A Corner Bet is an Inside Bet (like the Six Line Bet) on 4 numbers which pays out pays 8 to 1. You place your chip at the corner of four numbers (or in the middle of a square of four numbers). This bet is also called a Square Bet or a Quad Bet or even Carré in French Roulette. The house edge is the same as playing a single number bet. You have a 1:9.25 chance of winning the bet at a payout of 8:1.
A closely related bet is the Four Number bet which has the same payout, but includes the zero.
For example, above, we have 2 corner bets- one on 126.96.36.199 and one on 17,18,20,21.
If you place one corner bet on European Roulette, you have a 4:37 chance of winning (10.8%)
If you play American Roulette, your odds are 4:38 (1:19) for each square bet or 10.5%).
The House Advantage on this bet is the same as the other main roulette bets: 5.26% for American Roulette ("0" + "00" pockets) and 2.63% in European Roulette.
Roulette Strategies that Use the Corner Bet
There are plenty of systems that employ this Inside Bet- one is the 5 Quad Strategy, where you make 5 corner bets plus a single straight up bet (table coverage 21/37 on a Euro wheel, or 57%), or 54% if you use a number for your single number bet that is already covered by your corner bets).
So, it's a 6 chip bet. You'll make 3 chips if one of the corner bet numbers drops in and 30 chips if you land on the single number bet. It's a kind of hedge system on the single number bet, a "grind out the profit" typs of strategy.
Some of the more advanced Call Bets that you can play on the more premium variants use corner bets- the Number Combo is a good example. Another is the Complete Bet where you play all the possible inside bets of an individual number (including the Square or Corner Bet.
This is a standard bet like the Split Bet so it's best play on a European wheel- the odds are higher. Even more preferable is French Roulette that plays "la Partage". Try the Premium French Roulette over at Royal Panda.