Strands of Fate grant the Aeldari player a number of dice rolls you can fix for your advantage. Twelve dice are initially rolled to form your pool of substitute dice rolls, called fate dice. You can also choose to re-roll them all for a chance at a better selection. The trick is that each re-roll must be with one less dice. So how do we know when to stop re-rolling? Mathhammering optimal re-roll strategies for different purposes is what this article will aim to answer.
Note: This article is for the Strands of Fate rule for the Aeldari of 10th edition Warhammer 40000. Similarly titled rules from other editions will work differently.
The first thing to think about is what values would we ideally want to get. Obviously 6s are most desirable and 1s are least desirable but it is not quite a flat progression of increasing desirability from 1 to 6. In many important uses a 4 is just as good as a 6. For example, many Aeldari characters have a 4+ invulnerable save so a 4 will do just as well as a 6 in that case.
At the other end, even 2s have some small utility for auto-passing an armour save for a pheonix lord but 1s have no purpose at all.
What this means is that for example a roll of 2, 2 and 4 is actually a better roll than 1, 1 and 6 even though they both add up to the same. In former case all three dice could be used in some situation while in the latter only one could be used.
If all Strands of Fate dice came up all 1s it would be a no-brainer to re-roll, likewise if they came up all 6s it would be a no-brainer to keep them. The real dilemma comes at the edge case where a re-roll would have 50% chance of making things worse as better.
What kind of roll would be such an edge case? The edge case is not quite at the median roll because all values but 1s have some use. Also re-rolls are done with one fewer dice. However a median roll is a useful guide for a first pass at evaluating whether a particular roll is high or low.
The median roll for 12 d6 dice is 1,1,2,2,3,3,4,4,5,5,6,6. Knowing this helps with gauging whether a particular roll is high or low on particular dice. This is where to start when formulating an optimal re-roll strategy. Say for example you had decided that you want to minimise 1s. Knowing that two 1s is a median roll for 12 dice would tell you to re-roll if you had 3 or more 1s and keep it if it is 2 or less.
Each re-roll is made with 1 fewer dice, so the median shifts down with each re-roll. However since we are hoping to beat whatever we rolled initially we can still bear in mind that initial median.
Different dice values can do different things. Consequently, depending on the composition of your eldar force, your overall strategy and mission type, different re-roll strategies for strands of fate are called for. What follows are a variety of re-roll strategies for different aims.
Aeldari have high access to 2+ and 3+ hit rolls and fair access to 2+ and 3+ armour saves. Consequently even 2s and 3s do have some uses. 1s have precisely zero uses though. For this reason a basic Strands of Fate strategy would be to aim to minimise the number of 1s in your pool but treat other values as more or less equivalently desirable.
In this strategy we would re-roll if our initial roll had 3 or more 1s. Recall the median roll on twelve dice would give us two dice with 1s. So three or more 1s is a poor roll in this strategy and so worth losing a dice for a re-roll.
Every re-roll has a less than 50% chance of improving our overall pool (from a median roll) because we must re-roll with one less dice each time. Each re-roll also lowers the cap of total values as well. For this reason we should be very wary of re-rolling more than twice in this strategy.
On our second re-roll the maximum number of usable dice (values 2 to 6) will only be equivalent to the median number of usable dice on our initial roll using twelve dice.
Earlier I suggested that for certain uses like auto-passing invulnerable saves a 4 is as good as a 6. There are other circumstances however where 6s are very powerful and no other value will do. A roll of 6 can give us automatic critical hits and critical wounds which in combination with special rules like Devastating Wounds and Bladestorm stratagem would give powerful results.
The chance of getting 2 or more rolls of 6 on 12 dice is about 62%. Good odds but two rolls of 6 is just an average number of 6s on 12 dice. If we aim for three or more 6s the odds drop to 32%. Four or more goes to 13%. Six or more 6s goes down to less than 1% on 12 dice.
If we want to maximise 6s at the expense of other rolls we will need to be more aggressive with our re-rolls than we would be to minimise 1s. It is a quantity versus quality trade off.
Aggressive but not over ambitious. Even allowing six re-rolls that only gives us a less than 2% chance at ending up with six 6s at the high cost of six dice from the total pool.
Allowing up to six re-rolls also only gives us a 10% chance at five 6s.
If the target is four or more dice with 6s then we could get a 55% chance of that by going up to six re-rolls. These odds are almost bankable but realistically we should probably stop any time we get three or more 6s.
Incidentally if you would be happy with just three fate dice with a value of 6 then that becomes a virtual certainty after only four re-rolls.
1s are useless but there are other ways to remove them besides spending a dice for re-roll.
You can give a psyker in your army the Reader of Runes enhancement instead.
This enhancement allows one fate dice to be re-rolled per battle round. Assuming you can keep that psyker alive then you could potentially make up to five rolls of 1 into something usable (five out of six times) without reducing your total dice pool.
There is only a 1% chance of rolling six 1s out of twelve dice so re-rolling at the cost of a fate dice will almost never make sense if you have Reader of Runes.
Farseers also have a special rule, Branching Fates, that allows for one dice to be flipped to a 6 once per turn for a unit within 12″ of him. This by itself is a bit overpowered honestly, particularly since the wording specifies “per turn” rather than per battleround. This means you could be switching a 6 for a damage roll in your turn and then switching an armour save in your opponent’s turn.
Of course you have to take a farseer and keep him alive to do that but that could potentially turn ten 1s into ten 6s over the course of a game.
An honourable mention goes to the Harlequin Troupe Master who has the Cegorach’s Favour special rule. Like Branching Fates this rule allows flipping a Fate Dice to a 6 but only for those used by the Troupe Master himself on his hits, wounds and saving throws. He also can do this once per turn though, which means he can potentially eat as many as ten 1s per game.
There are plenty of ways for eldar to re-roll hits and wounds so it might be said that the best general use for precious fate dice is in keeping characters alive on their invulnerable saves. With a few exceptions, most eldar characters are on a 4+ invulnerable save.
With this in mind, we could aim to maximise fate dice with a value of 4 or more. On our initial roll we have a solid 61% chance of getting six or more dice with a value of 4 or more. Just one re-roll brings that up to a virtual certainty.
That is too easy, so let us be a little more ambitious and aim for eight dice with a value of 4 or more. Three re-rolls only gets us to a 37% chance of getting eight dice with those values. That could happen in a third of games but is not so likely that we should ever keep re-rolling if we ever got seven 4s and over.
Incidentally there is a 90% chance of getting seven dice with a value of 4 or more with just three re-rolls. That is probably the sweet spot for this strategy. Auto passing seven invulnerable saves is by no means a poor thing. Likely there will be a few 6s in the mix for some critical shenanigans too.
5 is a magic number for automatically passing battleshock tests assuming no modifiers in play. Eldar have a 6+ leadership across the board. Subbing one dice out of the 2d6 battleshock test for a 5 means the other die can have any value and the test will be passed. Alternatively we can use two dice to auto-pass by combining 2s with 4s and 3s with 3s to make the 6+.
So if you had in mind a strategy for creating unshockable eldar using fate dice, we can potentially use any dice 2s and over but 5s (and 6s) are worth two of any lesser usable dice.
Going back to the median dice roll we are using for a reference, the median roll would give us no less than seven auto-passed battleshock tests. The two 2s combine with the two 4s for two passes and the two 3s combine for another pass. Then the two fives would gives another two passes. Finally we could also use the two sixes to auto-pass although in practice 6s are probably more valuable for other purposes.
So this is the number we want to beat with our re-rolls, seven battleshock passes. There are a lot of combos that can do this because so many dice are usable for this purpose. Given that, we can use a basic minimise 1s strategy as above, with just an extra eye kept out for 5s and 6s since they are each worth two of the others.
While pursuing any of the above strategies, sometimes you might roll the dice and get a fluke roll that is super strong for a different strategy. Maybe you had built your list for the critical banker strategy. You have a Death Jester that you want to give a few 6s to wipe a Termie Captain from his bodyguard unit. But on your first roll you get no 6s but is stacked high with 4s and 5s instead.
It is a rare thing in itself to get say seven 4s and five 5s from your twelve dice. While there are no criticals in there, that is still a lot of invulnerable saves, high charge rolls and passed battleshocks. Should you re-roll it for criticals? The answer is probably no, you should adapt your strategy instead to use the dice given.
We can let the dice decide but we still need to recognise what is a high score though. To help us with that we can find our measure using the value sum of the dice. Then compare it with the average value sum for that many dice.
For twelve dice the average sum of values will be 42. Since 1s are useless we could ignore them, in which case the average sum is 40. So if you rolled seven 5s and five 5s that would add up to 60. This is far above 40 and clearly a rare high roll.
You may be surprised by how rare that is. A funny thing happens when you add up dice values. If you have just one dice the chance of getting a particular result is the same as another. You have exactly the same chance of rolling a 1 as a 3. If you roll two dice and add the numbers then you only get a 3% chance of rolling snake eyes. This while having a whopping 14% chance of getting a 6 for passing your battleshock test.
This is because when you add up more than one dice together there are more ways to make average values than outlier values. On a 2d6 there is only one way to make snake eyes; you need two 1s. However there are four ways to make the average value of 7 using a 2d6: a 2 and 5, a 3 and a 4, a 4 and a 3.
The more dice you add the more the average sums tend to reliably cluster in the centre. And so it is that 12d6 will tend to sum towards 42 remarkably often. The sum of 42 will come up 7% of the time. Compared that with the one in billion chance of getting 12 (twelve 1s) or 72 (twelve 6s).
Consider any roll higher than 42 to be a good roll even if it only sums to a little over. The odds of getting a 50 is only about 3%.
A fluke roll could also happen to us while re-rolling. However because less dice are used each time, so the average sum moves down too.
I will not list more because there really is not a single reason for re-rolling that many times more than that. Recall that even when aggressively fishing for 6s, six re-rolls only yielded a 2% chance of getting six 6s.
Finding the sum of 12 dice at the gaming table is likely not to be too easy for many people without the aid of a pocket calculator. However using a pocket calculator to sum your dice would probably narrow some eyes in your direction even in competitive environments.
That being the case either get good at mental arithmetic or go back to the measuring the median method mentioned at the beginning. You will be grouping your dice by their values anyway and while doing it you can mentally note which numbers are more, less or the same as the median roll of two for each number.
For example on twelve dice you should get an average of two 6s, so you know if you did well to get three 6s and poorly if you only got one.
At this point we ought to spare a thought for how taking Eldrad Ulthran can shake up the math here. Including Eldrad grants an extra three dice to your initial strands of fate roll. Naturally this shifts things upwards for all strategies mentioned.
Firstly the average sum on 15 dice will now be 52.5 rather than 42 for 12 dice. This will also give us re-rolls with average sums 3.5 less for each one: 49 for 14 dice, 45.5 for 13 dice.
He will also shift how many 6s, 5s etc we can expect on each roll too. Sadly since 15 dice is not so cleanly divisible by six as twelve dice we can not use whole numbers for the average number of a particular dice value we can expect. For Eldrad we can expect an average of two and half 1s, 2s, 3s etc. on his first roll.
If you want 6s then, three or four 6s is high and one or two is low for Eldrad on his first throw.
There we go, a simple but comprehensive guide on how to optimise your Strands of Fate re-rolls. What is the highest, or lowest, you have ever rolled for Strands of Fate? Did you ever work out the odds of getting that result?
Let me know in the comments or..
If you would like a nice tool for calculating dice roll probabilities I recommend Omnicalculator.