Texas Hold'em Jackpot
The question is, what are the odds of hitting RF on Turn and on River, if the player has to use their original two cards.
It would be greatly appreciated if somebody could share how these two values can be calculated.
At Turn, it’s C(52,5)/C(4,3)=649740/4=162,435, so 1 in 162,435.
Quote: acesideAt River, it’s C(52,5)/C(5,3)=649740/10=64,974, so 1 in 64,974.
At Turn, it’s C(52,5)/C(4,3)=649740/4=162,435, so 1 in 162,435.
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I believe that this is incorrect
Quote: MCRA Texas Hold'em game is offering jackpot that is won on Royal Flush. RF on Flop pays 100%, on Turn 20%, and on River 10%. The "catch" is that the player has to use their own two cards to form a RF.
The question is, what are the odds of hitting RF on Turn and on River, if the player has to use their original two cards.
It would be greatly appreciated if somebody could share how these two values can be calculated.
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I get the following numbers for my probabilities of getting the bonuses:
Royal on the flop: 1 in 649,740
Royal on the turn: 1 in 216,580
Royal on the river: 1 in 108,290
Any of the above: 1 in 64,974
Royal on the flop: 1 in 649,740
Royal on the turn: 1 in 216,580
What is the probability of any of the above?
Quote: acesideInteresting! I haven’t talked to you for some time.
Royal on the flop: 1 in 649,740
Royal on the turn: 1 in 216,580
What is the probability of any of the above?
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I get 1 in 162,435 (as the probability of my getting a royal on the flop or the turn using both my hole cards.)
I see 1 in 162,435 in your post as the probability of getting a royal on the turn.
p = 4 * C(5,2) / C(52,2)
= 40 / 1326
= 20 / 663
Then once you start with 2 royal cards you need to hit the royal.
P(flop royal) = p / C(50,3)
= p / 19,600
= 1 / 649,740
P(turn royal) = p * P(flop 2 to royal) * P(hit turn)
= p * (C(3,2) * 47 / C(50,3)) * (1/47)
= p * C(3,2) / C(50,3)
= 3p / 19,600
= 1 / 216,580
P(river royal) = p * P(4 to royal on turn) * P(hit river)
= p * (C(3,2) * C(47,2) / C(50,4) ) * 1 / 46
= p * (3243 / 230,300) * (1/46)
= 1 / 108,290
So I agree with ChesterDog's numbers.
Must on River, it’s C(52,5)/C(4,2)=649740/6=108,290.
Must on Turn, it’s C(52,5)/C(3,2)=649740/3=216,580.
Quote: acesideIf you define “on” that way, I will update my calculation too.
Must on River, it’s C(52,5)/C(4,2)=649740/6=108,290.
Must on Turn, it’s C(52,5)/C(3,2)=649740/3=216,580.
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C(52,5) is not 649,740. It's 4x that amount. You may be thinking of the odds of getting a royal in 5 cards -- that's not C(52,5) (there are 4 ways to make a royal in 5 cards -- 1 for each suit)
Must on River, it’s (1/4)xC(52,5)/C(4,2)=649740/6=108,290.
Must on Turn, it’s (1/4)xC(52,5)/C(3,2)=649740/3=216,580.
At River, it’s (1/4)xC(52,5)/C(5,3)=649740/10=64,974.
At Turn, it’s (1/4)xC(52,5)/C(4,3)=649740/4=162,435.
