The only semi-reasonable way to score points on The Atarians is to repeaedly build bonus, then collect it at the left saucer. The most reliable way to build bonus is from the top of the table, but returning here after the plunge is not easy: your best bets are the replunge lane in the middle right, or backhanding the ball and hoping to ricochet it toward the saucer off the posts that stick out next to the bonus collect and extra ball saucers.
First, know that there is absolutely no relevant information to the status of the game on the backglass. The credit count, all four player scores (!), and other icons like Tilt, Game Over, and Same Player Shoots Again are all in the apron, with most of them being near where you'll probably be resting your left hand. Don't try to look up to check scores during gameplay, as there's nothing there.
Second, in an attempt to seem futuristic, The Atarians does not have wire rollovers, traditional star rollovers, rollover buttons, or really any other switch that cuts into or pokes out of the playfield. Instead, anywhere you see a star icon on the playfield is a magnetic sensor button, which just activates if the ball is near to it. Take time to identify where all these star sensor icons are before starting a game for the first time. The remainder of this guide will use the familiar term "rollovers" to refer to these star icons.
At the very top of the game are two rollovers that score 50 points and advance the bonus. Nice, but not world breaking; don't go out of your way to try to find these on the plunge if it means sacrificing going into one of the Atari saucers.
The Atari saucers are 5 saucers across the top of the playfield. Each one scores 500 points, advances the bonus, and lights the corresponding letter in Atari. Spelling Atari lights double bonus for the rest of the ball, including on mid-ball bonus collects from the left saucer. The middle saucer, corresponding to the second A in Atari, lights the red pop bumpers for 100 points each.
On a plunge, the goal should be to land in any letter except for the I, then use nudging off the bumpers and various posts in the vicinity to keep the ball up there and hopefully grab multiple saucers. The I lane just kicks straight down to the bottom of the playfield with no posts or bumpers in the way.
This saucer is a repeatble full bonus collect, with the double bonus if it is lit. Collecting the bonus from this saucer does reset the bonus count, but does not unlight the double bonus. Easily the most important shot in the game, but the only real way to shoot straight for it is a backhand from the upper left flipper. If that flipper isn't strong enough to make that shot, good luck; your only hope then is a friendly bounce off the left red pop bumper.
Scores 2,000 points, which is honestly enough that if you can dial in this shot from a lower left forehand or (more likely) an upper right backhand, you can just shoot it for a while and grind out moderate points. After collecting 9 extra ball advances (from the #2 standup target, left in lane, or right out lane), this saucer is lit for an extra ball.
All score 10 points, or 100 when lit. The blue one seems to always be lit, while the red ones are only lit after making the center top saucer (second A in Atari).
On the middle-right of the table is an alleyway that connects back to the shooter lane. Putting the ball through here does not score any points, but does give an opportunity for a replunge. Use this liberally as a free trip to the top of the table for more easy-ish bonus advances.
#1 is a 2,000 point rollover in the nearly-impossible-to-shoot left orbit; 2 and 3 are yellow standup targets in the lower left playfield; 4, 5, 6, and 7 are the out and in lanes from left to right; 8 is the lower right standup target; 9 is a death target smack in the middle of the playfield. Hitting the nearby stnadup target (for 2, 3, 8, 9) or rollover (for all others) lights that number. #3, 4, 6, and 8 all advance the bonus. #2, 5, and 7 all advance the extra ball. #1 is worth 2,000 points and #5 and 6 are both 50, but all other numbers score 500. For some reason, the 1, the 3, and the 8 always seem to be tied together so that lighting any of the three gives credit for hitting all of them.
Lighting all of 1-9 lights a special that moves around the playfield. There are 6 places the special can be: the first 2 both correspond to the #3 target, the third is its own rollover near the #2 target, the fourth is the #9 target in the center, and the last two both correspond to the #8 target on the right.
A vaguely triangle shaped turnaround lane right in the center of the playfield has a rollover at the top which awards 50 points and advance bonus. The entry to this turnaround is very wide, but blocked off in an awkward way by a pillar post on both sides. It's only possible to go through the turnaround from the ball going above the posts by accident, and going below the posts requires a tight shot from the lower playfield that isn't really worth the risk. If you do try the latter, though, there are switches on either side that score 500 points and open the gate on their respective sides.
The center of the turnaround has the #9 standup target that scores 500 points and a possible special as described in the previous section.
The Atarians has a very wide take on the conventional in/out lane setup. The in lanes, out lanes, and slingshots are in their normal order on each side of the playfield, but because this is a widebody game, the slingshots and in lanes are very far apart from each other, and there are two flippers on each side in between. The vast majority of drains on The Atarians are scissor drains between the two flippers on a single side; get a leg up on your opponents or your own high scores by only using the lower flippers in extreme moderation.
The out lanes score 500 points, while in lanes score 50. The left out lane and right in lane advance the bonus, while the left in lane and right out lane advance extra ball. The four lanes, from left to right, award the 4, 5, 6, and 7 from the 1-9 number set.
There is a saver gate on both sides of the playfield. Gates are activated by the Opens Left Gate and Opens Right Gate rollovers in the center turnaround. The left gate channels a ball from the out lane to the in lane, while the right gate moves a ball from the out lane to the shooter lane for a replunge. Gates are not closed when used, and are instead only closed by hitting one of the Close Gates rollovers that are in front of the slingshots.
Bonus is advanced by the very top star rollovers, any Atari saucer, the rollover in the center turnaround, the #3 and #8 targets, the left out lane, and the right in lane. Max bonus is 19,000 points. Entering all 5 of the top saucers to spell Atari lights double bonus for the rest of the ball.
The left saucer scores the entire bonus (with doubler if lit) at any time, but resets the base bonus on kickout. This is where a very large percentage of points on The Atarians lie. Interestingly, 1,000 is put in the bonus for free at the start of the ball, but the bonus is kept empty immediately after a left saucer collect, so it's possible to drain with 0 end of ball bonus by collecting from this saucer and then immediately losing the ball without hitting another advance.
Bonus count and bonus multiplier cannot be carried from ball to ball.
Special can be set to score a free game, an extra ball, or 10,000 points. I was unable to determine if extra ball has a possible point value; I doubt it. (I was also unable to determine if there's a setting for disabling the extra ball- it doesn't seem like there is?)
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