hi what would be the best strategy to infer the range of probabilities of getting heads with a coin of Unknown Bias that is variable?
EDIT: Problem specification I'm working on a similar problem with a game AI.
I'm working on a AI to play a game that consists of multiple nodes in a graph network. Each node in the network switches between two values, either A or B, based on a probability variable unknown to the player in every round. This probability variable also changes with each subsequent round based on what move the players makes.
Its a two player game, and if at the end of the game there are more node with the value A, player A win and if more nodes with value B then player B wins. Each player has 5 moves that affect the probability by multiples of 5:
move 1 affect the probability variable of each node by 5%, move 2 by 10%, and so on. Each move has a set energy cost, the greater the percentage change of the move, the greater the energy cost. The chosen move affect all the nodes in the graph network. The value switch happens once both players have made their moves
So the optimal strategy for each player would be to increase the probability variable of a node if its has the opponents value and decrease it if it has the players value. Every node in the graph is assigned a random probability at the start of the game, and the probability variable of each node is unknown to both players.
so I assume I would need to infer the probability of each node in a specific round for my AIagent to decide on a move, so what would be the best strategy accomplish this? I assume it would be similar to inferring the probability of a biased coin, but I'm not sure how that would work considering that the probability variable of the nodes changes in each round
edit 2: Players are not made aware of the probability of a node, only their values i.e either A or B. The players also can not target specific nodes, their chosen move affect every node in the network by increasing the probability of switch for nodes with the opponent's value and decreasing probability of switch for nodes with the players value. However the players are aware of the entire switching history of each Node