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sniffnoyIn this entry I want to consider the questions, "What is the lowest possible surviving score in a game of Space Alert?" and "What is the highest possible score in a game of Space Alert?". (I like to say that dying is -∞ points, but that is not very interesting.)
Let's be clear on the parameters of the problem -- this is Space Alert without the expansion. (Because I don't have the expansion, and there doesn't seem to be a list of the cards available online.) 4 or 5 players may be used. The players are actively trying to achieve the lowest/highest score. Any deck of threats may be used, any set of tracks, etc.; we assume we are allowed to rig all the decks (damage tiles etc.) and that the players know in advance everything that will happen. The audio track must be one of the 8 normal missions provided.
Some terminology: Let's define the "total threat value" of a mission to be the number of common threats plus twice the number of serious threats. This is a useful quantity, because serious threats of a given difficulty level are (with a few exceptions) worth twice as much as common threats of that same level. Furthermore, it is constant across mission types -- it's equal to 3 for the test runs, 5 for simulation or advanced simulation (6 with 5 players), 7 for a mission (8 with 5 players), and if we include the expansion, it's equal to 8 for the easier double-action missions (10 with 5 players), and 10 for the standard double-action missions (12 with 5 players). So for our purposes now this quantity will always be equal to 7 or 8.
First, the maximum problem; this is the easier one. There's an obvious upper bound on the maximum possible score, which is 8*6+21=69. (8 total threat value, times 6 points for killing a yellow threat, plus 21 points from the window.) 69 points is a "perfect game"... but is it actually possible?
Well, after several hours of trying to construct such a scenario, I can report that the answer is yes. Solution (and hints towards my solution) is spoilered for those of you who really want to try this yourself. Note of course that there may well be other solutions that look very different; this is just the first one I found.
Use 5 players. OK, that's not really a hint. Use audio track 8.
Trajectories are as follows: T3 blue, T6 white, T4 red, T1 internal.
Threats are as follows: T+3 Overheated Reactor, T+4 Psionic Satellite, T+5 Nebula Crab, T+7 Juggernaut, T+8 Scout.
Players will move in the order Red, Yellow, Green, Blue, Purple.
Turn 1: Red hits C, all other players change decks. (Green, Blue, and Purple are delayed.)
Turn 2: Red changes decks, Yellow hits B, all other players do nothing.
Turn 3: All players press C. (7 points.)
Turn 4: All players press C. (7 points.)
Turn 5: Red uses heroic B (the other side of which shows upper red). Yellow presses B. (Overheated Reactors killed.) Green moves blueward. Blue changes decks. Purple heroically rushes to upper blue. (Psionic Satellite reaches X. All players are delayed.)
Turn 6: All players do nothing.
Turn 7: Yellow moves redward; all other players press A. (Psionic Satellite killed; Nebula Crab takes 3 damage. Nebula crab reaches X.)
Turn 8: Red and Green move redward. Yellow and Purple change decks. Blue presses C. (Nebula crab reaches Y.)
Turn 9: Purple presses C; all other players press A. (Nebula Crab killed; Juggernaut takes 4 damage. Scout reaches X.)
Turn 10: Blue changes decks; Purple presses C; all other players press A. (Juggernaut killed.)
Turn 11: Red moves blueward; Yellow heroically rushes to lower white; Green presses B; Blue presses A; Purple moves redward. (Scout killed.)
Turn 12: All players press C. (7 points.)
...I didn't list what the *other* sides of the cards do, but it's pretty easy to fill these in in a manner consistent with the contents of the deck.
I do have to say, though, that the maximum problem seems kind of silly if you don't include the expansion, which raises this upper bound to 12*8+21=117. Or... is it even higher? I seem to recall reading that threats that call in other threats have their scores a bit weird. And, actually, I guess just the possibility of calling in other threats should raise that bound, shouldn't it? I don't actually have the expansion. Crap. Yeah, this is why I'm ignoring the expansion.
Anyway, so the minimum -- how about lower bounds? Well, there's an obvious lower bound of -36 -- all penalties, nothing else. Now wait, you say, shouldn't that be 7*2-36=-22? Because you get 2 points for surviving a threat? No! It's possible to neither kill nor survive a threat without dying; remember you only count as having survived a threat if it reaches Z. That said, we can certainly make a lower bound based on this idea.
The longest track, T7, is 16 spaces long; a threat needs to advance 15 spaces to reach Z. If it has speed 3 or more (let's assume everything is constant speed for now), it will assuredly reach Z regardless of when it appears. If it has speed 2, however, it will have to appear by turn 6 to reach Z; and if it has speed 1, it will never reach Z. One can come up with similar numbers for the other tracks; I won't go into details here. Note that straight-up "speed 1" threats do not exist -- there are two "speed 1" threats, the Man-Of-War and the Juggernaut, and both speed up. It's straightforward to compute numbers for both of these. (Be careful, the Juggernaut has the odd property that it sometimes arrives *sooner* on longer tracks.) There are no threats that lose speed so these are not a concern.
[Previously here were two paragraphs giving a probable lower bound based on this idea. However, the numbers were wrong, and it ultimately yielded no improvement, so I don't feel like fixing it. Let's skip ahead a bit.]
I guess we'll have to analyze the actual audio tracks. There's only 8 of them after all. We'll consider both what happens with only 4 players and with only 5 players -- while having fewer threats may seem better, let's remember that with 4 players, one can only get -8 points from knockouts, not -10. After a bit of work, we find the following (not necessarily unique) minima for points let through:
Track 1: 10 points (put T7 on red); 12 points with 5 players.
Track 2: 12 points (put T6 or T7 on blue); 14 points with 5 players.
Track 3: 6 points (put T7 on blue and T6 on white, with T+6 being the Man-of-War); still 6 points with 5 players (put T5 on red).
Track 4: 10 points (put T7 on blue, with T+6 being the Man-of-War); 12 points with 5 players.
Track 5: 12 points (put T7 on red and T6 on white); still 12 points with 5 players.
Track 6: 12 points (put T6 on red); still 12 points with 5 players (put T7 on white).
Track 7: 10 points (put T7 on red and T6 on white); 12 points with 5 players.
Track 8: 6 points (put T7 on red and T6 on white, with T+5 being the Man-of-War); still 6 points with 5 players (put T5 on blue).
OK. And it's pretty clear these are indeed minima, so we get a lower bound of -30 points. Still, it's not clear whether this is achievable. Let's consider -- achieving this requires knocking out all players. But there's not too many ways to do that in the base game. Especially since whatever delivers the knockout must either A. be white or B. do so without reaching Z. The only white threats that knock out are the Battlebot Uprising and the Commandos (both serious internal). The only threats that knock out without reaching Z are the Battlebot Uprising (serious internal), the Executioner (serious internal), and the Power System Overload (common internal); however, the Executioner and the Power System Overload each lack the ability to knock *all* players out, and so if we are relying on one of them to deliver the knockout, we must have both. (Or rather, Executioner can knock all players out, but it can't both knock out all players and disable both battlebot squads.)
From this we can see that -30 is not achievable with track 8, since its only internal threat always reaches Z (meaning it must be white) but is also common, incompatible with the above. Track 3 can be ruled out for similar reasons. Thus -30 is not achievable. And since the only common threat that knocks out is Power System Overload, and it can't knock out all players by itself, one can deduce that -29 is not achievable either.
And -28, it turns out, is achievable. Solution is spoilered if anyone wants to sit down and figure it out themselves.
Audio track 8, 5 players. T7 red, T6 white, T5 blue, T4 internal. T+3 Hacked Shields (blue), T+4 Psionic Satellite, T+5 Man-Of-War, T+7 Frigate, T+8 Gunship.
I'm not going to go into details of how it's executed because, well, it's fairly obvious -- pick up battlebots, fiddle with the shields, get knocked out. You need 2 shield up on red. You also need exactly 2 shield up on white, which means first you'll have to hit B in lower red before filling up the white shield. Don't worry about the blue shield, it'll take care of itself. Point is, you'll survive with all players knocked out, both squads disabled, 6 damage on each zone, and a mere 8 points for threats survived, for a total of -28.
So we have an answer to our question: The maximum possible score is 69, and the minimum is -28.
...yeah, I basically spent all day on this instead of working. But now I'll never have to do this again! Unless I someday try to figure out how the expansion affects it, anyway.
-Harry
Let's be clear on the parameters of the problem -- this is Space Alert without the expansion. (Because I don't have the expansion, and there doesn't seem to be a list of the cards available online.) 4 or 5 players may be used. The players are actively trying to achieve the lowest/highest score. Any deck of threats may be used, any set of tracks, etc.; we assume we are allowed to rig all the decks (damage tiles etc.) and that the players know in advance everything that will happen. The audio track must be one of the 8 normal missions provided.
Some terminology: Let's define the "total threat value" of a mission to be the number of common threats plus twice the number of serious threats. This is a useful quantity, because serious threats of a given difficulty level are (with a few exceptions) worth twice as much as common threats of that same level. Furthermore, it is constant across mission types -- it's equal to 3 for the test runs, 5 for simulation or advanced simulation (6 with 5 players), 7 for a mission (8 with 5 players), and if we include the expansion, it's equal to 8 for the easier double-action missions (10 with 5 players), and 10 for the standard double-action missions (12 with 5 players). So for our purposes now this quantity will always be equal to 7 or 8.
First, the maximum problem; this is the easier one. There's an obvious upper bound on the maximum possible score, which is 8*6+21=69. (8 total threat value, times 6 points for killing a yellow threat, plus 21 points from the window.) 69 points is a "perfect game"... but is it actually possible?
Well, after several hours of trying to construct such a scenario, I can report that the answer is yes. Solution (and hints towards my solution) is spoilered for those of you who really want to try this yourself. Note of course that there may well be other solutions that look very different; this is just the first one I found.
Use 5 players. OK, that's not really a hint. Use audio track 8.
Trajectories are as follows: T3 blue, T6 white, T4 red, T1 internal.
Threats are as follows: T+3 Overheated Reactor, T+4 Psionic Satellite, T+5 Nebula Crab, T+7 Juggernaut, T+8 Scout.
Players will move in the order Red, Yellow, Green, Blue, Purple.
Turn 1: Red hits C, all other players change decks. (Green, Blue, and Purple are delayed.)
Turn 2: Red changes decks, Yellow hits B, all other players do nothing.
Turn 3: All players press C. (7 points.)
Turn 4: All players press C. (7 points.)
Turn 5: Red uses heroic B (the other side of which shows upper red). Yellow presses B. (Overheated Reactors killed.) Green moves blueward. Blue changes decks. Purple heroically rushes to upper blue. (Psionic Satellite reaches X. All players are delayed.)
Turn 6: All players do nothing.
Turn 7: Yellow moves redward; all other players press A. (Psionic Satellite killed; Nebula Crab takes 3 damage. Nebula crab reaches X.)
Turn 8: Red and Green move redward. Yellow and Purple change decks. Blue presses C. (Nebula crab reaches Y.)
Turn 9: Purple presses C; all other players press A. (Nebula Crab killed; Juggernaut takes 4 damage. Scout reaches X.)
Turn 10: Blue changes decks; Purple presses C; all other players press A. (Juggernaut killed.)
Turn 11: Red moves blueward; Yellow heroically rushes to lower white; Green presses B; Blue presses A; Purple moves redward. (Scout killed.)
Turn 12: All players press C. (7 points.)
...I didn't list what the *other* sides of the cards do, but it's pretty easy to fill these in in a manner consistent with the contents of the deck.
I do have to say, though, that the maximum problem seems kind of silly if you don't include the expansion, which raises this upper bound to 12*8+21=117. Or... is it even higher? I seem to recall reading that threats that call in other threats have their scores a bit weird. And, actually, I guess just the possibility of calling in other threats should raise that bound, shouldn't it? I don't actually have the expansion. Crap. Yeah, this is why I'm ignoring the expansion.
Anyway, so the minimum -- how about lower bounds? Well, there's an obvious lower bound of -36 -- all penalties, nothing else. Now wait, you say, shouldn't that be 7*2-36=-22? Because you get 2 points for surviving a threat? No! It's possible to neither kill nor survive a threat without dying; remember you only count as having survived a threat if it reaches Z. That said, we can certainly make a lower bound based on this idea.
The longest track, T7, is 16 spaces long; a threat needs to advance 15 spaces to reach Z. If it has speed 3 or more (let's assume everything is constant speed for now), it will assuredly reach Z regardless of when it appears. If it has speed 2, however, it will have to appear by turn 6 to reach Z; and if it has speed 1, it will never reach Z. One can come up with similar numbers for the other tracks; I won't go into details here. Note that straight-up "speed 1" threats do not exist -- there are two "speed 1" threats, the Man-Of-War and the Juggernaut, and both speed up. It's straightforward to compute numbers for both of these. (Be careful, the Juggernaut has the odd property that it sometimes arrives *sooner* on longer tracks.) There are no threats that lose speed so these are not a concern.
[Previously here were two paragraphs giving a probable lower bound based on this idea. However, the numbers were wrong, and it ultimately yielded no improvement, so I don't feel like fixing it. Let's skip ahead a bit.]
I guess we'll have to analyze the actual audio tracks. There's only 8 of them after all. We'll consider both what happens with only 4 players and with only 5 players -- while having fewer threats may seem better, let's remember that with 4 players, one can only get -8 points from knockouts, not -10. After a bit of work, we find the following (not necessarily unique) minima for points let through:
Track 1: 10 points (put T7 on red); 12 points with 5 players.
Track 2: 12 points (put T6 or T7 on blue); 14 points with 5 players.
Track 3: 6 points (put T7 on blue and T6 on white, with T+6 being the Man-of-War); still 6 points with 5 players (put T5 on red).
Track 4: 10 points (put T7 on blue, with T+6 being the Man-of-War); 12 points with 5 players.
Track 5: 12 points (put T7 on red and T6 on white); still 12 points with 5 players.
Track 6: 12 points (put T6 on red); still 12 points with 5 players (put T7 on white).
Track 7: 10 points (put T7 on red and T6 on white); 12 points with 5 players.
Track 8: 6 points (put T7 on red and T6 on white, with T+5 being the Man-of-War); still 6 points with 5 players (put T5 on blue).
OK. And it's pretty clear these are indeed minima, so we get a lower bound of -30 points. Still, it's not clear whether this is achievable. Let's consider -- achieving this requires knocking out all players. But there's not too many ways to do that in the base game. Especially since whatever delivers the knockout must either A. be white or B. do so without reaching Z. The only white threats that knock out are the Battlebot Uprising and the Commandos (both serious internal). The only threats that knock out without reaching Z are the Battlebot Uprising (serious internal), the Executioner (serious internal), and the Power System Overload (common internal); however, the Executioner and the Power System Overload each lack the ability to knock *all* players out, and so if we are relying on one of them to deliver the knockout, we must have both. (Or rather, Executioner can knock all players out, but it can't both knock out all players and disable both battlebot squads.)
From this we can see that -30 is not achievable with track 8, since its only internal threat always reaches Z (meaning it must be white) but is also common, incompatible with the above. Track 3 can be ruled out for similar reasons. Thus -30 is not achievable. And since the only common threat that knocks out is Power System Overload, and it can't knock out all players by itself, one can deduce that -29 is not achievable either.
And -28, it turns out, is achievable. Solution is spoilered if anyone wants to sit down and figure it out themselves.
Audio track 8, 5 players. T7 red, T6 white, T5 blue, T4 internal. T+3 Hacked Shields (blue), T+4 Psionic Satellite, T+5 Man-Of-War, T+7 Frigate, T+8 Gunship.
I'm not going to go into details of how it's executed because, well, it's fairly obvious -- pick up battlebots, fiddle with the shields, get knocked out. You need 2 shield up on red. You also need exactly 2 shield up on white, which means first you'll have to hit B in lower red before filling up the white shield. Don't worry about the blue shield, it'll take care of itself. Point is, you'll survive with all players knocked out, both squads disabled, 6 damage on each zone, and a mere 8 points for threats survived, for a total of -28.
So we have an answer to our question: The maximum possible score is 69, and the minimum is -28.
...yeah, I basically spent all day on this instead of working. But now I'll never have to do this again! Unless I someday try to figure out how the expansion affects it, anyway.
-Harry
