|Posted: November 30, 2006, 7:52 pm - IP Logged|
Whats most fascinating to me is how every single Pick 3 game that I've ever tested performs very, very similarly from a probability point of view. Take any amount of consecutive games from any pick 3 game in the country and you will see very similar results when it comes to how many different combos were drawn and/or how many remain to be drawn.
The 93.82% can be derived from the following formula. It will give you the probability based on n, which is the number of consecutive games played:
p = probability
n = number of trials
1-(1-0.001)^2783 = .938233395, which is 93.82%
If you want to know the how many games you need to play based on a particular chance of success (the Degree of Certainty, then you can use the FFG formula:
DC is the chance listed as a decimal (50%=.5, 95%=.95 etc..)
P is the probability of the event (Pick 3 is 1 in 1000 = .001)
log(1-DC)/log(1-p) = Trials
log(1-.9382)/log(1-.001) = 2782.43
The number that this formula spits out is the amount of consecutive games that are necessary to have the chance (DC) of winning.
It seems as though the real probability for anything to happen actually rests within how many different combos are drawn within measured time frames or consecutive amounts of games. In all reality, a string of outcomes creates an extremely large and ever-growing combination. In essence, what these formulas do is calulate the number of combinations that contain the desired outcome at least once within their total...this gives you your percentage of chance to hit AT LEAST once within the given time frame.
As accurate as these percentages truly are, the result is not just limited to an individual combination's long term probability, but rather the entire matrix as a whole. For example, if you want to know how many games you must play for a 50% chance of winning on a particular straight Pick 3 combination, you would run the FFG formula as follows: log(1-.5)/log(1-.001) = 692.8005 or 693 games rounded. Not only is that how many games that you must play to have a 50% chance of seeing that combo drawn, but it is also the amount of games required for 50% of the matrix to have been drawn in! Pick a state, any state...grab a chuck of 693 consecutive games and there will almost always be between 480 and 520 different number! Those two figures represent the max fluctuation 99% of the time. Its most common to see 490 to 510.
I have tested these formulas on an empiracal level in at least 20 states now and the results are amazing. I know of no other formula or theory that dictates the truth of how randomness works in these games better that those formulas. Its interesting to note that it only takes 693 games to have a 50% chance but it takes a whopping 9,206 games to attain a 99.99% chance! You see that first 50% chance is the median, which is game 1 through game 693...reliable, tight and consistent! The other 50% stretches out to infinity and includes more that 8513 consecutive games starting at 694.
Win D, since you like to include 50/50 odds in alot of your strategies, heres another one you could add. Always look at the last several straights drawn and see how long they have been out before their last hit: 50% of the time the next straight that hits will be one that was out less than or equal to 693 games ago. The other 50% of the time, the number will have been out at a value of 694 games or greater.
~Probability=Odds in Motion~