I am a complete novice when it comes to mathematics, however I am trying to calculate the most effective way to play a card game within a virtual casino on another online game I play. Dealer draws a card 2 thru Ace. You must then guess whether your card will be higher or lower than the dealer card. Aces are high, two's are low.
Standard 52 card deck.
Cards are NOT replaced into the deck, until the deck is shuffled.
Deck is ALWAYS shuffled every 9 or 10 'hands'. 1 hand = 1 dealer card + 1 player card.
Betting is in fixed amounts of 10, 100, 1,000, 10k, 100k, 1m and 10m.
Payout multiplier changes daily and ranges from 15% to 40%.
Every time you beat the dealer, you increase the starting bet by the payout multiplier. For example: 1m becomes 1.15m becomes 1.3225m
A draw, IE dealer has 8 and you draw 8, counts as neither a win or a loss. The game proceeds to the next round without any addition to the pot.
You may cash out at the end of a round for the full pot amount, or after you have seen the dealer card for a 50% reduction in pot.
I have made some basic calculations in excel that counts cards for you and tells you when you should pick higher or lower.
However, I'd like to calculate at what multiplier does the game have a positive EV.
I also think that there are more advanced strategies available where you play 10 hands until the deck is stacked in your favor; for example a minimal amount of 7,8,9's etc.
I'd love to find someone who can help me solve this problem!
Sorry if my post formatting is off or if I have broken netiquette here. This is my first post.
Many thanks, TJM