When was the first video game released to the public?
Perhaps the first game created solely for entertainment rather than to demonstrate the power of some technology, train personnel, or aid in research was "Tennis for Two", designed by William Higinbotham and built by Robert Dvorak at the Brookhaven National Laboratory in 1958. Designed to entertain the general public at Brookhaven's annual series of open houses, the game was deployed on an analog computer with graphics displayed on an oscilloscope and was dismantled in 1959. Higinbotham never considered adapting the successful game into a commercial product, which would have been impractical with the technology of the time. Ultimately, the widespread adoption of computers to play games would have to wait for the machines to spread from serious academics to their students on U.S. college campuses.
When was the first video game released that was designed to entertain the general public?
1958
History of video games
No context provided
When was the first video game released for sale to the public?
September 1972
History of video games
https://en.wikipedia.org/wiki/History%20of%20video%20games
The Magnavox Odyssey is the first commercial home video game console. The hardware was designed by a small team led by Ralph H. Baer at Sanders Associates, while Magnavox completed development and released it in the United States in September 1972 and overseas the following year. 
Magnavox Odyssey
The first video game, "Tennis for Two" designed by William Higinbotham and built by Robert Dvorak, was designed for public entertainment in 1958 at the Brookhaven's annual series of open houses. Higinbotham never considered adapting the successful game into a commercial product, which would have been impractical with the technology of the time. The Magnavox Odyssey was the first commercial home video game console, which released in the United States in September 1972, and overseas the following year. 