|
|
#1
06-14-2006, 01:14 AM
|
|||
|
|||
burning-half-the-deck problem
I'm trying to convince someone that I'm right (what else is new ...) I'm using the following example to explain how (some) probabilities work in an ordinary texas hold'em poker hand (or any other poker hand, or any other gambling game for that matter.)
Problem: * You take a standard 52 card poker deck. * Remove two Aces and set them on fire! Burn 'em! * Shuffle the deck * cut the deck in half, without looking at any of the cards, and set it on fire too. Burn it! The probability of the top card being an ace (in the undiscarded half) is 1-in-25. My friend thinks it's 2-in-25. How can I prove this to her?!?!?! It so irritating that I am unable to explain it to her further. 
|
|
#2
06-14-2006, 02:09 AM
|
|||
|
|||
|
Re: burning-half-the-deck problem
Instead of taking this convoluted problem, why not break it into a series of easy problems, and see where you guys first differ?
For instance, just ask about 4 aces in a shuffled deck. Then 4 aces in a half-deck. Then 2 aces in a half-deck. (I expect she'll disagree when you cut it in half.) -Sam
|
|
#3
06-14-2006, 11:33 AM
|
|||
|
|||
|
Re: burning-half-the-deck problem
After you burn two aces and shuffle the deck, there is clearly a 2/50 probability that the top card is an Ace. Taking off the bottom half of the deck and burning it (or doing anything else with any or all of the 49 cards not on the top of the deck) cannot affect this. 2/50 = 1/25.
|
|
#4
06-14-2006, 05:17 PM
|
|||
|
|||
|
Re: burning-half-the-deck problem
That's the exact difficulty i'm having! The confusion begins when I "split the deck" in half. She now thinks that there is a GREATER probability of finding an Ace in the non-burnt deck.
[ QUOTE ] Taking off the bottom half of the deck and burning it (or doing anything else with any or all of the 49 cards not on the top of the deck) cannot affect this. [/ QUOTE ] I tried showing her the deck face down in my hand, with two Aces removed. Then I ask her the odds of the top card being an Ace. 1/25 she replies. So far, so good. I remove the bottom card of the deck. What are the odds now?? 2/49, she replies. D'OH!!!!! This problem is also similar to the complaints that many bad amateur players have when a dealer burns the top card of the deck. They presume that it alters the probabilities of certain cards coming up on the flop, turn, or river. They are most distressed by the fact that the burn card may have indeed helped their hand had the dealer used it as one of the community cards instead of a burn card. Here's an example of what I'm trying to say: Say i'm holding Cowboys (KK) and out flops: Jd-Qc-As. Several players like their hand, but the cowboys are crying for help. The dealer burns a card, and the turn is a 4s. Unbeknownst to the players, the burn card was a King - this has suddently changed the outcome of the hand! A seasoned player would obviously not think this way. They know that all the cards in the deck are random, and all "unexposed" cards have the same likelyhood of being a King. So the likelyhood of the burn card being a K is the same as it appearing on the turn or river! Because we do not know the rank of the burn card, it could be anything. In fact, we can calculate the exact likelyhood that it is indeed a K - but we can never know for sure what it is. [ QUOTE ] Instead of taking this convoluted problem, why not break it into a series of easy problems, and see where you guys first differ? [/ QUOTE ] We breakdown the problem but we differ in some aspects. She thinks that the burn card, for example, might be an Ace, or a trey, or a King, and therefore is changing our odds and probabilities. I explain to her that if we knew what that card was she would definately be correct. But we do not know and therefore can only attempt to calculate the likelyhood that an Ace (or trey or King) was indeed used as a burn card. The kicker is, she'll say "but what if it *IS* a king" "but we don't know that, but we can calculate it's likelyhood" "but what if IT IS A KING AS A BURN CARD..." ... and around and around and around we go! [eyes rolling] ....
|
|
#7
06-14-2006, 07:32 PM
|
|||
|
|||
|
Re: burning-half-the-deck problem
Maybe instead of burning away 25 cards, burn away 49 of them. Have her think about this and have her apply her logic, and it might lead to a more obviously incorrect answer (that then leads her to clarity).
-RMJ
|
|
#8
06-15-2006, 09:43 PM
|
|||
|
|||
|
Re: burning-half-the-deck problem
Rocketman has an interesting idea.
Burn one card at a time and ask what the probability is after each card. She should get a weird answer at the end. There is another approach. Step 1: Buy a box of matches and a thousand decks of cards ...
|
|
#9
06-16-2006, 06:16 AM
|
|||
|
|||
|
Re: burning-half-the-deck problem
[ QUOTE ]
That's the exact difficulty i'm having! The confusion begins when I "split the deck" in half. She now thinks that there is a GREATER probability of finding an Ace in the non-burnt deck. [ QUOTE ] Taking off the bottom half of the deck and burning it (or doing anything else with any or all of the 49 cards not on the top of the deck) cannot affect this. [/ QUOTE ] I tried showing her the deck face down in my hand, with two Aces removed. Then I ask her the odds of the top card being an Ace. 1/25 she replies. So far, so good. I remove the bottom card of the deck. What are the odds now?? 2/49, she replies. D'OH!!!!! This problem is also similar to the complaints that many bad amateur players have when a dealer burns the top card of the deck. They presume that it alters the probabilities of certain cards coming up on the flop, turn, or river. They are most distressed by the fact that the burn card may have indeed helped their hand had the dealer used it as one of the community cards instead of a burn card. Here's an example of what I'm trying to say: Say i'm holding Cowboys (KK) and out flops: Jd-Qc-As. Several players like their hand, but the cowboys are crying for help. The dealer burns a card, and the turn is a 4s. Unbeknownst to the players, the burn card was a King - this has suddently changed the outcome of the hand! A seasoned player would obviously not think this way. They know that all the cards in the deck are random, and all "unexposed" cards have the same likelyhood of being a King. So the likelyhood of the burn card being a K is the same as it appearing on the turn or river! Because we do not know the rank of the burn card, it could be anything. In fact, we can calculate the exact likelyhood that it is indeed a K - but we can never know for sure what it is. [ QUOTE ] Instead of taking this convoluted problem, why not break it into a series of easy problems, and see where you guys first differ? [/ QUOTE ] We breakdown the problem but we differ in some aspects. She thinks that the burn card, for example, might be an Ace, or a trey, or a King, and therefore is changing our odds and probabilities. I explain to her that if we knew what that card was she would definately be correct. But we do not know and therefore can only attempt to calculate the likelyhood that an Ace (or trey or King) was indeed used as a burn card. The kicker is, she'll say "but what if it *IS* a king" "but we don't know that, but we can calculate it's likelyhood" "but what if IT IS A KING AS A BURN CARD..." ... and around and around and around we go! [eyes rolling] .... [/ QUOTE ] i went round and round with my buddy playing blackjack at a casino once with a similar argument. He swears a good third base player can help the rest of the table. I told him that would only be if third base was counting cards or was mrs. cleo. to this day, he wont believe me.
|
|
#10
06-16-2006, 05:55 PM
|
|||
|
|||
|
Re: burning-half-the-deck problem
Your problem is you are arguing with a female about a math problem. Let her stick to writing papers for you or something, or baking cakes.
|
 |
| Thread Tools | |
| Display Modes | |
|
|
Linear Mode
