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Poker related conundrums  0   
A few poker/gambling related head scratchers to get you thinking. Feel free to post your own if you can think of any.

1. You've just called to see the turn and there's two other players still left in the hand. The flop is 8c 10c Ah and the turn is Qc. You've got Jc Ad. The first player bets and the second flats. Before you can react the dealer reveals the river card. It's the 9c giving you the nuts. But the house rules that the card must be shuffled back into the deck and a new river card will be dealt.

How does this affect your decision? Is the 9c more, less or just as likely to be dealt on the river a second time?


2. A terrible magician is trying to predict a pack of cards. He declares "the first card will be the Jack of Spades". He turns over the 2h. He tries again with the second card. He predicts it will be 5d but the card he turns over is the 7d. He's slightly disheartened but he's a trooper. He predicts the third card.

Considering what we now know, are the chances of him getting the third card right any better?


3. A man walks into a casino and walks up to the roulette table. He notices an old man staring at the machine counting out loud in seemingly random numbers. He asks the nearby croupier "is that man ok". "Oh yes he's fine" comes the reply. "That's stingy Pete. He's here everyday." So the man not convinced, goes up to the old man and asks him if he's alright. "oh yes" he replies. So the young man asks "are you going to play?". The older man says "Oh no. I'm still working on my technique. You see I've watched this machine every day for five years and I reckon I can predict with about 90% accuracy, which number it will land on. And when I get to 100 I'll take this place to the cleaners." The young man is absolutely stunned and asks the old miser for a demonstration. "Well" he says "will you get me a beer if I can tell you the next three numbers." The price of a beer seemed hardly anything to this marvellous feat so he agrees and to his astonishment the tightfisted codger gets them all bang on.

So the young man goes to the bar and orders drinks for everyone convinced he can trick the old man into giving away his secrets. But how has he been fooled?


Edited by awood88 (14 November 2014 @ 03:56 GMT)

Not a head scratcher but i have been in almost the exact same position as the first scenario.

I had AQ on a Q 5 5 K board against the loosest player imaginable. I bet $25 on the turn, he check-raises me to $50, I shove, and before he calls the dealer burns and turns the river to reveal another Q. I pull back my stack, start counting, before the other guy starts saying that he didn't call before the river came (which he didn't). The pit boss came over, we recalled the hand, and the pit boss decided that it was a clear situation where it reverted to house rules, where the all in's were still all in and the river was shuffled back into the deck.

I was spewing, because in my haste I have revealed my hand, and he revealed his (called a 3-bet from early position with 8 5) after he realised the Q would be shuffled back into the deck and a new river was dealt. I was dirty on the house, but more dirty on him, because his decision to call came after everything else was revealed (he was going to call anyway, but I still wasn't happy with him). I almost go mental, but then the river is the other Q! Drew to 5% (unbeknowingly the first time) and came out ahead. I swore then and there I would never bemoan the river (a promise I have most certianly not kept if you have read any of my previous posts)

1) Just as likely
2) yes (less cards in the deck), unless he's so terrible, that he forgets to exclude the cards that were already drawn...
3) There's no penalty for getting it wrong, making it slightly +EV for the old man, and -EV for you (it's a freeroll). And if he can sell you his secret, it will be huge +EV... I.e. it's you that will be taken to the cleaners after all these years of trying to get these 3 numbers right and failing.

Edited by marqis (14 November 2014 @ 09:13 GMT)

The answer to no.1 is not just as likely. Although logically you would think that because it's the same process of selecting one random card from the cards available.

But before the 9c was shown, you could calculate the chance as 1 in (52 - 4(cards on the board) and -2 (your hole cards) and possibly -4(assuming neither opponent had that card) so 1 in 42.

However, now we know the 9c isn't in the muck or the burn cards. So assuming there were three others dealt in the hand and one card was burned before the flop, one before the turn and one before the false river, that's an extra 9 cards discounted meaning you can now consider the chance of the 9c being the river as 1 in 33, which is better odds than before.

Ok, so the actual cards in the pack hasn't changed but if you were talking in literal terms the initial chance of the 9c being the next card in the deck was 100% any time after the first shuffle. So you can only go on cards exposed for theoretical odds.

I knew there was a catch (considering who posted it)... It's like a "Montey Hall"...

Nice one!

Big Smile You got the second one right (at least from a purely mathematical perspective). Although you could argue that if he's a magician, even a really bad one, he's probably not just picking cards at random. It's impossible to say from the information I gave but if we propose that there was some sort of trick which went wrong then the chance of getting the first card is probably better than 1 in 52. But if he got the first card wrong then he probably fckd up the trick making it much harder to guess the second and third.

I'm just being pedantic. Without any more information, the answer is of course that the chances are very slightly better at 1 in 50.

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