How to bet on a binary event based on the markov transition matrix, state probabilities and the odds

There is a coupon full of football matches for a given day from a bookkeeper. I have scrapped another website and i have aquired continuous history of a particular match between AvsB. Using data involving only the pair AvsB i created a transition matrix for the over under bet (above 2.5 goals or below).

i have two states [0,1] that represent Over or Under (soccer). I have calculated the transition matrix from n games and i have an example state probability of [0.67 0.23] also the odds could be [2.3 3.1]. All here is made up. What is the most efficient way to allocate my bet? If there is interest ill look up some real data.

The transition matrix calculated from an array of 0's and 1's (over under respectively)

|0.3  0.7 |
|0.45 0.55|


By betting to clarify i mean that i have 10 dollars for example and i want to spread that 10 dollars in the most efficient way possible.

Also.

1. full reward for correct guess and no reward otherwise
2. The amount i win is the odds*amount example 5 * (2.3 over) = 11.5\$ return
• Could you give us more details? I may be missing something, but matrix of transition probabilities should be a matrix, e.g. a 2x2 matrix. How did you calculate those values? What exactly is your data? Moreover, what do you mean by "betting" in here? – Tim Sep 20 '17 at 8:52
• @Tim updated my answer above – George Pamfilis Sep 20 '17 at 8:58
• The information that is still lacking is some more details about your problem. Moreover, you need to give us information on the reward system (e.g. do you get full reward for correct guess and no reward otherwise, or are partial rewards possible, how does reward relate to the amount of the bet etc.?). Are you betting for a single game, or for a series of games? There is lots of things that possibly would need to be considered, so the more details you give us, the mroe likely you are to get better answer. – Tim Sep 20 '17 at 9:03
• @Tim i updated it once more. – George Pamfilis Sep 20 '17 at 9:28