4. A game uses a standard pack of 52 playing cards.
A player gives 5 tokens to play and then picks a card. If they pick a \(2,3,4,5\) or 6 then they gain 15 tokens. If any other card is picked they lose.
If they lose, the card is replaced and they can choose to pick again for another 5 tokens. This time if they pick either an ace or a king they gain 40 tokens. If any other card is picked they lose.
Daniel is deciding whether to play this game.
- Draw a decision tree to model Daniel's possible decisions and the possible outcomes.
- Calculate Daniel's optimal EMV and state the optimal strategy indicated by the decision tree.