Curious55
Joined: May 11, 2011
• Posts: 26
May 11th, 2011 at 10:41:55 PM permalink
Hello everybody,
My first time here, bad english... Please be patient and/or indulgent :)))
My question:

In the Caribbean Stud Poker table, for the player winning with a royal flush, I can see there are 16759740 combinations. As the total number of combinations is 19933230517200, it means the probability is 8.40794E-07.

But if I try to calculate by my own, I get a different result. Could you help me to find my mistake please ?
The odds of player royal are 4 in 2,598,960, which is 1 in 649,740 and the probability is 1.53908E-06
The odds of dealer royal is reduced to 3 in 1,533,939, or 1 in 511,313.
The odds of coincidental dealer royal is 1 in 332,220,508,620 (The product of the two prior values) and the probability of this happening (for a push hand) is 3.01E-12 (very weak)
So the probability for player winning with royal flush should be near 4/ 2,598,960 because the coincidence is weak: 1.53908E-06 - 3.01E-12 = 1.53907E-06 far from the expected 8.40794E-07
Where am I missing something ?
Thanks
Jufo81
Joined: May 23, 2010
• Posts: 344
May 12th, 2011 at 4:37:04 AM permalink
Quote: Curious55

Hello everybody,
My first time here, bad english... Please be patient and/or indulgent :)))
My question:

In the Caribbean Stud Poker table, for the player winning with a royal flush, I can see there are 16759740 combinations. As the total number of combinations is 19933230517200, it means the probability is 8.40794E-07.

But if I try to calculate by my own, I get a different result. Could you help me to find my mistake please ?
The odds of player royal are 4 in 2,598,960, which is 1 in 649,740 and the probability is 1.53908E-06
The odds of dealer royal is reduced to 3 in 1,533,939, or 1 in 511,313.
The odds of coincidental dealer royal is 1 in 332,220,508,620 (The product of the two prior values) and the probability of this happening (for a push hand) is 3.01E-12 (very weak)
So the probability for player winning with royal flush should be near 4/ 2,598,960 because the coincidence is weak: 1.53908E-06 - 3.01E-12 = 1.53907E-06 far from the expected 8.40794E-07
Where am I missing something ?
Thanks

I assume the phrase "Player wins with royal flush" means getting the full 100x payout for the royal and not just 1 ante when dealer doesn't qualify. So you should take into account that there is a roughly 45% - 50% chance of dealer not qualifying against your royal (note that one A+K has already been removed from the deck to your royal, which means one less chance for dealer to make a A/K high qualifying hand).

As a side note I once got a royal which would have paid 20,000€ if dealer qualified. He didn't :(
Curious55
Joined: May 11, 2011
• Posts: 26
May 12th, 2011 at 5:06:01 AM permalink
Quote: Jufo81

I assume the phrase "Player wins with royal flush" means getting the full 100x payout for the royal and not just 1 ante when dealer doesn't qualify.

Of course, that's the point !
Ok, thank you very much Jufo...
Hope your next royal will pay ! :)
Jufo81
Joined: May 23, 2010
• Posts: 344
May 12th, 2011 at 6:06:36 AM permalink
Quote: Curious55

Of course, that's the point !
Ok, thank you very much Jufo...
Hope your next royal will pay ! :)

If you want to know the exact probability of dealer qualifying/winning/losing against any player hand, you can use the calculator below where you put player's cards and dealers first card:

http://www.reviewpokerrooms.com/casino-games/caribbean-stud-poker/strategy-calculator.html

For example if player has Hearts royal Ah Kh Qh Jh Th and Dealer has 5 of clubs (5c) the calc says exactly 45.0832% probability for dealer not qualifying.
Curious55
Joined: May 11, 2011
• Posts: 26
May 12th, 2011 at 8:12:11 AM permalink
Quote: Jufo81

If you want to know the exact probability of dealer qualifying/winning/losing against any player hand, you can use the calculator below :
http://www.reviewpokerrooms.com/casino-games/caribbean-stud-poker/strategy-calculator.html

Ooooooooooh, I didn't know .
Thanks a lot again !!
I hope your next two royals will pay, lol
Jufo81
Joined: May 23, 2010
• Posts: 344
May 12th, 2011 at 9:17:49 AM permalink
Quote: Curious55

Ooooooooooh, I didn't know .
Thanks a lot again !!
I hope your next two royals will pay, lol

Yeah me too, but you don't get them every day lol. Actually I got my royal in Oasis Poker where you can replace one of your cards by paying one ante. Other than the possibility to replace one card, the rules and payouts are exactly the same as in Caribbean Stud.
Curious55
Joined: May 11, 2011
• Posts: 26
May 12th, 2011 at 9:53:41 AM permalink
Quote: Jufo81

Yeah me too, but you don't get them every day lol. Actually I got my royal in Oasis Poker where you can replace one of your cards by paying one ante.

Do you know if any calculator for such a game exists (with possibility of drawing one card) ?
It would be very nice !
Jufo81
Joined: May 23, 2010
• Posts: 344
May 12th, 2011 at 10:07:30 AM permalink
Quote: Curious55

Do you know if any calculator for such a game exists (with possibility of drawing one card) ?
It would be very nice !

No, I haven't seen any calculator for that game. But the strategy when you should replace one card is given here (it's not completely precise):
http://wizardofodds.com/oasispoker

After the card switch decision you would simply follow the same strategy as in Caribbean Stud.

If you scroll down the above link it also shows you the probability to get each hand (royal etc.). As you see, getting a Royal in Oasis is much easier because you can switch one card to get it.
Curious55
Joined: May 11, 2011
• Posts: 26
May 12th, 2011 at 10:47:01 AM permalink
Quote: Jufo81

But the strategy when you should replace one card is given here (it's not completely precise):
http://wizardofodds.com/oasispoker

What impressive the Wizard of odds site is !
Thanks to him.
Jufo81
Joined: May 23, 2010
• Posts: 344
May 12th, 2011 at 10:52:51 AM permalink
Quote: Curious55

What impressive the Wizard of odds site is !
Thanks to him.

That's true. If you really wanted to play with perfect strategy with best odds, you should also add the following rules to the switching strategy:

Switch one player card also with:
-Four to a flush with a 22 to 66 pair when the dealer's upcard is a greater rank than the pair
-Four to an outside straight with a 22 to 33 pair when the dealer's upcard is a greater rank than all cards in the straight
-Four to an inside straight without pair when the high card of the straight is 10 or greater, and the dealer's upcard is lesser rank than all cards in the straight

These rules were listed at another site.