[RPG] What are all the ways to increase the chance of a critical hit

Here's what you're trading for the alertness feat if you don't take the abil score upgrade and instead take the feat:

• +1 to damage
• +1 to hit
• +1 to AC
• +1 to Dex saves
• +1 to Dex checks
• +1 to init

The question then, ultimately, becomes, is +5 init (net +4), no surprise and no advantage on attacks against from hidden opponents worth it.

The latter two features are very dependent on your campaign and DM. Surprise should be a fairly frequent occurrence on both sides of combat, but that still depends on how willing your DM is to allow it or stage his monsters to have them obtain it (and kind of how cautious your group tends to be). Monsters attacking from hidden is another one that really depends on your DM, you group and how well you guys are at nosing out monsters from the shadows.

So ignoring those two items since they are DM and campaign dependent (and thus can't be weighted objectively), the question then becomes, is +1 to Dex more or less beneficial over 4 levels than +5 to init.

For pretty much any character other than the Assassin Rogue, I'd probably argue that they should take the stat upgrade early, the feat at L8 and then the last stat upgrade. However +5 init has amazing synergy with the Assassin Rogue and you're going to get a ton of mileage out of it.

If you're already at 20 Dex (if you managed to start at 20, or 18 and are at L8), then there really isn't any stat upgrade that is worth taking over this feat (though there may be better feats). Rogues are skill monkeys, yes, but +5% in a single ability set of skills is not worth the +25% to initiative and other features o this feat. The only one that would be worth considering at all is Con for the extra HP, but it's really not that many and you're better of boosting your damage significantly.

Take the feat at L4 (or even better, play a human and take it at L1).

My group uses the GameMastery Critical Fumble deck. We don't use it on every natural 1, but we use it on 1's when there's something else going on (in an area that's Unhallowed, for example, or in a cursed place or wild magic place or plane of the Abyss) to add to the atmosphere of threat besides a random roll penalty. It is also available as iFumble as an iPhone app. There are Melee, Ranged, Natural, and Magic options (so 1's on spellcasting rolls can have magical side effects as well).

Randomly drawn examples:

• Melee: "I Told You It Was Sharp" - You take 1d6 points of bleed
• Ranged: "Klutz" - You drop your weapon
• Natural: "Got Too Close" - Your attack hit the target, but the target may start a grapple against you for free
• Magic: "Mind Drain" - You take 1d4 points of ability damage to Int, Wis, or Cha (rolled randomly).

There's 52 cards with all 4 types on each so it doesn't repeat too often. The conditions are unfortunate but not instant death or decapitation type stuff, usually inflicting short term conditions (flat-footed, confused, dazed, etc.). Usually for 1 or a small die of rounds. Pulling some cards... -2 to AC for 1d4 rounds, sickened for 1d6 rounds, confused for 1 round... So this might be a better fumble-selection method than the current table. I do recommend trying to get him to lighten up on fumbles all the time, try to sell him on the idea of "it should happen when, you know, we're in an evil shrine or plane or someone's put a curse on the group or something, that would make it cooler."