My daughter Amanda is a quick study in the game of poker

Two days ago I taught my two older daughters how to play seven card stud. That night we played a few hands before they went to bed. Last night we played a few more hands.

Tonight I got home from work and one of my daughters, Amanda, was particularly eager to play poker. So eager that she had already dealt out the first three cards to each of us, two face down and one face up. My up card was an eight; her up card was a king. We played through the hand with her betting aggressively on every turn. This is not surprising, because she tends to bet no matter what she has. I called all the way to the final card, even though I only had a pair of tens.

At the end of the hand, she turned over her two down cards. Pocket kings to match the king she got dealt as a third card. What are the odds of getting dealt a hand as good as that? About 1 in 2,500. Perhaps she just got lucky. More likely she had a little spare time on her hands this afternoon and did a little deck-stacking in advance of my arrival. That’s my girl!

Tomorrow night she promised to teach me how to deal off the bottom of the deck.


RandyfromCanada

maybe she read the blog about "smart" kid and the teeth money and she thinks now you will believe anything , she give back the money ?

zbicyclist

Actually, learning how to stack the deck and how card tricks work can be quite educational. I seem to remember Martin Gardner threw in the occasional problem based on a deck of cards.

Just be SURE she realizes that this is an amusement, not a skill to use with her friends.

Chewxy

Quick! Give her a game theory book!

(which unfortunately, to this day, I still suck at playing poker. I wonder if Von Neumann and Nash had a problem. Nash probably had someone telling him what other people's cards were - unfair advantage :()

phiphika1453

Not to be a nit but your 1 in 2500 is a little off considering a truly random deck.

Odds of any three of a kind on the first three cards is 1 in 424.

Odds of getting exactly (KK)K in the first three cards is about 1 in 5858.

Lol, obviously it sounds like the deck was not at all random.

phiphika1453

cant edit, but I was wrong on the (KK)K, it is 1 in 5524.

Equation: (4/52)*(3/51)*(2/50)

Taed

My son once tried to do something like that to me, but I knew what he was up to, so I distracted him and swapped his deal with mine. He was very disappointed when he saw his cards and said, "Hey, you're cheating!" I feigned ignorance.

frankenduf

you should be merciless and not let her win- else she might develop the gambling bug

middlepat

I know I'm getting nit picky here, but assuming a randomly shuffled deck, and assuming proper dealing sequence (player, dealer alternating) then the true odds are:

(48/52)*(4/51)*(47/50)*(3/49)*(46/48)*(2/47)
or
1 in 5885.

prosa

Ugh, poker. Not that I have anything against the game on its own merits. What I cannot stand is the way ESPN has renamed itself the Eternally Showing Poker Network.

NeverLimp

She should have dealt you rolled-up queens.

furiousball

NeverLimp is right, sticking you with pocket queens might have prompted an all-in and cleaned you out.

castle

I am guilty of deck-stcking at the Game of Candyland...I think I was 5, and my dad never lets me forget it.

brit

Sorry, middlepat, I think phiphika1453 is right. Your equation is off just a little bit because it assumes the dealer doesn't get ANY kings. In fact, the dealer is allowed to get one of the kings.

Therefore, the equation (writing it the complicated way), is:
(49/52)*(4/51)*(48/50)*(3/49)*(47/48)*(2/47) = 1/5525.

More simply, it can be written as (4/52)*(3/51)*(2/50), which is also 1/5525.

j.a.s.o.n

brit is correct. Another way to compute the probability of little Amanda receiving three kings is (4 choose 3) / (52 choose 3). There are (52 choose 3) possible starting hands and there are (4 choose 3) ways to receive exactly three kings. Google tells me that (4 choose 3) = 4 and it tells me that (52 choose 3) = 22100. Therefore the probability is 4/22100 = 1/5525.

However, I do have a minor point. Several posters have mixed up the definition of odds and probability. Odds are are a ratio of probabilities; namely if an event has probability p of occurring then the odds in favor of the event occurring are p / (1 - p) (so, for example, the probability of a coin flip being heads are 1/2 while the odds are (1/2) / (1/2) = 1, notated 1:1). The probability of little Amanda being dealt three Kings is 1/5525 whereas the odds of little Amanda being dealt three Kings is (1/5525) / (1 - 1/5525) = 1/5524; this is more commonly notated as 1:5524.

Lastly, the logit of little Amanda receiving three Kings is the logarithm of the odds, namely log(1/5524). logit was used famously by Nobel laureate Daniel McFadden in development of a certain economic model.

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Steven D. Levitt

We are all doing the same math. What I meant by a hand as good as three kings was either three aces or three kings, so I am taking your 1 in 5500 and dividing it by two (and then doing a little rounding). I should have made my calculation clearer.

Chewxy

Whoa.. did you just reply to the comments?

frankenduf

although then you would have to subtract the odds that you got dealt 3 aces- cuz ironically 3 kings is then the worst hand to get dealt!?

sgspecial

Those probabilities are only correct if you play 7-card stud high. If you play razz, you start with rolled up trips much more often ;)

RandyfromCanada

maybe she read the blog about "smart" kid and the teeth money and she thinks now you will believe anything , she give back the money ?

zbicyclist

Actually, learning how to stack the deck and how card tricks work can be quite educational. I seem to remember Martin Gardner threw in the occasional problem based on a deck of cards.

Just be SURE she realizes that this is an amusement, not a skill to use with her friends.