Post by mrweasely on Sept 12, 2006 18:00:39 GMT 1
The Lidless Eye is actually good. I thought it sucked.
The trick to the Lidless Eye, is its a card that's better held in reserve than actually played. That's because playing it costs you bzongaloads of actions. Holding it reserve, on the other hand, gives you extra actions.
How can this be? If you have TLE, allocate 0 eyes to the hunt instead of 1. That means you'll get an extra action die per turn. Well, actually you'll get an extra 5/6ths of an action die per turn, since 1/6th of the time the die will just flip over and roll an eye anyway.
Okay, so you get an extra 5/6ths of a die. But how often do you have to turn around and play TLE to add two dice to the hunt pool, because you rolled no eyes and the FSP rolls some swords? Well that depends on how many dice each faction has. Lets say its turn one, so SP=7, FP=4. I'd say that no eyes is acceptable against 0-1 sword. One eye is grudingly acceptable against as many as 4 swords. You roll 0 eyes on 7 dice 28% (aka 5/6^7) of the time, but 31% (aka 5/16ths) of the time you don't care because the FP roll one or zero swords. Multiplying, we find that TLE only must be played 19% of the time, and it costs two dice (although so early in the game, both are probably relatively worthless palantir and character results, so they're even bad dice). So allocating zero eyes with TLE in hand uses up .38 dice on average, and gives .83 dice on average, for a net gain of .45 dice/turn!
On turn 2, with a 4-8 dice split the math is similar, and TLE gives .51 dice.
In a 5-8 dice split, allocating zero eyes is still as good on turn 1: .46 dice. But then we have to worry seriously about another situation, and enter it into the calculations. If the FP roll 4-5 swords, we have to consider that a problem against just one eye, and maybe allocate more eyes mid turn burning our TLE. But maybe not - a Nazgul to Frodo's throat solves the problem with only a single die, when you can do it. At this point I throw up my hands and say that I still think it "feels" good to allocate zero eyes.
Even in the "SP nightmare" of a 6-7 dice split, allocating zero eyes still gains .34 dice on average, and you'd better do it too because the FP will be looking for military victory.
So TLE has just shot up in my estimation from terrible to great, great card. Given that it generates half a die per turn on average, it pays for itself the first turn you have it in your hand. Unlike Saruman and the Witch King, it starts generating dice immediately, with no upfront investment. TLE can be thought of as half a minion in your hand.
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Math footnotes. The dice generation formula I'm using is:
5/6 - [ 2 * (5/6)SP * (1 - (1 + FP)/2FP) ]
Where SP is the number of Shadow dice, and FP is the number of free dice.
Looking at subterms, the first 5/6 is the payoff die. The "2" is the fact that it costs 2 dice to put a die in the pool with TLE. The 5/6^SP is just the probability of rolling zero eyes, and the last term is the probability of the FP rolling 0-1 swords.
The trick to the Lidless Eye, is its a card that's better held in reserve than actually played. That's because playing it costs you bzongaloads of actions. Holding it reserve, on the other hand, gives you extra actions.
How can this be? If you have TLE, allocate 0 eyes to the hunt instead of 1. That means you'll get an extra action die per turn. Well, actually you'll get an extra 5/6ths of an action die per turn, since 1/6th of the time the die will just flip over and roll an eye anyway.
Okay, so you get an extra 5/6ths of a die. But how often do you have to turn around and play TLE to add two dice to the hunt pool, because you rolled no eyes and the FSP rolls some swords? Well that depends on how many dice each faction has. Lets say its turn one, so SP=7, FP=4. I'd say that no eyes is acceptable against 0-1 sword. One eye is grudingly acceptable against as many as 4 swords. You roll 0 eyes on 7 dice 28% (aka 5/6^7) of the time, but 31% (aka 5/16ths) of the time you don't care because the FP roll one or zero swords. Multiplying, we find that TLE only must be played 19% of the time, and it costs two dice (although so early in the game, both are probably relatively worthless palantir and character results, so they're even bad dice). So allocating zero eyes with TLE in hand uses up .38 dice on average, and gives .83 dice on average, for a net gain of .45 dice/turn!
On turn 2, with a 4-8 dice split the math is similar, and TLE gives .51 dice.
In a 5-8 dice split, allocating zero eyes is still as good on turn 1: .46 dice. But then we have to worry seriously about another situation, and enter it into the calculations. If the FP roll 4-5 swords, we have to consider that a problem against just one eye, and maybe allocate more eyes mid turn burning our TLE. But maybe not - a Nazgul to Frodo's throat solves the problem with only a single die, when you can do it. At this point I throw up my hands and say that I still think it "feels" good to allocate zero eyes.
Even in the "SP nightmare" of a 6-7 dice split, allocating zero eyes still gains .34 dice on average, and you'd better do it too because the FP will be looking for military victory.
So TLE has just shot up in my estimation from terrible to great, great card. Given that it generates half a die per turn on average, it pays for itself the first turn you have it in your hand. Unlike Saruman and the Witch King, it starts generating dice immediately, with no upfront investment. TLE can be thought of as half a minion in your hand.
____________________________________________________
Math footnotes. The dice generation formula I'm using is:
5/6 - [ 2 * (5/6)SP * (1 - (1 + FP)/2FP) ]
Where SP is the number of Shadow dice, and FP is the number of free dice.
Looking at subterms, the first 5/6 is the payoff die. The "2" is the fact that it costs 2 dice to put a die in the pool with TLE. The 5/6^SP is just the probability of rolling zero eyes, and the last term is the probability of the FP rolling 0-1 swords.