If lower than 7, choose Higher. If higher than 7, choose Lower.

Switch if 6,7,8

Cash out around after 3 wins

The optimal play is to choose the side with better probability.
Example: 6 has 5 cards lower and 7 cards higher.

You can improve your odds in a game if you choose to switch to a card with better optimal probability.
Example: 6 has an 7/12 chance of winning. If you choose to switch, there are 10 other cards with a better chance than 7/12.
The cards you should switch on are 6,7,8. (Proof left as an exercise)

Your chance to win in a game (without switching) is ~61% (proof left as an exercise).
Expected value of the game is nx * 0.61^n where n is the number of times you choose to continue and x is the amount you bet.
https://www.desmos.com/calculator/fp5g0u5zyw