You have AA every hand . . . when do you quit?
 

My apologies if something like this has already been posted. I don't frequent the Theory forum much.

Here's an interesting thought experiment that came up because of a recent post on another board about Daniel Negreanu buying into a $5-$10 no limit hold'em game at the Wynne with $125,000.

Let's say that you are sitting at the $5-$10 NLHE table one morning. You've just bought in for $500, and are waiting for other players to come along. Up walks Daniel Negreanu. He sits down across from you, introduces himself, he's a nice guy, you chat. No one else is showing up to play though. So to cure his boredom, he offers you a proposition.

Daniel buys in for $125,000. He offers to let you keep the Ace of clubs and the Ace of spades, while he is dealt two random cards from the well-shuffled remainder of the deck. Daniel will then go all-in preflop every single hand. Just to make this clear, every hand you will have pocket aces against Daniel's two (new) random cards (i.e. he gets new random cards each hand), and he is going all-in every hand. If you call, the flop, turn, and river will be dealt and the best hand wins.

Edit to add: If you go broke, the game is over. You cannot rebuy.

How many hands do you play?

Re: You have AA every hand . . . when do you quit?
 

Until I have 125,000. Can I rebuy?

Re: You have AA every hand . . . when do you quit?
 

No. If you get busted the game is over; you can't rebuy.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
How many hands do you play?

[/ QUOTE ]

All of them.


Seriously though, this game couldnt last more than 8 hands (unless you folded, but where or why would you?). If you won 7 hands in a row, your stack would be $64,000 and you'd have him covered. However, even 27 off has a 1 in 8 chance of beating AA. Either way, this wont last more than 8 hands, with one of you having all of the chips.

Your question was, when would you quit? I dont think any player on this site is standing up from this proposition. Anyone of us will risk that $500 for the chance at $125k with those odds.

MDoranD

Re: You have AA every hand . . . when do you quit?
 

Until he's broke (or you are)

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
[ QUOTE ]
How many hands do you play?

[/ QUOTE ]

Either way, this wont last more than 8 hands, with one of you having all of the chips.



[/ QUOTE ]

This is false.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
How many hands do you play?


--------------------------------------------------------------------------------



Either way, this wont last more than 8 hands, with one of you having all of the chips.




--------------------------------------------------------------------------------



This is false.

[/ QUOTE ]

How is it false? You have $500. If you win the 1st hand you have $1000, hand#2 you win youve got $2000, win#3 $4000, then $8000, then $16000, $32000, $64000, then all of it. Or youve lost all of it. Unless of course you folded a hand. But whos doing that?

MDoranD

Re: You have AA every hand . . . when do you quit?
 

On hand 8 if you lose you are not busted, since you have Daniel covered.

Re: You have AA every hand . . . when do you quit?
 

I'd quit when one of us went broke.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
I'd quit when one of us went broke.

[/ QUOTE ]

easiest question of the day.

Re: You have AA every hand . . . when do you quit?
 

you guys r a bunch of gamblers...seriously I'd go maybe 3 hands, 4 max if I felt really lucky. I don't think I've ever won with Aces more than 3 times in a row... Don't you know how often Aces get cracked? You really think there gonna win 8 times in a row...lol

Re: You have AA every hand . . . when do you quit?
 

Ok. For all of the guys who say, "Until one of us is broke," would your answer changed if Daniel bought in for say, $2,000,000 instead of $125,000?

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
you guys r a bunch of gamblers...seriously I'd go maybe 3 hands, 4 max if I felt really lucky. I don't think I've ever won with Aces more than 3 times in a row... Don't you know how often Aces get cracked? You really think there gonna win 8 times in a row...lol

[/ QUOTE ]

Off the top of my head, you're going to win more than 10% of the time...so you win the $125K 1 time and lose $500 9 times. EV= +$120,500 for taking it to the end...if you only did it 4 times you would win about a third of the time and so your you would win $8,000 one time and lose $500 twice....EV= +$7,000

Are you going to pass up $113,500 just like that?

Re: You have AA every hand . . . when do you quit?
 

Then it starts to get interesting, at some point getting 80% (or whatever those aces have) chance to double up is
-U, but I think this point is higher than $2 mill for me personally.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
Ok. For all of the guys who say, "Until one of us is broke," would your answer changed if Daniel bought in for say, $2,000,000 instead of $125,000?

[/ QUOTE ]

no.

Re: You have AA every hand . . . when do you quit?
 

I like free money.

Re: You have AA every hand . . . when do you quit?
 

I am going to say a max of 16 hands without AA losing no more than every once every 8 times.

Re: You have AA every hand . . . when do you quit?
 

by hand 8, daniel is broke.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
by hand 8, daniel is broke.

[/ QUOTE ]

I aksed if anyone's answer would change if Daniel's buy-in were upped.

Re: You have AA every hand . . . when do you quit?
 

i'd quit at hand 8.

Re: You have AA every hand . . . when do you quit?
 

And as a follow up to my own post. I would not quit. I would keep going until one of us is broke, since I am getting really good odds each time. Isnt this the same thing as saying "if someone gave you the option to call heads are tails and if you win the coin toss you get 8 dollars if you lose you pay 1 dollar...how many times would you make this bet.

Re: You have AA every hand . . . when do you quit?
 

yeah, but, we dont have a lot of money, so, we quit when we're up six figures, and, go play our normal game and be glad we didnt lose $168,000 that we wont see again for ages.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
Isnt this the same thing as saying "if someone gave you the option to call heads are tails and if you win the coin toss you get 8 dollars if you lose you pay 1 dollar...how many times would you make this bet.

[/ QUOTE ]

no it isn't because you are not allowed to decrease your stack between hands

this is closer to "if it's head I get 8 dollars, tails you get 1 dollar; if I win, the bet for the next flip is heads I get 64 dollars, tails you get 8 dollars, etc." the point being you are risking all of your money as long as he has you covered.

this is also similar to who wants to be a millionare only without the stop loss.

Re: You have AA every hand . . . when do you quit?
 

Can you give us a hint as to why this question isn't as stupid as it sounds?

eastbay

Re: You have AA every hand . . . when do you quit?
 

What in the FARK is going on here?

Can you guys be serious?

Do you guys really think that it matters how many times you go all in with AA vs any random hand?

You are getting 80% on every hand you play, you are a favorite to win.

I can't believe anyone has mentioned your EQUITY here, this is EXACTLY what you need to consider.

If you play every hand until one of you is broke then consider your EQUITY

You are placing a $500 wager for a freeroll chance to win a maximum of $125,000

you are getting $500 to $125,000 odds or a 1 to 25.

You have to win 8 times in a row in order to take the full $125,000, so...

WHAT ARE THE CHANCES OF AA HOLDING UP 8 TIMES IN A ROW?

.8^8 = ~16% of the time, THATS ABOUT 1 in 6!!!!

A 1 to 6 shot getting 1 to 25 on your money

You have a positve expected value of about $20,800 if you take this wager until one of your busts out.

Re: You have AA every hand . . . when do you quit?
 

YOU ARE A DUMMYHEAD

everybody here knows AA is a pretty good hand vs. a random hand. OP's question isn't "is AA really any good?", it's really a question about risk tolerance.

WHAT ARE THE CHANCES OF AA HOLDING UP 7 TIMES IN A ROW?

it's 1/5.

So OP is saying, would you rather have a 1/5 shot at 62k, or a 1/6 shot at 125k? etc.



CAN YOU BE SERIOUS THAT YOU DONT UNDERSTAND THIS?


WHY ARE WE SHOUTING???

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
Ok. For all of the guys who say, "Until one of us is broke," would your answer changed if Daniel bought in for say, $2,000,000 instead of $125,000?

[/ QUOTE ]

I think what you are asking is how much risk tolerance do people have. I mean you could just ask something like this:

You just won $1,000,000 in the lottery but as you are gong to cash your check a gambler wants to play one hand with the scenario you describe. Would you do it?

The easy answer is YES since the math is certainly in your favor * but are you willing to lose the $1,000,000, which would already be a life changing amount for an extra million? If yes would you do it for 2,000,000 or 10,000,000, etc.


*Basically you are describing the Martingale System and if it doesn’t work with Black Jack it wouldn’t work here for poor Daniel.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
Ok. For all of the guys who say, "Until one of us is broke," would your answer changed if Daniel bought in for say, $2,000,000 instead of $125,000?

[/ QUOTE ]

500 to 2,000,000, so 1 to 4000 pot odds

You need to only win 11 times to win the total pot

AA is favorite over xx 85% of the time

.85^11= 1 in 6 !!!!!!!!!!!!!!

You will lose 500 dollars 85% of the time, 15% of the time you win 2 million... and you would refuse this offer?

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
You need to only win 11 times to win the total pot

[/ QUOTE ]

you don't seem to understand that you can win 10 times and reevaluate, and your "pot odds" are much different. people with a net worth of 1.001 million dont necessarily like making million dollar bets, even as a huge favorite.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
[ QUOTE ]
Ok. For all of the guys who say, "Until one of us is broke," would your answer changed if Daniel bought in for say, $2,000,000 instead of $125,000?

[/ QUOTE ]

500 to 2,000,000, so 1 to 4000 pot odds

You need to only win 11 times to win the total pot

AA is favorite over xx 85% of the time

.85^11= 1 in 6 !!!!!!!!!!!!!!

You will lose 500 dollars 85% of the time, 15% of the time you win 2 million... and you would refuse this offer?

[/ QUOTE ]

No, I would not refuse that offer.

Unfortunately, that wasn't the offer.

It'd be trivial to say, "I'll give you 4000:1 on a wager of whether pocket aces will hold up 11 times in a row versus 11 randomly dealt hands."

This is not the same question as asking, "Now that you've won 10 times in a row and have over a million dollars in front of you, five times more than your entire net worth as of last night, would you like to bet your one million dollars, most of your current life savings, on whether pocket aces will hold up in the next hand?"

Personally, I would not wager the majority of my net worth simply to double my money, even if I were an 85% favorite.

So I guess my answer to the guestion is that I would stop when my stack exceeds my net worth prior to the start of the game.

The question is basically about risk tolerance and utility, rather than expected value. The highest expected value play of course is to play until someone is broke. The expected value is not as high as you may expect though; it's only about $35k for the first case and [$300k] for the second. But the highest EV case is also the most likely case for you to end up out $500 instead of up a few thousand or tens of thousands.

As several authors including Sklansky and Brunson have noted, forgoing a +EV gamble with a significant risk of going broke, so that you are able to take advantage of future +EV gambles is not a bad thing.

If you were to keep playing until somebody is broke, it will usually be you.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
you guys r a bunch of gamblers...seriously I'd go maybe 3 hands, 4 max if I felt really lucky. I don't think I've ever won with Aces more than 3 times in a row... Don't you know how often Aces get cracked? You really think there gonna win 8 times in a row...lol

[/ QUOTE ]

Yes. This is not a question of tolerance. You should stop playing when it's a -EV game. We all understand that. Here's how you should look at it:

1 hand : 85%
2 hands: 72%
3 hands: 61%
4 hands: 52%
5 hands: 44%

so you should stop after 4 hands.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]


Yes. This is not a question of tolerance. You should stop playing when it's a -EV game. We all understand that. Here's how you should look at it:

1 hand : 85%
2 hands: 72%
3 hands: 61%
4 hands: 52%
5 hands: 44%

so you should stop after 4 hands.

[/ QUOTE ]

So, after 5 hands you have a 44% chance to build your $500 into $16000. That's -EV in your opinion?

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
[ QUOTE ]
you guys r a bunch of gamblers...seriously I'd go maybe 3 hands, 4 max if I felt really lucky. I don't think I've ever won with Aces more than 3 times in a row... Don't you know how often Aces get cracked? You really think there gonna win 8 times in a row...lol

[/ QUOTE ]

Yes. This is not a question of tolerance. You should stop playing when it's a -EV game. We all understand that. Here's how you should look at it:

1 hand : 85%
2 hands: 72%
3 hands: 61%
4 hands: 52%
5 hands: 44%

so you should stop after 4 hands.

[/ QUOTE ]


consider switching to slots

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
[ QUOTE ]
you guys r a bunch of gamblers...seriously I'd go maybe 3 hands, 4 max if I felt really lucky. I don't think I've ever won with Aces more than 3 times in a row... Don't you know how often Aces get cracked? You really think there gonna win 8 times in a row...lol

[/ QUOTE ]

Yes. This is not a question of tolerance. You should stop playing when it's a -EV game. We all understand that. Here's how you should look at it:

1 hand : 85%
2 hands: 72%
3 hands: 61%
4 hands: 52%
5 hands: 44%

so you should stop after 4 hands.

[/ QUOTE ] You have a 27.8% chance of winning the whole thing, $125k after 8 hands. You're putting up $500 to do so. So you're getting 250:1 on your money and you will win a little bit better than 1/4 of the time. Definitely +EV.

Ok, I can see the argument that in a 1 time shot after the 4th hand you're risking $8000 to double up with only a 44% chance to do so, but considering you only put up $500 of your money to begin with, the odds say you should gamble.

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
[ QUOTE ]
you guys r a bunch of gamblers...seriously I'd go maybe 3 hands, 4 max if I felt really lucky. I don't think I've ever won with Aces more than 3 times in a row... Don't you know how often Aces get cracked? You really think there gonna win 8 times in a row...lol

[/ QUOTE ]

Yes. This is not a question of tolerance. You should stop playing when it's a -EV game. We all understand that. Here's how you should look at it:

1 hand : 85%
2 hands: 72%
3 hands: 61%
4 hands: 52%
5 hands: 44%

so you should stop after 4 hands.

[/ QUOTE ]

http://en.wikipedia.org/wiki/Gambler%27s_Fallacy

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
Ok, I can see the argument that in a 1 time shot after the 4th hand you're risking $8000 to double up with only a 44% chance to do so, but considering you only put up $500 of your money to begin with, the odds say you should gamble.

[/ QUOTE ]

You do not have a 44% chance of doubling up. You have an 80%ish chance of doubling up. That 44% figure includes the times you bust out in one of the first three trials, but if you even got this far then you didn't bust out during those trials. The 44% figure only applies if you haven't actually started playing yet.

Think of it this way...the chances of you being dealt AA is 220-to-1. So what are the chances of having AA if you already know one of your cards is an A? According to the voodoo mathematics above, it would still be 220-to-1, which is clearly incorrect.

Re: You have AA every hand . . . when do you quit?
 

You're right, I miscalculated that.

Re: You have AA every hand . . . when do you quit?
 

Ok I had to try this out just for fun.. out came the trusty deck of cards.. I decided to go for two black aces as they are far cooler [img]/images/graemlins/cool.gif[/img]

Hand 1

A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/club.gif[/img] vs T [img]/images/graemlins/heart.gif[/img] 9 [img]/images/graemlins/spade.gif[/img]

Board 3 [img]/images/graemlins/spade.gif[/img]2 [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/diamond.gif[/img]K [img]/images/graemlins/diamond.gif[/img]7

$1000 please

Hand 2

A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/club.gif[/img] vs K [img]/images/graemlins/diamond.gif[/img]Q [img]/images/graemlins/diamond.gif[/img]

Board 9 [img]/images/graemlins/spade.gif[/img]k [img]/images/graemlins/spade.gif[/img]7 [img]/images/graemlins/spade.gif[/img] 3 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/spade.gif[/img]

$2000 Please

Hand 3

A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/club.gif[/img] vs 4 [img]/images/graemlins/club.gif[/img]9 [img]/images/graemlins/diamond.gif[/img]

Board T [img]/images/graemlins/diamond.gif[/img]3 [img]/images/graemlins/diamond.gif[/img]7 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img]

Damm it! Good Bye easy money!! This game is rigged [img]/images/graemlins/mad.gif[/img]



EDIT: P.S, I've tried this a few times now (too much time on my hands) My best score is $32000, anyone beat that???

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
P.S, I've tried this a few times now (too much time on my hands) My best score is $32000, anyone beat that???

[/ QUOTE ]

The first eight hands I dealt out, the Aces won. (2 sets and a nut flush, too [img]/images/graemlins/tongue.gif[/img] )

..going to keep going to see how far I can get. [img]/images/graemlins/smile.gif[/img]

-Aces full rivered against K [img]/images/graemlins/club.gif[/img] 2 [img]/images/graemlins/club.gif[/img]'s flush on hand 11, still going.

Lost on Hand #14 with A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/club.gif[/img] to Q [img]/images/graemlins/club.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img]
Board: 5 [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img] 4 [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/heart.gif[/img] 3 [img]/images/graemlins/spade.gif[/img]

So, I ran my $500 into $4,096,000 ... hope Danny didn't buy in for $10M+ [img]/images/graemlins/tongue.gif[/img]

Re: You have AA every hand . . . when do you quit?
 

[ QUOTE ]
I think what you are asking is how much risk tolerance do people have.

[/ QUOTE ]

Yes, it's just a complicated way to ask about risk aversion (how not all dollars are created equal and utility is not identical to cash value).