On Bicycles, and.... what else is there?

The baccarat problem got me thinking about the random walk problem, because each of the three times in my game I reached the $200 betting limit my revenue became a random walk. At this point the problem was: which was going to come first, was I going to get into the black on $200 bets or was I going to burn through all of my cash? This is a random walk: my revenue bounces back and forth, an approximate 50% chance of each, and the game ends when I reach either of two targets: $200 above where I started (between $5000 and $6000) or $0. Many years ago, I can't remember when, I encountered a problem in random walk probabilities which was: suppose a robot, starting at x = 0, steps either in the +1 direction or the -1 direction, at random, for infinite time. What is the probability he never returns to 0 after his first step? Wow -- this is a heady problem. It always seemed to me the probability was zero: surely in infinite time he has to eventually reach all points of finite x. ...

I was reading the first pages of Casino Royale, not the Daniel Craig film, not the David Nival film, but the Ian Fleming novel. In the Daniel Craig movie, James Bond plays Le Chiffre in a high stakes poker game. The film is perhaps the most loyal of any Bond film, rivaled only by Her Majesty's Secret Service, in adherence to Ian Fleming's books, and not too surprising, these are thus two of the best bond films made. Craig is certainly a great Bond but neither of the films which followed, Quantum of Solace or Skyfall, was in the class of Casino Royale. Meanwhile On Her Majesty's Secret Service starred Roger Lazerby, the only one-timer (unless you count Niven). While he was young and energetic, a striking contrast to Roger Moore, there was still a reason Lazerby never returned. So the conclusion is clear: Fleming wrote some solid books. The earlier Casino Royale, the 1967 film starring David Nivan (who was actually a serious candidate to play Bond in Dr. No) was a come...