = 36/100 (36%) chance of failure or a 64/100 (64%) chance of success. 

If I roll three D10, the chance of success increases further. With 3D10 the chance of failure = 6/10 x 6/10 x 6/10 = 216/1000. Therefore, the chance of success = 784/1000 = 78.4% 

So, the more dice you get to roll the lower the chance of failure, although I expect you found this fairly obvious. Where, I think this idea becomes more useful and informative is deciding upon the spellcaster and spells for your army. 

Spells and Spellcasters

The lowest casting number of a spell in Oathmark is 4 and the highest is a 10. Having a low level spellcaster attempt to cast a high casting number spell such as Lifebane (CN10), is likely to result in a failure. 

So let us consider the chances.  

As the chart shows the higher the casting number the lower the percentage chance of successfully casting a spell. Equally, the more dice you can use to cast a spell the higher the chance of being successful. So, what represents a 'good' chance?  

I am inclined to feel that above 75% is a 'good' chance. This would represent a spell working three out of four times. Above 90% I would be expecting to work almost every time. I can now start to decide on which spells and spellcasters I would like to complement my army.

Having looked at these percentage chances, I see little value in taking a level 1 spellcaster. They have a small chance of being successful when casting even with low casting number spells. They are in short, a waste of points. Equally, I think the level 5 spellcasters, whilst highly likely to be successful with all but the highest casting number spells, are just too expensive in points. This, therefore, leaves me with the level 2, 3 and 4 spellcasters. 

All three of these different level spellcasters are worth taking, but the choice should be made based on the spells you wish to use. If you wish to use spells with a casting number of 6 or lower, then a level 2 spellcaster should be sufficient. For spells with a casting number of 7 or less, a level 3 spellcaster. For spells with a casting number of 8 or less, a level 4 spellcaster.   

I would be very cautious of trying to use spells with a casting number of 9 or 10, if you like your spellcasters to be reliable. 

Personally, I favour the level 3 spellcaster as my main wizard. This character has three spells, which you can expect to be reliably cast if they have casting numbers of 7 or less. Spells with a casting  number of 7 or less, provides you with a good range of spells, including Fireball, Fleet feet and many of the race specific spells. The character has a reasonably points cost, although they are still too expensive for smaller games. The main issue with a level 3 spellcaster is that it requires a terrain slot in a kingdom chart, but if you can accommodate this then this character is well worth taking. 

The level 2 spellcaster makes for an excellent secondary wizard. This wizard allows you to take a second backup version of the spell you really need to pull off your grand plan. This wizard also allows you to take those lower casting number spells that are not worth giving to the high level spellcaster

I found researching the article very helpful. I now have greater insight into the spellcasters and spells I will be taking in my army. If you have questions, please drop them in the comments below, I love to read them.  Happy Hobbying!