From a thread on the ADB boards:
_____
RAT 31 game 2.11 Up_All_Knight (Fed) over BanTheFed (Fed)
I had a bye from the first round which is sometimes nice, but one of the players in the round 1 match I was waiting on had to be replaced. So I got to wait all this time for a Fed Civil war in my opening game of this RAT. Not a happy experience.
/Rant
Turn 1
Me facing D, Brook facing A
I juice all photons, plot 17/16/24, hold a SS and put 2 points on my #6 for fun. Brook plots 16/26. we both move forward a couple of impulses, then I turn to E and launch a shuttle. I waddle around for a while and then turn back to D. Brook eventually turns left to F and we finish the turn around range 10, He's facing my #6 and I'm facing his #1. We are close to the shield boundaries. My shuttle fires at range 8 on Brook's #6 and does nothing. What do you expect from a p3 anyways?
Turn 2
My master plan here is to take his shot at < range 2 and then burn him through a rear shield as he turns off. If he decides to get closer we'll just have to play who-can-roll-better.
I plot 16/31/24/12 and Brook plots 26/13. I have 2 in HET and I'm still holding a SS. He has a pre-allocated HET, a couple points in tractor and a .5 power in transporter. He's holding 3 16 point photons and a 12 pointer at this point. I slip out once and then start slipping back in once my SC kicks in. Brook closes to F for a While and then turns back to A on impulse 8. I slip left to give us range 3 1 hex off perfect oblique on each others #6 shields. I have the advantage in that I'm turn eligible and he has the advantage in that he can HET and I cannot at 31. A few things can happen at this point.
1 - He fires and I don't. I lose some weapons, but can eventually get range 2 or closer on his rears unless he has a SC which is entirely possible.
2 - I fire and he doesn't. He loses some weapons, but now I'm the one being chased and that violates my manliness.
3 - We both fire. Who-can-roll-better BS takes precedence and that sucks.
4 - Nobody fires. We can get R1 or 2 next imp and who-can-roll-better again takes precedence which still sucks.
I'm betting that he does #1 or #2, so I fire 1 photon, my lf/l p1s and 1 p3. Brook holds fire which is really good for him since my photon misses and my phasers combine for a whopping 7 damage. Next impulse he slips left and I can either turn left to give him a forward centerline on my #2 (dumb), turn right to give him R2 on my #5 (monumentally dumb) or go straight for R1 on each others #6 shield with him having more to shoot at me. I tell myself "Self - at least he'll take more feedback than you will!" and I go to range 1. I launch another admin figuring a SS will never catch him. He fires everything and gets 64 + 40 (phasers) + 12 feedback for 116 damage to me. I stop 5 with batts and take my 81 internals which leaves me useless. I do 48 + 19 (4 p1s + 1p3!) + 16 feedback to him for 83 damage to a 23 box shield. it turns out that Brook used batts to fully OL his 4th photon, so he only stops a couple and takes 58-ish internals. I surrender. If my 1st photon had hit and I would not have rolled absolute minimum on my phasers, it may actually have been a game as my 2 shuttles on the map suddenly become a huge deal. But it didn't work out that way and Brook played a solid game anyways.
Good luck against Romwe next round Bud!
_______
There are a few interesting things here, including the merits of same v. same and it's dice-dependent nature (I happen to think same v. same is not as bad as most and that dice actually play no more or less than in a race 1 v. race 2 game, but not here to discuss that yet), but what I want to discuss is the choice matrix Marcus put forward and build it into a game theory answer (how fun, game theory actually applied to a game!).
Firstly, lets make some assumptions, assumptions some of which I think are actually wrong, but that I think Marcus employed in his decision above:
1. Range 3-4 fire against a front (30 box) shield with 4 photons and 6 p-1s is no better than Range 2 or closer against a rear shield with 3 photons and 4 p-1s.
2. If I accept a range fire, I am likely to lose 1 photon, and 4 phasers.
3. If I fire from range 3-4, I am unlikely to avoid a better shot from my opponent (see condition 1).
ok, let's look at the matrix, with some arbitrary numbers tossed in, and then we'll explore the further the assumptions and refine our numbers to come to the best solution.
[NOTE: I can't make a pretty chart here, because I don't know how to do formatting yet, so I cut out the part with the game theory charts - I'll re-add them if I can.]
Let's start by weighing it based on some initial assumption, in particular assumption #1.
IF range 3-4 fire with 4 photons and 6 p-1s is no worse than range 2 fire with 3 photons and 4 p-1, THEN the only ting to be gained by firing 1 photon and 2 p-1 is whatever increased odds of winning are the result of having some additional shield damage several turns down further along in the game - for now, lets assign that value as an extra 10%, and we'll discuss the probability of that result later. That, in turn has to be weighed against other probabilities: 1. The probability of exchanging fire at R2 or closer on different shields - we'll call that result a 75% loss probability (and again, worry about it's probability later) and 2. the probability of doing less damage on the range 2 or closer exchange because of part of your fire happening at R3-4 - we'll call that a 20% additional loss - probabilities coming later and 3. in the event that the opponent does fire at 4, the reduced value of firing less than you could have, if no photons were lost or if less than 4 phasers are lost - we'll call that 25% reduction in win probability and now move on to discuss the various probabilities.
1. the Range 3 shot - what it is actually likely to do.
Phasers - 6 p-1s average 26 damage. The Photons do 0, 16, 32, 48 or 64, so your total damage is 26, 42, 58, 74 or 90.
Which of those really matter? Well, 26 and 42 are extremely unlikely to do internals getting 1 photon + 4 phasers. 58 is, after batteries, 23 internals. To hit a photon, that takes an 11 - a probability of 2/36. To hit a photon in 23 internals is a probability of - 73% (or expressed differently, a 27% chance of NOT losing a photon). What about Phasers - remembering we need to hit all 4 ? Well , that is harder, since you can't just plug it in to the binomial equation, but at 23 internals that results in a probability of less than 3% to lose all four. What about 3? Approximately 20%.
So, what it comes down to is that there is a substantial probability of not losing 1 photon and 2 p-2 at 26, 42 and 58 damage. The phasers make all this a bit messy - so lets drop them for now and look at just the photon.
Probability of having 4 Photons after accepting R3 fire:
26 - 100%
42 - 67%
58 - 27%
74 - 11%
90 - 4%
OK. Now lets add in the probability of that damage (again, approximating phasers at 26)
Damage (exactly)*
26 - 1%
42 - 10%
58 - 30%
74 - 40%
90 - 20%
*101% because of rounding
Now, lets multiply and add - 100%*1% + 67%*10% + 27%*30% + 11%*40% + 4%*20% = 21% chance of not losing a photon after taking a Range 3 shot.
this helps us with the ???s.
We now have a an added 21%*25% = 5.25% chance of winning a game by just holding fire - IF we believe or original premises.
Let us quickly examine that:
Range 2 damage with 3 photons and 4 p-1: phasers - 19. But let's assume we get a rear shield out of all of this and add 6 damage to reflect the smaller shield - leading our total equivalent damage to: 25, 41, 57 and 73. The first thing to note, of course, is that, before adding in probabilities, this damage chart looks a lot like the R3 shot - except it is missing the 90. Let's look at probabilities, and then do some comparisons (for internals we'll again subtract 35 because we added the 6 for the smaller rear shield into our damage numbers).
25 - less than 1%
41 - 7%
57 - 35%
73 - 58%
O.K. - now let's think about what this damage means - that is, let's subtract 35 and get our internals, at less than 1%, we'll ignore the 25 damage line.
6 - 7%
22 - 35%
38 - 58%
Alright - well, clearly 6 internals is nothing. 22 and 38 are pretty close to each other on a Fed. Both are likely to kill a photon and 2-3 phasers. The 38 is likely to cost the Fed about an extra 3 power. 38 will also eliminate most of the fluff, except some Fhull and Lab. 22 will leave the Fed with a lot of internal protection left.
What about that range 3 shot again? Well, there is an 81% chance of doing 22 or more internals from range 3 and a 93% chance of doing the same at R2, but with fewer weapons.
There is a 60% chance of doing 38 or more with the range 3 shot and a 58% chance with our range 2 shot here. Those are all close, so what you are basically gaining is an additional 8% chance to not "whiff" (6 or fewer internals) in exchange for a slightly less probable chance of doing good damage and completely giving up your 20% chance to do critical damage (apx. 50+ internals).
It is clear to me, that if all you are gaining is your R2 shot on the rear - that is a terrible exchange.
What about R1?
Well, if you feel confident you can get it - here is your exchange phasers do 21 + 6 for the small shield + 48 at 100% probability (plus you take 12 to yourself) - 75 damage.
That is a 100% chance to do 40 internals - or put in a better way an additional 40% chance to do 40 internals in exchange for losing a 20% chance to do 50+ internals. That exchange seems fair, but it's still close.
In the end, to hold fire at R4, the choice can only be made if you are very certain you can get range 1 or better and if you do you should absolutely never partially fire at R4, but instead it is always the right choice to either hold fire or fire everything.
My thoughts on the game.
When I announced impulse activity at range 3 in our game I fully intended to fire the "wad". Then I thought to myself....."I better gut him good, or he'll just come to range 1 and gut me." He was going speed 31 with his turn mode satisfied, he would of caught me. Even if I blew off a photon he would of got me with 3 ol and about 5-6 phaser ones. The whole thing would of been about a wash if I jackpotted when I fired, but to expect that at range 3-4 is asking a lot I think. So I held fire and planned on getting range 2 with whatever was left. Luckily for me, he only fired what he thought he would lose if I fired. To make things worse for him, he missed with a OL and only did 7 with phasers. Then the next impulse we moved to range one and gave each other the business. I do agree with Paul, in the fed, don't fire at all, or fire everything. It's just the mentality you need when flying this ship. Also, I'm psyched that we will get to fly the G-rack Fed at council, I think it's the perfect fit for that ship. Any possibility the Gorn can have the corronade? :)
That was the game theory part I ended up deleting
but, I think you reached the wrong conclusion. I can't make a chart, so I'll have to just explain it in words. Here is why you both should have fired, and fired everything:
He fires - If you held fire, he, because of his speed, knows you cannot do better than a R2 shot - which is (as demonstrated above) much worse than his R3 shot. If you fire, exchange is even.
He holds - If you fire, he gets a R1 (or 0) shot, which is better than your R3 shot if he fires nothing. If you hold, exchange is even.
For you things are reversed, obviously. BUT there is a hook. He cannot HET, you can. This makes his holding for fire much riskier.
If he holds and you fire his #6 is down and he has some number of internals (20-40). Now, for him to win this exchange, he needs to hit you on a rear shield and NOT through his #6. But he cannot HET. So the best he can do is turn in. You, knowing this, would simply slip out . Next impulse, , to keep you off his #6, he has to slip left. You, at this point, have two very good options: Turn right so he stays at R2, now on a rear shield. Or, better yet, HET180, so his fire is at R3. Let's assume for now, you reserve your HET, next impulse he has to move forward. You, in turn, slip left and now he has his range 1 shot on a rear shield, except all his feed back are internals and you also get to fire 2 p-1 and 2 p-3 through his down shield to boot.
That, in turn means that the generic situation above has to be recalculated. In fact, his he holds, you fire is also worse for him. That leaves him in a MUST fire situation. With him firing, in turn, your only option is to fire as well.
Either way, from his perspective or yours, the best choice for both players was to fire and in both cases the firing player was better off if the opponent held fire.
To fire or not to fire
So you're basically saying that we both should have fired at range 3 and let the dice determine the outcome? That's the exact situation I was hoping to avoid. Heck, I could have slipped out to get a perfect range 4 oblique that impulse if I wanted to play it that way. But chances where good that somebody would have won strictly on die rolls and neither of us had any control of that.
I also agree that it's generally best to either hold fire or fire everything, but I felt that firing what I did when I did it was still a good idea. Even if he HETs away the next impulse after firing at range 3 I can simply turn and fire my remaining weapons on a rear shield, knowing that I have also hurt a front one if that first photon hits.
If he fires and slips out (right), then I can turn in and have a range 2 centerline on his #6 shield with 3 photons and all of my remaining phasers. If I get 3 total photon hits over those 2 impulses then I'm in decent shape here as long as he didn't jackpot at range 3.
If that 1st photon hit, I doubt that he would have slipped left. The damage would have been about even, but I would have had a slight edge because I had 2 shuttles on the map and both ships would have lost their shuttle bays. I'm assuming average phaser fire from both of us here, which didn't happen.
You're also assuming that I knew Brook would be maintaining speed 26 for a while. I had no way of knowing that at the time. He could have HETed and had a plotted increase up to 31 himself for all I knew.
Marcus, I appreciate that you
Marcus,
I appreciate that you did not want to, as you put it, "let the dice decide the game" (though, I do reject your premise that this was magnified in any way by being in a Fed v. Fed game). I was not at all trying to comment on the "most fun" or "most exciting" or "least random" way to play. I am speaking merely about optimal outcomes reflected in the highest probability to win the game. In each case, the optimal outcome - once having reached R3 under the conditions that existed - was for both of you to fire everything.
The worst possible outcome - in terms of probability to win the game - was for either of you to do what you did - fire part of your weapons.
"...but I felt that firing what I did when I did it was still a good idea."
That is provably untrue (again, evaluating the game exclusively from a "best chance to win" perspective, not from a "most fun" or something else perspective). If you ever find yourself in that exact situation again, knowing what you knew at the time, and are primarily focused on winning the game, both you and your opponent should fire.
"If that 1st photon hit...I would have had a slight edge..."
OK, let's assume that is true. You are trading a 66% chance for, in your words, "a slight edge" for a 33% chance of a large disadvantage. Plus, frankly, if your opponent made the right decision as well and fired, you would be looking at a 60% chance of an almost certain loss.
We should fire
Let's say in this case I do fire everything and Brook holds his fire as he did in the game. In fact, I'll go right ahead and fire my p3s as well. But I only hit with less than 3 photons which is 39% likely to happen. We'll say I hit with 2 to be fair. I do ~60 damage which is 30 internals if no batts are used to block anything. Next impulse I must turn right or Brook can HET to F and get range 1 on either my #6 if I go straight or my #2 if I turn left. So I turn Right and Brook now has me centerlined at range 2 with 3 photons and 6-7 p1s to burn me through my #5. This is still dubious in my mind. I did the "right thing", but it still didn't help. Now it is the right thing if he also fires, but he did not do this in this case and I have no way of knowing if he will oblige me by doing the right thing. Sure, he *should* do it. But I've lost games where opponents didn't do what I though they should do. Just like this one.
There is an additional factor here that both of us know each others' playing styles well (we have after all literally played 100s of games) and we both have a tendency to try something off the wall to throw the other for a loop. This factored heavily into the thinking of both players. That being said, it wouldn't factor into most Fed vs Fed matches like it did this one. In other words, your assessment of the entire situation is very valid for a generic Fed vs Fed fight, but there's this extra X factor tossed into this specific game that changes things a bit.
Well
if you take a map out and look at that situation AND if (as you should not) you don't add in the p-3's, even if you get unlucky and hit with 2 photons (30% chance) and do your 30 internals, then after his range 2 fire on your #5, you will be guaranteed a R1 or R2 shot through his down shield with 2 p-3 and 2 p-1, for an additional 20ish. So even in your unlucky scenario, he does 40-50 to you, through your #5, you do AT LEAST as much to him, but in two separate volleys. Still a good exchange for you and that assumes you get unlucky.
I agree on your x factor. That can be a very big deal. I still think that even if you know that Brook will hold fire and has allocated and will use his HET, your best move was still to fire. If you hit with only 1 torp, well there is your 11% chance to practically guarantee a loss. But that is at least only 11%. With your choice, you practically guaranteed a loss at a 33% rate.
By the way
I'm not trying to call you an idiot or anything, just so we are clear. I saw the post by Brook and my gut told me that both players had made a mistake, but I also thought it was likely many people would think that the situation legitimately was a toss up for either player on whether to hold or fire. I know if I was in that situation, I would have had to take time to really think it out and it is certainly possible that in f-t-f (where I can't do a forth-order binomial in my head) I might have talked myself into holding fire.
It was a rare situation where I think the right answer for both players is actually pretty clear, but only after you really grind some numbers. Pattern recognition is where i get all my "gut reactions" from, so it is useful to use this situation as a great example of an SFB position that actually has a single, best solution for both players.
By the way
"I'm not trying to call you an idiot or anything, just so we are clear."
Of course not, this is a good debate and you raise some very valid points. Feel free to point out where you think I'm wrong in a game at any time, I won't mind a bit. I may debate you, but it never bothers me :)
Fed vs Fed *is* different
Quote: ...I do reject your premise that this ["let the dice decide the game"] was magnified in any way by being in a Fed v. Fed game...
Clearly, when anything involves DF or the DAC, dice will decide it. It's simply that in a Fed, the variance in damage dealt is greater than in any other ship. Compare a Lyran vs Lyran exchange: the phasers are the same as the Fed; ESGs probably cancel out, so the rest is in 3 or 4 UIM disruptors, which are a) more reliable and b) less damaging. Not only that, but the positions at the start of the next turn (and the tactics used to get there) have more impact.
Likewise in a Fed vs Fed, there's probably only one viable tactic, whereas most other civil wars give you options. You could fire at 8 in a Fed - that would certainly leave it in the hands of the dice goddess - and 3 hits might well be a win. But I suspect that 2 hits is a very likely loss, so it doesn't look a good idea. Any other choices?
Binomial Distributions
I know if I was in that situation, I would have had to take time to really think it out and it is certainly possible that in f-t-f (where I can't do a forth-order binomial in my head) I might have talked myself into holding fire.
If you can do fourth order binomial distributions in your head on SFBOL, why can't you do them in FTF play? :) (I have been known to keep an Excel sheet open in SFBOL play for running a few odds tables in unusual situations. But that doesn't qualify as 'in my head'.)
Or is there a reason why you have a USB port in the back of your neck? :)
>but instead it is always the
>but instead it is always the right choice to either hold fire or fire everything.
Whenever someone makes a statement like that, I immediately question it.
I think you've made some mis-assumptions, too. The biggest being that the benefits from firing 1 photon and 2 P1s at R4 are negligble (OK, you assigned a 10% increase in winning 'several turns further down ...'. One distinct benefit, without even doing any numbers, is that you fire two phasers on one side, and then next move turn, bringing the other side phasers into arc. So, IF you can fire on the same shield, you have increased the amount of damage (~8 pts) (and hopefully number of internals) done.
Except
that in the situation Marcus laid out, that was impossible.