Here it is, a short example of combat in Traveller.
A gunfight between 'Red', a gunslinger (a career in the mercenary book for traveller) and Jake, an ex-navy man and drifter.
Red has the following attributes and skills (only relevant to this situation though)
Gun combat (slug pistols) 2, athletics (coordination) 1
Gun combat (Energy pistols)1, Gun combat (energy rifles) 1, athletics (coordination) 1
A little back ground first.
Both of the above have been having a 'strong' debate in a seedy little bar in a star port, and Red, being a little hot headed takes offence at Jakes statements, and falls back on her standard behaviour when insulted, or for that matter, in any situation, and goes for her guns.
As this situation has just got violent , it’s time to roll initiative. In traveller , Initiative is rolled on 2d6, modified by the characters DM for their attribute, so in this case Red has a +1 for her high DEX, whilst Jake has no modifier to his roll.
Jake rolls 9 on 2d6
Red rolls 6, plus her +1 for a total of 7.
Red has a gauss pistol and wears cloth armour, and Jake has a laser pistol and also wears cloth armour.
Jake, seeing Red going for her gun, decides that he is just to close and dives for cover whilst drawing his laser pistol (The drawing of his pistol is a minor action, and his other action, significant as traveller calls it, is to dive for cover) diving for cover is 'dodging' and as he will end up in cover, so following the traveller rules, his initiative will be reduced by -1 next round, but Red will have a -2DM to hit him, for the dodge into cover. This action has also put Jake about 3 metres from Red, which in traveller is close range. (In range combat, each range band will provide a modifier to each shot, either no modifier when fired in the weapons optimal ranges, or negative if beyond optimal, as an example, pistols have no mod at close or short range, and -2 at medium range)
Red now acts, she draws her gauss pistol as her minor action, and shoots at Jake as her significant action. Her modifiers are her skill, which gives her +2, her DEX that gives her +1, but Jakes dodge and being in cover also applies a -2, so her DM for the roll is +1.
Reds (player) roll is abysmal, 2D6 comes up a 6, and adding the +1DM, a total of 7. As in traveller 8 or more is needed to succeed any roll, that is a miss, so her round hits the wall behind Jake.
That is the first round of combat over, other patrons in this bar are at this moment are either running out of the bar or finding cover from the fire fight that just broke out.
Initiative in traveller is dynamic, it is modified each round by a player/characters actions, as Jake dived for cover, his initiative is reduce by 1, so becomes 8 for this round. Reds initiative stays at 7.
Jake takes aim (his minor action) and then fires at Red. Red can always react, so she dives for cover herself, she is hot headed but not stupid. This will apply the -2DM to Jakes attack roll.
Jake (player) rolls the dice, getting a really good roll of 11 on them. To this his added his skill, +1, and his aim bonus, also +1, for a total of 13. This is reduced by the -2DM from Reds dive, and leaves 11. This is a hit despite Reds dive (any roll of 8 or higher is a success in traveller).
The damage of the laser pistol, Jakes old but reliable TL11 model is 3d6+3, and this is further modified by the 'effect' of Jakes roll. The 'effect' is simple how much Jake rolled over 8 on his hit roll, so as his final modified roll was 11, that was an effect of 3, so the total damage roll to Red will be 3d6+6. Jakes player rolls and gets a total of 16.
Red is wearing some armour though, so the damage is reduced by its value (5) leaving her to take 11 points of damage. All damage is taken from endurance first (the third number in her attribute line,
and then from either her strength (first number) or her dexterity (second number).
So the damage of 11 reduces her endurance to 0, and she decides the rest can go reduce her strength, so that drops to 5. Red is hurt, and hurt bad, but is not yet out of the fight, and being a stubborn *****, she switches her pistol to auto fire mode (her minor action) and fires back (her significant action) despite her injury.
Red rolls a 5 though, and with the same mods as last round, plus an extra -1 for her diving for cover, she misses, her burst tearing up the table Jake is behind, but not hitting him at all.
Jake initiative resets back to 9 as he has done nothing other than aim and fire, Reds initiative is reduce by 1 for her dive, so is now 6, so Jakes goes first again.
He repeats what he did last round, aims and fires at Red, seeking to end the fight in this shot. Red reacts again, dodging into her cover, which gives Jake a -2 DM for the dodge into cover, and also an extra -1 for the cover she is already in (over turned tables) for a total of -3DM to Jakes roll.
He rolls a 10 on the dice, which with his mods of +2 (his skill and aim) but the -3DM above, means the total is 9, so hits Red again. The damage rolls is 3d6+4 this time (the effect of his roll was 1, so that is added to the damage) for a roll of 12 on the dice, plus 4, the total is 16.
Reds armour reduces this by 5, leaving her to take 11 points, which any way you look at it is going to reduce one of her remaining physical attributes to zero. Reds strength is dropped to zero by 5 of the damage, and the rest (6) comes off her dexterity leaving that at 4. With two of her physical attributes reduced to zero, she is unconscious, seriously wounded by Jakes last shot and crash down to the floor. Jake decides this would be a good time to leave the bar before security turns up, and leaves Red to whatever fate awaits her.
That is all there is to traveller combat, in short, you just have to remember the DM (dice mods) and also be aware that it can be very deadly. Hopefully this was clear and that my maths adds up