The Walking Liberty half dollar set is conceptually divided into three groups: the 1916-1929 "early dates," the 1933-1940 "middle dates," and the 1941-1947 "short set." The 1933-S sits on the cusp of the transition from early dates to middle dates. Interestingly, mint state examples of the early dates were not saved in any meaningful quantity at the time of issue. Starting in 1934, even though it was in the middle of the Great Depression, significant quantities of original rolls and mint bags of all denominations of U.S. coins were saved by the growing number of coin collectors and dealers. In terms of number of coins saved at the time of issue, the 1933-S Walking Liberty half dollar is more like an early date Walker than a middle date. I have seen hundreds, if not thousands, of original mint state rolls of 1934 Philadelphia Walkers. But I have never seen a roll of 1933-S Walkers, though many years ago I heard about a few. Bottom line, the 1933-S in a scarce coin in mint state and a very scarce coin in Gem condition.
This issue can come very frosty. Strike doesn't seem to be as much of a problem as on the earlier S-Mints and you definitely bump into well struck examples from time to time.
According to a notice in the June 1934 issue of The Numismatist (p. 416), collectors could still purchase Uncirculated 1933-S Half Dollars directly from the U.S. Treasury for "the face value of the coins and an amount sufficient to cover the mail charrges by first-class mail."