Three card poker odds

Three Card Poker question. I understand that the odds of a "tie hand" as per the rules of the game (dealer qualifies with queen or better) are about 1 in 1517. In other words, the dealer has K/7/4 and player has K/7/4 the hand is a tie. But these calculations don't account for a scenario where the dealer and player both hold a hand like 10/6/2 since it's a non-qualifying hand and therefore not considered a 'tie" according to game play. I would like to know what the odds are of a tie regardless of the dealer qualifying or not. In other words, player holds a hand like 8/6/2 and dealer holds the same. I'm assuming it's much lower than 1517 to 1. Thanks in advance.

Quote: SoCalCasinoGuy

Three Card Poker question. I understand that the odds of a "tie hand" as per the rules of the game (dealer qualifies with queen or better) are about 1 in 1517. In other words, the dealer has K/7/4 and player has K/7/4 the hand is a tie. But these calculations don't account for a scenario where the dealer and player both hold a hand like 10/6/2 since it's a non-qualifying hand and therefore not considered a 'tie" according to game play. I would like to know what the odds are of a tie regardless of the dealer qualifying or not. In other words, player holds a hand like 8/6/2 and dealer holds the same. I'm assuming it's much lower than 1517 to 1. Thanks in advance.

From https://wizardofodds.com/games/three-card-poker/ Player Wins Ties section.

Quote:

For academic purposes only, if the player always raises then the probability of a tie is 450528/407170400 = 1 in 903.76.

My understanding of that is that it still only considers a tie when the dealer has a qualifying hand and the outcome is an actual "tie". Let's assume for mathematical reasons that the dealer doesn't need to qualify (it's the dealer's 3 cards against the player's 3 cards). How would that change the math? Your math doesn't consider the 132,652,800 out of 407,170,400 hands that are folded which now potentially can be "ties" if the dealer doesn't need to make a qualifying hand.