Gambling has provided centuries of inspiration to probabilists and statisticians. The process continues. There also exist fundamental links between betting and a newer subject, Information Theory, which began with Claude Shannon and his ground-breaking 1948 paper A Mathematical Theory of Communication. It is a result which arises very naturally. A successful gambler and a successful data compression algorithm must both accurately estimate probability distributions. There are practical results as well as theoretical: Shannon and colleagues, including the legendary gambler and mathematician Edward Thorp, actually attempted to apply results from information theory in Las Vegas casinos and stock market transactions.