Initial Level: Starting Gambling skill is equal to 20% + (3% x Luck) Average characters will have a 35% skill. Uncertain as to which game this refers.
In Fallout 2 The initial Level is equal to 5% x Luck. Average characters will have 25% skill.
This skill increases the odds of winning at roulette, slots or the "Mole-Rat Mambo" (Fallout 2, Redding. Interestingly, it does NOT increase the odds of winning at craps, Fallout 2. Den. One can easily save right before betting, and bet all of their caps on a craps roll, win > save, lose > reload, without needing any investment in Gambling.
In Fallout Tactics, at least without the patch, just your main character will be able to gamble. The process is also bugged: you can offer nothing for all, then hit the gambling button rapidly. In 10 seconds you can win, even with 30%.
In Fallout, Gambling could be used as an exploit with some small heavy objects and some spare time. Go to the Hub and go south till you hit the bar, the Maltese Falcon. Talk to the black guy by the roulette table; when the dialog comes up use something (like a pair of 9v batteries, or get creative with tape) to hold down the 1 and 3 on your keyboard. Leave it alone for a while and when you come back you should be well off. This requires a minimum of 60% gambling to turn a profit. The higher the skill, the more caps per hour one can expect to get. With this, one does not need to invest any points in Barter, as one has an unlimited source of income.
In Fallout 2, one can perform a similar exploit as above at any slot machine. Simply use a weight of some kind to hold down either the 1,2,3,4, or 5 key. The keys correspond to different betting amounts (1,2,5,10,25). The higher the number, the higher one needs in Gambling in order to win more than 50% of the time. Even a 50% gambling skill can earn money with the lowest value, though it takes a while to earn any decent amount. By 80%, one can bet $10 and win consistently, easily earning in an hour or so all the money one is likely to need for an entire game.
This skill can be increased with the Gambler perk, which adds 20% to the gambling skill.