Three Card Poker

But the dealer may not qualify, in which case player wins, regardless of his cards, this should give him an extra advantage.
To confirm, one hand, player 3 cards, dealer 3 cards, dealer must qualify. What are players odds of winning?

(Part of this question needs the answer of odds dealer will even qualify. I'd like to know that too)

Im ok at math. Captain of my high school math team. ( I got to wear the coveted number pi). Perfect 800 on math achievement test. 4th place in NYC math competition. Sooooo.... if the 70% figure is correct.... the dealer wont qualify 30% of the time. So 30% of the time a hand will be j high or worse. So 9% of the time you will both have j high or worse (an approximation because if you know 3 cards are out and are j high or worse then the remaining 49 cards a re 'rich' in higher cards). And half of the time you both don't 'qualify' you would have had a worse hand than the dealer, but will now win because the dealer is forfeiting. So if 70% is correct, then you will win approximately 54.5% of the time.

Give the man a medal, he CAN do math AND read. Thanks.

So, first off, can anyone else confirm this? (Just like to double and triple check things)
And if it is 54.5%, does that mean the player has a 4.5% edge over the dealer, to WIN?

Quote: QikGT

Give the man a medal, he CAN do math AND read. Thanks.

So, first off, can anyone else confirm this? (Just like to double and triple check things)
And if it is 54.5%, does that mean the player has a 4.5% edge over the dealer, to WIN?

Qik- as I pointed out earlier, the members of this site are happy to answer questions that are clear, and also, as sometimes it might require a bit of work on their part, might want to know WHY you are asking. The phrase 'edge over the dealer' is ambiguous. Let me give you an example. If I went to a roulette table and put $10 on numbers 1 - 33, I would be risking $330, and more often than not I'd win. But I never would have had an 'edge over the dealer' in my mind. I knew I'd be more likely to win a small amount than lose the big amount, but I never had an 'edge'. Another example would be video poker. You will never come close to winning half of your bets, but because some wins are greater than even money, even winning 25% of the time you 'might' have an edge over the dealer, depending on paytable and game.

Quote: QikGT

Give the man a medal, he CAN do math AND read. Thanks.

So, first off, can anyone else confirm this? (Just like to double and triple check things)
And if it is 54.5%, does that mean the player has a 4.5% edge over the dealer, to WIN?

I'm still really confused by what you want to know. Yes, you'll win 54.5% of the time. But some of the wins will be 2 units (when the dealer qualifies), and some of the wins will be 1 unit (when the dealer does not qualify). All of the losses will be 2 units. This is NOT a winning strategy for the player.

The ONLY time you can get away with playing blind and be correct is if you know one of the dealers 3 cards and it is a 2 through jack.

Pop quiz for the APs or lateral thinkers:

When would it be realistic to play this game blind and still have a strong edge over the house (without any knowledge of the dealer's cards)?

Hint: the answer is contained within this thread.

Let me help clarify. He's asking a question that the answer has no practical application whatsoever.

That's why I didn't bother trying to figure it out.

Quote: FinsRule

Let me help clarify. He's asking a question that the answer has no practical application whatsoever.

Au contraire. Let me assure you that I have little interest in problems like this without practical application.

If the cards are not shuffled correctly after each hand. Got it.