The Great Universal Theory is basically a mathematical description of how roulette numbers hit in a sequence of spins. A German roulette tinkerer published his way to look at roulette in several online forums and called it Great Universal Theory or short G.U.T. Like the Law of the Third it can be calculated using the Binominal Distribution formula. The Law of the Third describes the expected amount of roulette numbers that got hit after exactly 37 spin and the amount of roulette numbers that did not. G.U.T. is simple an extent of that snapshot and continuously calculates the expected amount of hit numbers starting at the very first spin to the end of a game but practically to a maximum of 111 consecutive spins. It does not only calculate the results for hit and non hit numbers but also separates the hit numbers in categories of one time hit number, more than one time hit numbers, two times hit numbers, more than two times hit numbers, etc. The formula to calculate the Binominal Distribution for roulette is:
n…Number of trials k…Successes - means here to hit spun roulette numbers exactly k times in n spins
If you calculate the results for all the spins of a full rotation of 37 consecutive spins and for all the amount of successes from exact zero hits to exact four hits including the values for the categories "hit more often than" for >0 to >4 you get the matrix shown in the following Table. The green marked figures are the spins, the orange marked figures are the categories of how often numbers get hit, and the figures in the white area are the expected amount of roulette numbers in the respective category after the respective number of spins. At spin 0, means before the first spin, you certainly expect 37 numbers to have hit zero times – no number has hit. Similar clear is that after the first spin you expect 36 numbers to have not hit and one number to have hit more often than zero times and exactly one time. After the second spin there is already a chance that you will not see to different number got hit but you could see the first number having hit a second time. After ten spins you can expect 28 numbers to have not hit and out of the 9 numbers having hit 7 may have hit one time and 1 may have hit two times. The results after the full rotation of 37 spins display exactly what the Law of the Third is about – 13 numbers should not have been hit and 24 numbers should have been hit. But additionally the table shows that out of the 24 hit numbers 14 numbers should have been hit one time, 7 numbers should have been hit two times and at least 2 numbers should have been hit three times.
Using the binominal distribution I can chart the expected behavior of all the categories which would be the same if I would run an endless number of rotations of 37 spins and calculate the average. To give you a broader understanding of what is going on I will show you the expected value charts for a 400 spins sequence instead of 37 spins as the bet strategies derived from this theory require more than 37 spins too. A crucial fact and the chief point of Winkel's bet strategy is that the lines cross each other. The very spot where a line crosses another one is called Crossing. The very spin which may cause one line to cross another line is taken as a bet opportunity. But this way to look at roulette offers many more strategies to bet than just the simple crossings. G.U.T. is explained best in Randy Jones eBook.