Casino Royale - Final Hand Odds

4 players go all in preflop. (Holdem)

Final results :

p1 - Flush

p2 - Full House

p3 - Full House

p4 - Straight Flush

According to this page on Wikipedia,
Frequency of 7 card hands, the probabilty for each hand is :

Straight flush : 0.0311%
Full house : 2.60%
Flush : 3.03%

So 0.000311 * 0.026 * 0.026 * 0.03 = 0.00000000630708

And 1.0 / 0.00000000630708 = 158,551,976

So 1 in 158,551,976 times this could happen.

.. Assuming 4 players going all in at least 158,551,976 times

Are the numbers right ?

Mike

Think so.. very interesting...
well movies hunh? you can't expect more than this. hahaha very good movie by the way, but I prefer Rounders. I wonder if the movie made Matt Damon start playing poker.

LOL thats pretty sick. Even if you are wrong, the numbers are pretty much realistic. Very unlikely all those will happen unless its on FT or PS lmao.

One of the best Bond movies ever, but one of the worst poker movies ever IMO.

Personally I found the string bets, incessant minraising and the pissing and moaning when he went broke with a hand nobody in their right mind ever folds evar to be more tilting though.

For a poker movie you're right, the final hand is hideous. I let it slide in a Bond movie though, since in the grand scheme of space lasers and whatnot it's really not that out there

oh JAMES!!!

I'm not entirely sure that the last hand is the most crazy thing in that movie. But nice math on the hands.

Lets not forget when he takes the punishment of his balls getting the shit beat out of them and is still able to use them. Now this is remarkable.

That math is not correct. The odds of those hands occurring change given the what cards are on the board.

So while the actual number is far more likely than what you calculated, it's still pretty low.

^^^What thirteenlisk said.

Having one hand makes the other hands more likely to hit.

If there are three suited cards on the board that can complete a straight flush then there are automatically three cards on the board that can complete a flush.
And if the board pairs to give one person a full house, the board is already paired so that someone else can have a full house.

I also thought it was idiotic they made him all upset he lost with AK on a board of AKKJJ ... you'd have to be a complete retard to fold there... especially in a rebuy

Depends on what you're calculating.

I think the numbers are correct if you were asking what the odds were for those hands occuring before any cards were dealt.

After seeing the flop, that's a different calculation, as is the calculation from any one players hand versus the odds of other hands occuring.

Mike

^^^ This +1.

BTW - I don't think the final hand was all-in preflop. If I recall, Bond checked the turn where he made the straight flush which was checked all around, and also checked the river before all the short stacks pushed all-in. He then re-raised the villian to put him all-in.

Standard trap with a great turn card. The whole thing sucked as far as portraying poker goes... and it was supposed to be Baccarat as in the original book, but the producers thought NLHE would be more relatable to the American-centric audience.

You're right about the sequence of events :


(I don't remember the "lol" in the movie though )

Mike

OMG I'd forgotten about the most epic tilting part of the whole thing - that showdown is wrong in soooooooooooooooo many ways.

For starters, showdown doesn't just go clockwise around the table. Bond and Le Chiffre are supposed to show their hands first because they're the two biggest stacks. As the person who made the last aggressive action, Bond is actually supposed to show first. Bond shows his straight flush and everybody else mucks in disgust. I know that for dramatic effect they had to do it the other way around but... well, bleh.

Plus also dealers don't put the player's hole cards in line with the board cards. They just push up the board cards used to make the winning hand. Otherwise there could maybe be some time wasting conjecture about exactly what was in the hand and what was on the board. You keep them separate.

But the absolute worst bit is this: the math is wrong!

When we pick up the hand everybody checks the turn and Mathis points out there's 24 million on the pot. On the river, the first all in is for 6 million, the second is for 5, Bond gets all in for 40.5 million and Le Chiffre calls him for a maximum of another 40.5 million*. Before the showdown, Mathis points out that there's now 150 million in the pot. But:

24 + 6 + 5 + 40.5 + 40.5 = 116

Either Mathis was wrong about the 24 million or the crew simply couldn't add and the pot's short by at least 34 million - maybe more, depending on how much Le Chiffre actually had (the game is over after the hand, so it must have been 40.5 million or less he had behind). And that's not something you need for dramatic effect, you just get the numbers right before the hand.

*sigh*

FYP

... And Bond should have lost ... for splashing the pot

Ah - accents are a killer, huh. If Le Chiffre has 39.5 million then yep, that makes sense.

Still issues though, because a few scenes later the Swiss banker has $120 million to transfer to him. Smaller error, but still an error.

115 is closer than 150 though (and "115" is what he says)

Yeah - now that you mention it he's definitely saying 115. My Australian ears had always heard it as 150. Go figure, and the other mistakes still stand.

Of course if it's $115 million that means only three people rebought too - weak! Oh, one last one. WTF is with tipping the dealer at the end with a tournament chip?!? :P

I think PokerStars deals that many hands every day, or is it McDonalds serves that many hamburgers every day.

I get so cornfused!
Senility is a bitch..........

Here are just a few of the MANY goofs found in the movie as pointed out on IMDB.com (the 2nd greatest website IMO)

Early in the movie when Le Chiffre is playing poker with another gentleman, he says, "All in. I have two pair and you have a 17.4% chance of making your straight," the 17.4% is correct from his opponents perspective since he knows his own 2 cards plus 4 community cards leaving 46 unknown cards and 8 cards which would give him a straight (8/46=17.4), but from Le Chiffre's point of view, he knows 2 more cards and therefore the probability of a getting a straight would be 8/44=18.2%. It does not matter that he doesn't truly know his opponents cards, he is merely stating the probability assuming he has an outside straight draw.

At the end of the major poker tournament Bond passes a chip from the table to the dealer as a tip. While this is done in cash games, in a tournament the chips have no actual value. They chips are just markers to play with as the money is pooled together and paid out to those that cash, in this case in the special account that is unlocked by the password. If the chip had any value Bond would be tipping the dealer with the casino's money as all his winnings were in that account


When Bond enters the encrypter password before the tournament, he enters 836547. Later in the film, the password is revealed to be VESPER, which does not match. (It should be 837737.)

The Boeing 747 does not have afterburners, as depicted during the airport chase scene, when it used them to avoid hitting the Miami police vehicles.

Just a few of the many many many goofs found in the movie.

Not quite. The probabilities would be correct if all players were drawing from their own decks of cards. But since all players share a deck, what P1 one has in his hand affects what P2 can have in his hand. So, there are dependencies that affect the probabilities.

For a concrete example, consider a deck containing only four cards: A, K, 3, and 2. Each player gets dealt one card and only one card is in the community cards. Thus, each player's hand consists of only two cards. The probability of forming a hand with at least one face card is 5/6 = 83.3%.

For two players, when trying to compute the probability that both players have a hand with at least one face card, if you just multiply 5/6 by 5/6, you get a probability of 69.4%.

However, this "game" only contains 24 different possible hand combinations. If you enumerate them all and see which contain hands in which both players have at least one face card, you will see that 16/24 = 66.7% do.

So, while the multiplication method yields a 69.4% probability, the actual probability is 66.7%. That's a close approximation, but not exact.

As I'm sure we all know from seeing so many different probabilities published for the same events, my numbers could be wrong. If so, please let me know!

-Dave

My brain just exploded

This has gotta be the coolest freakin' post...EVER!! Hi5 on the math!
Oh, and pointing out those flaws in the film

Dave,

If the deck only has 4 cards, and 4 players each get dealt one card, how do you end up with one community card ?

Or do you mean 4 different cards ? .... (16 cards in the deck) ?

Mike

No, it was 4 total cards but only 2 players. Each player gets 1 card and then 1 community card. So 1 card doesn't get dealt. Sorry about that. Yeah I know, a pretty dull game, but (hopefully) illustrative.

-Dave