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

This isn't a math question, we know the answer. You are roughly a 4-1 fav on every hand. The fact is if you lose, you are out, if you win you are still a 4-1 fav. The odds don't change, and there is no 'secret hand' in which you are suddenly a dog.

It is a personal question, what are you willing to risk as a 4-1 fav, knowing that you can win up to $125,000. For almost everyone, the answer would be to go all the way.

But---if say, you could open up a business for 64K, then reaching that point you might want to quit, as it is no longer worth it to try and double up as a 4-1 fav.

Here is how to find your answer---
Bill Gates puts up 50 billion, and you get the same deal.

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 ]


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?

[/ QUOTE ]

This is where reality hits the theorists here. It's only a one time offer and once you lose a hand it's over so all your EV+- in the world isn't going to help with an answer. Since AA is probably going to get cracked at least one time in 8 hands played the farther you go the more likely you will lose the entire stack you just won. On the last hand you'd be risking $62,000 (with a guarantee of keeping the other $2000). Is there anyone here who would seriously risk $62,000 on one hand? I wouldn't. I'd take the $63,500 profit, thank Daniel profusely and offer to buy him dinner. :-)

[ 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 ]

Nobody is saying they'd refuse the offer. What we are saying is that we wouldn't take it all the way if we won, say the first 5 hands. We'd be happy with our $63,500 profit. The offer stated that we could stop at any point. I certainly wouldn't risk $62,000 to make $62,000. If you would then you either have too many dollars or not enough cents(sic).

4th hand:

AA vs 34o

Flop Q25TA

Bye bye money.

:-)

[Unabridged]

play until someone goes broke, if the risk gets too high sell off some of it

[PokerAmateur4]

Yep it's been done before. I'd go on beyond 125k, I'm not sure where I'd stop it's a big decision. Maybe $1Mil, at the point where I can start making investments where I could live off the interest with a nice lifestyle I think the U becomes negative to continue gambling. Skalnsky or other millionaires, I'd be interested to see where you stop.

[Xhad]

[ QUOTE ]
This is where reality hits the theorists here.

[/ QUOTE ]

Only the ones who don't understand the assumptions behind EV and decision making. Those who are familiar with concepts like "standard deviation" and "risk of ruin" can explain why most people have an upper limit when it comes to this game. Actually staying in this game might not even be +EV if you're an excellent poker player who is underbankrolled, because you might be more EV if you just take the money and go play a high-limit poker game with it.

[Borodog]

[ QUOTE ]
this is akin to the "St Petersburg paradox"

St Petersburg Paradox

the answer to the question depends on your wealth utility curve.

[/ QUOTE ]

Excellent link. Are you an economist or a game theoretician?

[trumpman84]

I'm surprised at how many people put "until he busts me". Theoretically, what if someone sat down with an infinite amount of money and made the same propisition? If you tried to keep going until you busted him, he would eventually win your money even though each individual bet you make is +EV.

For me, I would keep going until I was really uncomfortable losing what I had in front of me which is basically how I handle buying into games. I definetly wouldn't be betting 100,000+ on a hand..even with aces, because I only have about $2,000 to my name right now (in college) and tens of thousands in student loans so keeping that $100,000 would mean so much to me than to risk it all even as an 80% favorite. I'm sure all of you have this cap that you'd risk too. If someone offered you 100 million dollars and said you could keep it or risk it all on one hand of poker (you getting AA and him drawing a random hand) I'm sure 99% of you would keep the money...even if he was paying 2 to 1.

It's a concept that is sort of discussed in tournament poker for advanced players. If you can make a great bet tommorow, then you should pass on a merely good bet today, if losing that good bet means you don't get to bet tommorow. If a great poker player kept his $100,000 (or whatever amount he wasn't comfortable losing), he could move up to a much bigger limit and since he's a great player, he has a 100% chance of winning at that limit if he practiced good bankroll management and eventually make the amount of money he could if he took the maximum wager and more given enough time and hands played.

I believe the paramount factor in this situation in not "expected value", but "expected utility" as a few people have hit on. The question has nothing to do with math, because anyone with any math skill would conclude that all-in with pocket aces vs two random cards is an easy call all day long, mathematically speaking. But how many people would risk $32,000.00 on the second to last hand of the deal for an 80% chance to double up, probably not the guy making $15/hr with a wife, kid, and $32,000.00 left on his mortgage, because the $32,000.00 he has would mean a lot more than the extra $32,000.00 he might expect to make if he won. Some may quit after doubling up only one or twice, if $2,000.00 is what they needed to make them happy, and risking that was not worth the extra $2,000.00 they would expect to make 4/5 times.


A more extreme example would be if you won $10,000,000.00 playing the lottery and that $10,000,000.00 constituted your entire worth. Afterwards you were given the option to place that $10,000,000.00 on the line to spin the "big wheel" that offered a 1/10 chance to win $10,000,000,000.00 more. Of course you are 10% to win but have a 1000/1 return on investment. Mathematically speaking that is a no brainer, but the relative value of the extra $10,000,000,000.00 vs. the 90% chance you will go broke is probably not worth the risk for any rationalt person. Keep the ten million and be set for life, take your chance and 10% of the time come out filthy rich with almost too much money to spend, and the other 90% be broke and back humping a 40/hr a week job. I guarentee everyone will people pick the first option.

The only person who might take the option to spin would be someone who was already extremely rich and $10,000,000.00 was not a significant increase in net worth whereas $10,000,000,000.00 would have would have a much larger relative value to him. A person like Bill Gates for example.

That is why people play slots, keno, the lottery, etc. Anyone with any knowledge knows they are not even a favorite to win or that they are even making a +EV decision, but it is not about "expected value", the "expected utility" of winning millions playing the lottery outweighs the relative value of that $5 they are almost certainly going to lose playing it.