Why didn't Romans fight in a single line formation?

I don't have my references handy but my recollection is:

• The three-line, checkerboard formation (princeps, hastati, triarii) was used only in the Republican period, having been developed by Camillus and largely abandoned by the time of Marius. So depending on the time period you are gaming use of the three lines and checkerboard may or may not be anachronistic.
• There has been debate about exactly how the checkerboard formation was used. It is quite possible (even probable?) that the checkerboard was only used during the advance to contact, as it provided greater maneuverability to the legions than a long line/phalanx. Note that this is analagous to the use of columns vs lines in the Napoleonic period. Very shortly before contact the rear lines of each block of troops would move to the flanks of the front lines of that block, linking up with adjacent blocks to form a single line. This type of maneuver was done in the climactic battle scene in Spartacus (see this exerpt starting at about 3 minutes in).

If you have a single line, it means that a man fights until exhaustion or death. While when you have several lines, you can rotate them to let them rest and keep fresh men fighting.

In real battles men don't die while fighting in the line, most casualties occur when the line breaks and disbands, because when the line opens each man loose the protection of his neighbors. Therefore, in ancient battles the purpose of the fight was to hold the line more time than your enemy and prevent an attack from behind or the sides.

Finally, when you have several lines, you have a reserve to cover gaps or prevent a side attack.

I strongly recommend a nice historial novel which describes the live of Scipio, wrote by Santiago Posteguillo. He describes the battle of Zama and Magnesia, with all changes in the lines while the men fight.

You made a common error amongst miniature war game players: you fight according to the rules, not to the historical situation. I've played a lot of Napoleonic miniature games, where cossacks - due to the rules - were almost invincible. In real life they were good, but definitely not supermen. Otherwise every army would have had cossack units.

Some players learned the rules by heart and build an army to make the most out of it. Often they would win, but not because their army was historically better managed, but because they build an army that would work best with that particular rule set. That very same army could be trashed with a different rule set where other units had different/better advantages.

The Romans were very pragmatic. Whatever worked, they used. If something didn't work anymore, they tossed it away. The Romans used the checkerboard formation ... because it worked well for them. Very well.

There isn't a a game that simulates combat 100% accurate. It's always a toss up between realism and playability. You can add some extra realism to any game, be it a board game or a computer game:

First march 25 km in full gear. Then do 50 push ups followed by a 100 meter dash, again, all in full gear. Ask your friends to paddle you with sticks while you have to play the game with specific short time limits to make your decisions. -- And even that is not real combat. ;-)

In the army I had to do just that to qualify for a shooting badge. Minus the paddling, of course. Shooting a pistol at 25 meter on 5 targets is not very difficult. But it is with the above extras. It was still a heck of a lot easier then real combat as the targets didn't shoot back.

"Defense in depth" was the key to winning, after the earliest battles. With a "long thin line," you will either "kill or be killed" at the first shock of battle. That's how wargames play, but not how warfare was conducted by the time of the Greeks and Romans.

The Romans won mainly because they "outlasted" almost everyone else. With their training and experience, they would want battles to last a whole day, and hope that the other side breaks first, instead of staking all on the first contact. Their system of rotating troops was the best for their time, and they used "checkerboard" formations to advantage. Other armies weren't as efficient in this regard, and they fell apart sooner.

The frontline was still quite long:

• a maniple typically consisted of 120 soldiers arrayed in 3 ranks of 40 men when engaged in battle.
• each line had about 10 maniples and neighbouring maniples had a space of a maniple between them.

That makes the frontline 19×40 = 760 men wide. Lets say that each man had a "personal space" of 1,5 meter (which is not that much considering that they needed space to use their weapons) then you have a frontline of 1140 meter. That's quite long. Given the communication methods of that era there was a limit of how long a frontline you could effectively supervise and command - the Total Rome is indeed realistic in many ways but the way you see the entire battefield and can command instantly any troop in the game is a pivotal difference between the game and the reality.

So it could have been a rare case where the enemy choose to stretch out their troops to have a much longer frontline but if they did the Romans still could opt to have a longer frontline by changing their tactics (like making their maniples longer but less deep).

The flanks were usually guarded by cavalry and auxiliary units like light infantry. If those were defeated before the Roman main force (the heavy infantry) could break the enemy's center then it was entirely possible to launch an attack at the flanks and rear of the legion which could easily lead to a catastrophe for the Romans (like what happened at the battle of Cannae).

Other thing is, that we don't really know how the Romans fought exactly, so it's highly probable that the line which was in combat didn't use a checkboard pattern but a straight line. The lines behind them used the checkboard pattern while waiting for their part to allow the retreating troops go through.This video explains quite well how could it work.

The main advantages of having multiple lines is having reserves. For one, having reserves mean that you can react to unseen situations (like your line breaking somewhere). The other really important aspect is that you can rotate your troops when the ones currently fighting start to tire. That's really important and gave an edge to the Romans in longer battles.