From: ionsaliu@gmail.com   
      
   Doollow et al.:   
      
   Axiomatics, I don’t know exactly what gambling system Alan Turing is writing   
   about. I can only see his letter has a tile: “Gambling System”. Then he   
   refers to “batches of 10 spins”.   
      
   I don’t think a ‘1/37 bet in 10 spins’ is feasible in roulette. Only an   
   ‘18/37 bet’ can be applied to a roulette gambling system. Thus, we can   
   apply the ‘normal probability rule’ to an event of probability p = 18/37.   
   It is the case of ‘   
   even money’ betting (red/black, high/low, even/odd).   
      
        
   In the case of an event of probability   
    p = 18/37 (.48648649) in 10 trials,   
    88.9340988586645 % of successes will fall within   
    1 standard deviation(s) from 5    
    i.e., between 3 and *7*    
    the standard deviation is: 1.58056   
      
   This is how roulette is paying. You win an ‘even-money’ bet; they pay you   
   a profit of 1, plus they give you back 1 (your bet). So, you need to make the   
   adjustments for the ‘1/37’ probability cases. Only when you win, they give   
   you back your bet.   
      
   At best: 7 wins x 2 = 14 betting units won in 10 spins; profit: 14 – 10 = 4   
   units.   
   At worst: 3 wins x 2 = 3 betting units won in 10 spins; loss: 6 – 10 = – 4   
   units.   
      
   •	Minimum number of wins to make a profit in 10 spins: 6 (12 – 10 = 2)   
   •	Probability of *at least* 6 wins in 10 spins: 34%.   
      
   Probably Alfred Beuttell played a roulette system like this:   
      
   •	Play ‘even-money’ bets only   
   •	Divide your playing sessions into “batches” of 10 spins   
   •	If you reached 5 or fewer wins in the 1st batch, increase your bet in the   
   next series of 10 spins   
   •	Increase again if fail   
   •	If 5 or more losing batches, start martingaling.   
      
   The best roulette gambling is for ‘p=2/3=66%’ bets (double-dozen,   
   double-kolumn).   
      
   •	https://saliu.com/best-roulette-systems.html   
   •	 “The Super Roulette Strategy: The Best Roulette Systems Ever:   
   Win–Loss Streaks, Progression Betting”.   
      
   Ion Saliu   
   Founder of Gambling Science   
   Spin Doctor in Roulette Mathematics   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)