Basic All-In Win Chances

It's good to know the rough chances of winning for some basic all-in scenarios.  This occurs in no-limit hold'em when you or your opponent goes all-in preflop, and all 5 board cards are shown without action.  This is known as a "race", the person who winds up making the best 7-card hand wins.  The common scenarios are :

pair vs. two overcards (eg. 55 vs. K9) : 54% favorite
pair vs. one overcard (eg. TT vs. A5 or 55 vs. A5) : 70% favorite
pair vs. two undercards (eg. AA vs 56) : 80% favorite
pair over pair (eg. KK vs 66) : 80% favorite
pair over covered card and undercard (eg. KK vs. KT) : 90% favorite

higher card, no pairs, both live (A5 vs. K9 or AK vs. 56, etc.) : 55-65% favorite
higher card, no pairs, covered (A5 vs. K5 or AQ vs. AT) : 75% favorite

You can reduce this to a very rough rule, there are only two primary situations : one of dominance (eg. pair over pair, or when your outs are covered), and one that's nearly a coin flip (pair vs. overcards or nonpaired higher cards).  Obviously you want to be playing in a situation of dominance, and it's very very bad to get all-in when you're dominated.  Putting all your chips in the pot with near coin flips is a big mistake, so for example low pocket pairs are terrible to get all-in with.  In the best case you're facing overcards and it's nearly 50/50, and in the worst case you face a higher pair that has you dominated.

Important cases of dominance to avoid are pair-over-pair and being out-kicked with an Ace.  Playing something like TT, you dominate lower pairs, you're 50/50 against overcards, but you are dominated by the higher pairs, so they're what you must try to sniff out.  Playing AJ, obviously you fear any pair JJ or higher, but lower pairs are roughly 50/50 against you; you are dominated by AK and AQ, so you need to watch out for them.