Game logic development

Write the game logic and test it.  

Game about opening boxes. There are 25 boxes, one contains a prize with a game currency, and the rest contain game stickers (multipliers) or nothing. 

The player places a bet. The game randomly selects 1 safe out of 25, and the player has the opportunity to choose 3 safes. When the safes are selected, the player clicks open. 

If the player guessed the designated safe, they receive a prize of х0.1*bet, х0.25*bet, 0.5*bet, х0.75*bet, х1*bet, х2*bet, х5*bet, х10*bet, х20.

The player also receives stickers when collecting a series of stickers of the same denomination, the winnings are multiplied (if the player has also opened a safe with a prize in this game) or the bet is multiplied. 

Coefficients when the player opens a safe with a prize and collects a combination of stickers. 

With some probability, the designated case with coins will be highlighted for the player.

It is necessary to develop a game model where the player's balance depends on a linear function Balance(number of games). B(q) = 1.6 * q + 200

The game model is built around a linear function so that the player cannot win too much or lose too much. 

It is necessary to create a mathematical model of the game in which the player's balance follows the given formula. Different stickers will be issued, but not collected, for example, 20 green stickers х100, and no red sticker to close the series and issue a prize. As initially specified, a х100 prize cannot be awarded. 

The probability of wins is set specifically for the coefficients, i.e., there is a probability of winning х7.5; if it appears as a big win for the player, the game is adjusted so that at some turn the player guesses the box with х0.75, and on the same turn closes the series with х10. 

The box with the win is generated before the game, and the finding of stickers and the win in this box occurs after the game. 

 Create the possibility to test the model over a large number of games, depending on the formula and the probabilities of coefficients.  Display minimum, average, and maximum values: balance, winnings, series closures, and data for each sticker, data for each win. 

Model the graph B(q) of the player, from a single game and the average over many games.