15) The Rings of Kether Solution

[champskees]

This book is similar to Space Assassin in that you can use your Energy Pills at any time (including during combat). This, combined with the gunfight rules means you have a very decent chance of completing this book no matter how weak your initial rolls (I do recommend at least Skill 8 though, as ‘test your skill’ rolls require you to actually roll less than your Skill in this book). Note that there are many ways to complete this adventure; the suggestion below intends to minimise the impact of the dice with as few fights and skill/luck rolls as possible. In fact luck is not used at all in this solution.

- Go to system’s starport on Kether.
- Find a shady starport canteen to conduct a few discreet enquiries.
- Approach one of the barmaids.
- Pay her 500 Kopecks.
- Approach the man.
- Enter 1201.
- Force your way into the room.
- Meet Clive tomorrow in place of Arthur.
- Try to find his address.
- Pose as one of Clive’s colleagues.
- Let the gunmen lead you into the house.
- Agree to go to the meeting (D6 Damage).
- Follow the sloop.
- Wave the car down.
- You did not stop to shoot.
- Anticipate a corner and slow down a bit.
- Push the car faster.
- Do not push it off the road.
- Try to draw up next to them.
- Shoot at them.
- Ram them in the back.
- Easy path: Enter one of the ordinary entrances (311).
        o Password is Wrench.
        o Turn up to the side passage.
        o Take Key.
        o Go down the passageway.
- Hard path: Have a look at the antigrav dray.
        o Drive it into the freight door to give a nasty shock to those behind it.
        o Search the man to see how he was killed.
        o Take 4 Energy Tablets (zing!).
- Begins with ‘A’.
- Go left.
- Fight Sk 8 St 11 Zera Gross. (You can fight either hand to hand or with blasters).
If you have less than 3 Shields, or you have Skill 11/12, or your Skill > Firepower:
    - Carefully manoeuvre instead.
    - Test Skill. Fail = Lose 2 Shields.
If you possess 3 or more Shields:
    - Shoot your way through the mines (Lose 1 Shield).
- Fight Ws 9 Sh 6 Asteroid Defences (use 2 Smart Missiles to take 4 of its shields).
- Dock at one of the few emergency airlocks set into the asteroids surface.
- Continue down the tunnel.
- Try to dive past it.
- Test Skill. Fail = 2 Damage.
- Go straight ahead.
- Get to the other side by jumping from sphere to sphere.
- Test Skill. Fail = 4 Damage.
- Test Skill. Fail = 4 Damage.
- Test Skill. Fail = 4 Damage.
- Take the corridor.
- Take Satophil-d as evidence.
- You possess Satophil-d.
- Easy path: Turn right.
        o You have the key that fits the hole.
        o Your mission is a success.
- Hard path: Turn left.
        o Press up.
        o Press left.
        o Try to think of an alternative course of action.
        o Fight Sk 10 St 8 ‘Blaster’ Babbet. Hand to hand.
        o Your mission is a complete success.

Hard path percentages:

[sraut]

Why has no-one commented here?

[CharlesX]

Jan 2, 2022 15:09:59 GMT sraut said:

Why has no-one commented here?

While I don't agree with one online reviewer who wrote Rings was irrelevant, it has a narrow path with tight description and development. I wouldn't disagree Rings was average, whatever that means. The main choice with Rings is to go for the easy path or the longer one, and Rings feels too easy and short if you go for the easy path. It feels a bit short and easy with the more proper path, as well.

[scouserob]

Well that is monumentally embarrassing. 😳
Whilst the mathematics were I somehow had the mechanics of Blaster Combat completely wrong.
(Despite coding them correctly for my iPhone app.)
Blaster Combat is not just Hand to Hand Combat with double the damage it is a series of rolls where getting less than your Skill grants a hit. 🤦🏻‍♂️

That means all the conclusions drawn were nonsensical due to the foundations of sand upon which they were built.
Shame, I had such fun with them.

Not that my own stupidity will stop me!
Coming soon: Zera Gross: Blaster Combat or Hand to Hand Combat? Redux!

I've kept all the maths below, as it is quite fun, if irrelevant to the game book.

SPOILER: Click to show

Zera Gross: Blaster Combat or Hand to Hand Combat?

TLDR: Hand to Hand Combat is always better.

I’ve just got to this part of the gamebook and the choice between combat modes interested me enough to pause and investigate.
Zera Gross has Skill 8 Stamina 11 for both Blaster and Hand to Hand Combat.

Intuition tells me that if you have an advantage in the battle then you should reduce variance and choose Hand to Hand Combat, whereas if you have a disadvantage in the battle, you should increase variance by choosing Blaster Combat.

My thinking was that your expected number of Stamina points after the battle will be the same with either combat mode, but Blaster Combat will spread out the distribution of probabilities around that mean value, making you more likely to survive if that mean value was negative but more likely to die if that mean value was positive.
Kind of like this, with the green curve being a completely made up low variance Hand to Hand Combat probability density graph and the red being the a high variance version with the same mean for Blaster Combat:



The edge case that should show this is when your Skill is 7.
You are an underdog in every combat round but as you have 4 or 8 Energy Tablets in your pocket, and can use them in combat to restore 6 Stamina points each, you will still be a favourite to win the fight, and so should, if my intuition is right, choose Hand to Hand Combat.

---

Your probability, p, of winning the next non-drawn round with Skill 7 is about 37.63%
Proof:

SPOILER: Click to show

Let p be the probability of winning the next non-drawn round.

---

When you have a Skill of 7 your expected Stamina loss against Zera Gross, with either battle mode, is about 20.
Proof:

SPOILER: Click to show

For Blaster Combat you need to win R=3 rounds and the damage per round is D=4.
For Hand to Hand Combat you need to win R=6 rounds and the damage per round is D=2.
(Note that the product of D and R, DR, is 12 for both combat modes.)

So your expected Stamina loss in the fight is:

---

When you begin the fight you will have, previously at the Botanic Gardens, sustained 1D6 of damage and so your Stamina will be between 8 and 23.
You will have either 4 or 8 Energy Tablets worth 24 and 48 Stamina points respectively.
Your Effective Stamina for the fight will, therefore, be between 32 and 71.
This is way more than the expected Stamina loss of about 20 so you will be a favourite in the fight.

If you need to win R rounds to kill Zera Gross and the probability of winning the next non-drawn round is p, then the probability of losing n rounds against her will be:

Proof:

SPOILER: Click to show

If you lose n rounds before beating Zera Gross then the non-drawn rounds will happen in a sequence such as:

Won, Lost, Lost, Lost, Won, Lost, …, Won

If you need win R rounds to defeat her then there will be R wins in the sequence and the n losses, so the sequence will have length R+n.
As the last round will always be won, to finish the fight, the number of different sequences will be the number of ways to choose n places to put your losses from the first R+n-1 positions, which is:

The probability of each of these sequences occurring will be the probability of having R wins and n losses in the non-drawn rounds, which is:

So, adding up the probabilities across all these sequences gives a total probability of losing n rounds to be:

Now if N is the maximum number of rounds you can lose and survive, then the probability of survival will be:

---

Using this I created a graph in Desmos to illustrate the probability of survival for the two combat modes against your Effective Stamina for the battle.
Link to Desmos Graph


I ran my usual probability calculator, fixing the effective Stamina for the fight at 39, and got a match, so unless I somehow made an identical mistake in both the pure maths and the Big Matrix calculation, which is VERY unlikely, it seems that the calculations are correct.

---

Including the 1D6 damage from the gunfire at the Botanic Gardens I got the following for the probabilities of surviving to the end of the Zera Gross battle.


As expected choosing Hand to Hand combat is always better (or matching to 1 decimal place).
So you should always choose Hand to Hand Combat if you want to maximise your chances.
Though if you have a Skill advantage and you’d prefer a quicker fight then with the size of your advantage, you can safely sod it and choose Blaster Combat. 😂

[scouserob]

Zera Gross: Blaster Combat or Hand to Hand Combat? Redux!

TLDR: Blaster Combat is always better.

Ignore that fool in the post immediately above, Blaster Combat has completely different mechanics to Hand to Hand Combat.

In every combat round the chance of landing a hit is constant regardless of whether your opponent hits.

---

Let's find the actual probability of winning Blaster Combat.

Let N be the number of Blaster hits you can survive.
Let M be the number of Blaster hits your opponent can survive.

For the next round in which somebody is damaged:
Let P(Y) be the probability that you hit your opponent and your opponent misses.
Let P(Z) be the probability that you miss your opponent and your opponent hits you.
Let P(B) be the probability that both you and opponent hit each other.
Let P(W) be the probability that you hit your opponent.

Then the probability of you winning the Blaster Combat is:

Proof:

SPOILER: Click to show

Ignoring rounds where you both miss, a winning blaster combat will consist of a sequence of rounds where you hit your opponent M times and you get hit yourself N times or less. This sequence will then finish with an additional winning shot.

Here is an example of a winning sequence with N = 7 and M = 5:
Y B Z Z Z B Y B W
In this sequence you are hit 6 times (Three Zs and three Bs),
you hit your opponent 5 times (Two Ys and three Bs) and then deliver the kill shot with the W.

The probability of getting a specific sequence with y occurrences of Y, z occurrences of Z and b occurrences of B, followed by the winning W is:

The total number of winning sequences with this number of occurrences of Y, Z and B is:

The number of occurrences of B in a winning sequence cannot be greater than either M or N so, using this restriction, and the fact that b + y = M, and b + z ≤ N

---

For a quick check of the formula lets use the battle against Zera Gross (Skill 8 Stamina 11) with a Skill of 7 and a minimum Stamina, going in to the battle, of 32.
Then N=7, M=2 and:

Proof:

SPOILER: Click to show

For any single round, allowing both of you to miss, let:
P(YH) be the probability you hit Zera.
P(YM) be the probability you miss Zera.
P(ZH) be the probability Zera hits you.
P(ZM) be the probability Zera misses you.

Then:

Now let:
P(HM) be the probability you hit Zera and Zera misses you.
P(MH) be the probability you miss Zera and Zera hits you.
P(HH) be the probability that both you hit Zera and Zera hits you.

Then:

Now to calculate the probabilities when only considering only those rounds where somebody is hit, we divide by the sum of the probabilities of such rounds:

Plugging these into the formula gives us a probability of about 94.1%
Proof:

SPOILER: Click to show

To test both the formula and my probability generating Big Matrix generator which used a combat descent method to calculate the survival I tested whether they generated the same answer and ... they did.  😀



Now I'm confident with the formula and the matrix combat descent, here are the probabilities of getting past Zera Gross in the adventure for both Hand to Hand Combat and Blaster Combat.
Blaster Combat is the better (or equal) option in every case.



Not by much and it makes hardly any difference at all with 8 Energy Tablets, but yes.
Blaster Combat is the better option. 😉

[CharlesX]

Hi scouserob

Perhaps you would remind me how Blaster combat differentiates from hand to hand as I don't recall or have The Rings Of Kether? My understanding is the case for hand to hand would be if you had a stronger adventurer and didn't want to run the risk Zera Gross 'gets lucky' and deals more damage, and also that by implication an adventurer with fewer energy tablets should have more of a chance not less.

   What I'm not factoring in is where you have a Skill 8 Stamina 11 opponent they aren't that much of a threat. It might be interesting to resolve whether you'd be best off fighting 'Blaster' Babbet hand to hand or via Blaster but again, not having The Rings Of Kether with me or having played it for about 30 years I do not know if there were even a choice. 

[scouserob]

Apr 24, 2024 7:25:51 GMT CharlesX said:

Hi scouserob

Perhaps you would remind me how Blaster combat differentiates from hand to hand as I don't recall or have The Rings Of Kether?

Hi Charles

For Blaster Babbet you can only fight Hand to Hand.
For Zera Gross you get the choice with both combat types being on different paragraphs.

Hand to Hand:
Just like standard Fighting Fantasy combat except that you can't use luck in battle.
The chance for both parties to hit their opponent is based on the difference between their Skill scores.

Blaster Combat:
You take turns shooting, with you starting. (Which is an advantage in itself.)
If you roll strictly under your Skill then you hit your opponent and take 4 Stamina points off.
The chance of either party hitting their opponent is based purely off your their own Skill.

---

For a Skill 7 Adventurer

In Hand to Hand Combat against Zera:
Chance per round of Hitting Her: 33.6% (145/432)
Chance per round of being hit: 55.6% (721/1296)

In Blaster Combat against Zera:
Chance per round of Hitting Her: 41.7% (5/12)
Chance per round of being hit (Her Stamina > 4): 58.3% (7/12)
Chance per round of being hit (Her Stamina ≤ 4): 34.0% (49/144)    [As you have to first miss to be able to get hit.]

Hand to Hand:
Considering Zera has 6 Hits allowed for hand to hand:
Expected number of rounds taken to defeat her is: 17.9 (6/(145/432))
Expected Stamina Loss is: 19.9 (2*17.8*721/1296)

Blaster Combat:
Considering Zera has 2 hits to get down to under 4 Stamina:
Expected number of rounds taken to get her down to under four Stamina is about: 4.8 (2/(5/12))
Expected Stamina Loss is that time is: 11.2 (4*4.8*(7/12))
Expected number of rounds taken to finish off Zera: 2.4 (1/(5/12))
Expected Stamina Loss is that time is: 3.3 (4*2.4*(49/144))
Total Expected Stamina Loss: 14.5

So, in terms of expected Stamina loss, you are about 5.4 Stamina points better off when choosing Blaster Combat in this case, which even the reduced variance of Hand to Hand Combat cannot overcome.  (Apparently)

---

For a Skill 12 Adventurer

In Hand to Hand Combat against Zera:
Chance per round of Hitting Her: 84.1% (545/648)
Chance per round of being hit: 9.7% (7/72)

In Blaster Combat against Zera:
Chance per round of Hitting Her: 97.2% (35/36)
Chance per round of being hit (Her Stamina > 4): 58.3% (7/12)
Chance per round of being hit (Her Stamina ≤ 4): 1.6% (7/432) [As you have to first miss to be able to get hit.]

Hand to Hand:
Considering Zera has 6 Hits allowed for hand to hand:
Expected number of rounds taken to defeat her is: 7.1 (6/(545/648))
Expected Stamina Loss is: 1.4 (2*7.1*(7/72)) 😂

Blaster Combat:

Considering Zera has 2 hits to get down to under 4 Stamina:
Expected number of rounds taken to get her down to under four Stamina is about: 2.1 (2/(35/36))
Expected Stamina Loss is that time is: 4.8 (4*2.1*(7/12))
Expected number of rounds taken to finish off Zera: 1.03 (1/(35/36))
Expected Stamina Loss is that time is: 0.07 (4*1.03*(7/432))
Total Expected Stamina Loss: 4.9

So expected stamina loss wise you are about 3.5 better off by choosing Hand to Hand Combat in this case.
Which is great intuition on your part. 😎👍🏻

For a Skill 12 adventurer the probability of surviving the battle with either method is 100.000000% to six decimal places.
If there were any further significant Stamina attrition down the line that 3.5 Stamina point may come in useful but I'm guessing not...

---

The only numerical survival advantage for Hand to Hand I've found up to six decimal places starts at Skill 10 (Initial) Stamina 14 with 4 Energy Tablets only:
Hand to Hand: 99.999999%
Blaster Combat: 99.999997%