Million $ Bad Beat Promotion

The Rivers Casino in Pittsburgh will soon be initiating a Million $ Bad Beat Promotion wherein you will have to lose with 8-9 suited to A-K suited on a FLOP of 10-J-Q of the same suit! (Before you go nuts, the Casino will be putting up the money and it will NOT be taken out of the rake.)
(Note, I believe this has to occur on the FLOP but I'm not positive of that.)

What are the odds of this happening on the FLOP?

And what are the odds of this happening with all 5 cards on the board by the river?

Thanks for your help.

The probability of a suited Q-J-10 on the flop is 4 / combin(52,3) = 1 / 5525
The probability of the dealer having A-K of the same suit is 1 / combin(49,2) = 1 / 1176
The probability of you having 8-9 of the same suit as well is 1 / combin(47,2) = 1 / 1081
The total probability = 1 / 7,023,689,400

If Q-J-10 can be anywhere on the board:
The probability of the dealer having suited A-K is 4 / combin(52,2) = 1 / 663
The probability of you having 9-8 of the same suit is 1 / combin(50,2) = 1 / 1225
There are combin(48,5) different sets of five-card boards from the remaining 48 cards; combin(45,2) include Q-J-10 of the same suit, so the probability is 5 / 8648
The total probability = 1 / 1,404,737,800
OOPS - I just realized; this is true only in heads-up (I got this confused with the High Card Flush thread, where it's player against dealer)
The true probabilities depend on how many other players are in the game, as any of them can have the suited AK.

Let me see if I am working this out correctly:
For the "must be in the flop" version:
If there are N other players in the game besides you, there are combin(47,2) different hands that the player on your left can have; for each one, there are combin(45,2) that the next player can have; and so on, so the total number of sets of opponents' hole cards is combin(47,2) x combin(45,2) x ... x combin(49-2N,2).
Of these, if one player has AK of the board suit, the next player has one of combin(45,2) pairs; for each pair, the player after that has combin(43,2) pairs, and so on.
Since any of the N players can have the AK, the probability that somebody has it is N / combin(47,2) = N / 1081, and the total probability = 1 / 663 x 1 / 1225 x N / 1081 = N / 7,023,689,400.
Assuming this holds true for the "Q-J-10 anywhere on the board" version as well, that probability would be N / 1,404,737,800.

Personally I wouldn't do this I would be worried someone might find a way to cheat. I have no idea how easy or hard it would be especially with authentic shufflers and surveillance but it would still make me nervous.

I'm wondering if something like this really attracts people ? I assume anyone that has an interest in poker knows that they are just playing a lottery.

Quote: AxelWolf

Personally I wouldn't do this I would be worried someone might find a way to cheat. I have no idea how easy or hard it would be especially with authentic shufflers and surveillance but it would still make me nervous.

I'm wondering if something like this really attracts people ? I assume anyone that has an interest in poker knows that they are just playing a lottery.

I certainly won't be going just for this.

Thanks for your analysis. I'm assuming this will happen about once every 75 years or so!

Quote: PGHJOE001

Thanks for your analysis. I'm assuming this will happen about once every 75 years or so!

They should call this the Halley's Comet Bad Beat promotion.

I've seen a straight flush lose to a straight flush in the manner described once in my life. But it was the river card that made both hands.

^^^^^^^^ At least not that I can recall (soooo many hands) but I don't think I've seen a straight flush lose to another straight flush? Eh, I probably have and don't remember =P.

Quote: AxelWolf

Personally I wouldn't do this I would be worried someone might find a way to cheat. I have no idea how easy or hard it would be especially with authentic shufflers and surveillance but it would still make me nervous.

I'm wondering if something like this really attracts people ? I assume anyone that has an interest in poker knows that they are just playing a lottery.

I'd imagine surveillance will be HOUNDING the dealers if a hand like this hit. They'd go back and watch the previous X hands and ensure the dealer didn't set anything/cheat/etc.

Any poker player, even the bad ones, must know how improbable this is. Even at our WoV Spring Fling poker game, PokerGrinder (I think) said he's never had a royal flush... and his name is POKERGRINDER lol... Where as for the countless hands I played I've had 3 or 4 (can't remember).

Funny enough we did have a board with Ac-Kc-Jc-10c and I held the 9c in my hand... but MaxPen couldn't bluff me from it (though I was rooting he had the Qc) =).

Also funny enough, Axel is bad at poker.

Quote: Romes

^^^^^^^^ At least not that I can recall (soooo many hands) but I don't think I've seen a straight flush lose to another straight flush? Eh, I probably have and don't remember =P.

I'd imagine surveillance will be HOUNDING the dealers if a hand like this hit. They'd go back and watch the previous X hands and ensure the dealer didn't set anything/cheat/etc.

Any poker player, even the bad ones, must know how improbable this is. Even at our WoV Spring Fling poker game, PokerGrinder (I think) said he's never had a royal flush... and his name is POKERGRINDER lol... Where as for the countless hands I played I've had 3 or 4 (can't remember).

Funny enough we did have a board with Ac-Kc-Jc-10c and I held the 9c in my hand... but MaxPen couldn't bluff me from it (though I was rooting he had the Qc) =).

Also funny enough, Axel is bad at poker.

Now you see there Romes, you are rubbing salt into the wound of another. Usually ( not always ) not the best of approaches ;-) You already posted that someone had guys that would kill, your words. I suggest you just send the money back, cheaper than extra security details .....;-)

I've seen SF over SF once, in 0-8 at the bike. I got a share of a jackpot that was $39k or so. The big one wasn't a royal.

The guy with the losing SF, and winner of the big end of the jackpot for about $20k, went broke on the hand. They payouts take a long time so, while waiting for his 20 Gs, he went to the ATM to get more money to play with.

Quote: Greasyjohn

They should call this the Halley's Comet Bad Beat promotion.

LOL.