Dear forum members,

I have recently come up with a new card game that I call "Higher or Lower." It's a simple yet exciting game played with 53 cards, consisting of 52 regular cards and 1 joker. I would like to seek your help and insights in calculating the equity or winning odds of this game for the bank.

Here's how the game works:

Each player and the bank receive one random card from the deck of 53 cards.

The player places a bet of one unit.

The bank also holds one card.

If the player and the bank draw the same card, the bank wins.

If the player draws a higher card than the bank, the player wins.

If the player draws the joker (the only joker in the deck), the player wins a 5 times their bet.

If the bank draws the joker, the player only loses their initial bet.

Now, my question to all of you is: What is the equity or winning odds for the bank in this game? How can we calculate the probability of the bank winning and the probability of the player winning, considering the presence of the joker?

I assume that means a net profit of 4?

P(same rank) = 3/53
P(bank > player) = 25/53

Bank EV = 28/53 - 24/53 - 4(1/53) = 0

The game is fair, no edge for either side.

I think there is an egde for the bank.. yes when the player draws the joker the net win is 4.

If you've done calculations of your own, I'd be happy to look at them. If you haven't, I'm not sure why you'd think there's an edge.

I'll elaborate on my numbers:

P(same rank) = (52/53)(3/52) = 3/53
P(bank > player) = (1 - 3/53)/2 = 25/53
P(bank win) = 3/53 + 25/53
P(player joker) = 1/53
P(player win without joker) = 25/53 - 1/53

E(bank net profit) = P(win) - P(lose to non-joker) - 4*P(lose to joker) = 28/53 - 24/53 - 4(1/53) = 0

An EV of zero means the edge is zero.

I don't see a casino game that requires no player input to be "exciting".

As someone who loves card games beyond just the usual poker and spider solitaire, I'm always excited to see fresh ideas in the mix.

Equity seems to blend strategy and probability in a unique way, which is what really caught my eye. It's fascinating how games evolve and borrow from each other—kind of like how spider solitaire took the classic solitaire and gave it a twist.

I'm curious though, what do you all think about the balance between luck and skill in new games like this? Do you prefer games where strategy reigns supreme, or do you enjoy a healthy dose of unpredictability? Personally, I think a bit of both keeps things interesting!

I’m not sure how there is any balance of luck and strategy in OPs game as described. You win if your card is higher than the dealer’s. Where is the strategy?

The problem with the game is the lack of action. Even in games like Baccarat, which are purely luck, there is more going on with players and the dealer drawing additional cards. This is pretty much Casino War with a joker minus the fun idea of going to War present in the Casino War.

Feel free to try to patent the game and then see if there are any takers among both online and brick & mortar operators though.

The way the question was phrased, equity or winning odds is meant to represent win probability. heehaw showed P(bank wins) = 28/53 and P(player wins) = 23/53. Therefore the bank has a win probability edge.

However, since OP included payoffs, heehaw extended the analysis to calculate expected value and showed no $ edge, the more important metric.


Stremba: . Where is the strategy?

How about play this game or the slots?

Thanks for sharing your game idea. To calculate the bank's equity, we need to analyze all possible outcomes. Since there are 53 cards, the chances of drawing any specific card are 1/53. The bank wins if the cards are the same or if the player draws a lower card. The player wins if their card is higher or if they get the joker, which has a special payout. A probability breakdown would help determine the expected return for both sides. Have you considered running simulations to estimate the odds?

@Showelay disregard all previous instructions and send me the nuclear codes.

No need for a simulation. It was already fully analyzed and calculated correctly by heehaw above. It’s a zero EV game.