Hi CDrake and Martor,
I am interested in the application of Markov Chains to the lottery, but haven't come across anything that describes
specifically how the theory should be applied.
According to
Wikipedia:
A Markov chain (discrete-time Markov chain or DTMC[1]) named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another on a state space. It is a random process usually characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property. Markov chains have many applications as statistical models of real-world processes.
So, this would seem to describe the random process of a lottery number as it changes from one state (e.g. 27) to another state (e.g. 32). Or am I off base here?
Anyway, I have created an excel spreadsheet that applies this process to lottery numbers by position.
For example, if the last draw had the number 7 in the first position, I can see from my spreadsheet that this has happened 94 times in 1,690 draws and that the transitions to the next draw are to a
lower number 58.5% of the time, remaining the
same (i.e. repeat in position) 5.3% of the time and transitioning to a
higher number the remaining 36.2% of the time. I can also see that 43% of the time the number that followed 7 in the first position was between 1 and 4 and that 1 followed 7 19.4% of the time and 2 followed 7 10.8% of the time (as well a probability for every other number). I can see that no number higher than 22 has yet followed 7 in the first position.
But, even with all this information, the spreadsheet doesn't seem to be very helpful in predicting a specific number for the next draw, or even a tight range of numbers.
Is there something more that I should be doing here?
Martor -- you suggested combining with Bayes Theorem. I'm not a mathematician, so how would that work?
Looking forward to your insights,