10-31-2023 , 09:18 AM
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?
10-31-2023 , 12:09 PM
Quote:
If the player draws the joker (the only joker in the deck), the player wins a 5 times their bet.
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.
10-31-2023 , 12:33 PM
I think there is an egde for the bank.. yes when the player draws the joker the net win is 4.
10-31-2023 , 01:15 PM
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.
11-01-2023 , 02:27 PM
Quote:
Originally Posted by u poker crusher
It's a simple yet exciting game...
I don't see a casino game that requires no player input to be "exciting".
07-08-2024 , 07:38 AM
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.
07-11-2024 , 08:17 AM
Quote:
Originally Posted by Hevesttix
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!
07-12-2024 , 10:57 AM
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?

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