Someone offers you a wager. He’ll shuffle an ordinary deck and deal you 13 cards. If none of your cards ranks above 9, he’ll give you a thousand dollars. Otherwise you must give him one dollar.

Should you accept?

Depends, Are aces high or low ?

No, it depends if he deals face down or face up and gets to choose which ones he deals that way.

If HE is shuffling the deck, forget it!

Well, if he's offering a thousand dollars, then that's suspicious in itself. However, for the sake of 1 dollar, I'd probably accept. Seeing whether his false shuffles under pressure would fool me, would be worth the dollar itself. Especially as it could spark off a productive conversation about magic. If he knows how to do a false shuffle, he probably knows other stuff. Plus it will give me an opportunity to show him a trick and those opportunities are rarer than I would like.

Tim

If he shuffles it sounds like an argument is about to start...

John

I think you nailed it. Remember this is a bar bet.

There will be always be at least one card over a nine in 13 dealt.

I assume that you mean that is a good bet because we all know that there are a lot of combinations where 13 cards can be combined and none over a nine.

Accept only if you want to lose a dollar!

I was going to be a wise guy and make the following post- "I just did it 1,000 times. 327 times I lost on the first card. 922 times I lost by the 5th card. In all cases I lost by the 9th card". But I took out a deck of cards and tried it a few times. In each case I did an (imperfect) faro shuffle, then cut the cards. All very fairly. On the 8th try I dealt 9 cards off the top and NONE of them were higher than a 9! However, I do think that is an amazing achievement! And I do think it would be VERY hard to duplicate. I would have NEVER believed it if I didn't do it myself! It's a bet that I would feel pretty confident in making if I was risking the $1,000. But you had better have the $1,000 ready just in case!

From the phrasing of the question it seems that there must be a catch. As Acesover stated, it is a bar bet.

The odds.
(A series where you choose from the number of nine and under (ace low) cards remaining.)

36/52 * 35/51 * 34/50 ... all the way down to: 24/40

Multiply all that out and you get about 1 out of 275 against. take the bet.

For ace high, the series starts at 32/52 and ends up totalling 1 out of 1828 against. Don't take the bet.