Hypothetical Gambling Situation

[DavidC]

Shill, I ALWAYS smoke the good stuff. [img]/images/graemlins/smile.gif[/img]

Eegah's right, but I considered time to be a minor factor in this case.

Badger has the correct answer, and the correct reason.

I made our "hero" have very small marginal utility of money, but positive marginal utility of money, between 15k and 30k, therefore it's best to quadruple up, because it sucks to lose the 10k, just like badger said. [img]/images/graemlins/smile.gif[/img]

This saves you from that 25% of the time where you win the first one but lose the second one. [img]/images/graemlins/smile.gif[/img]

So there are three factors:

1) Time (not really important)
2) Utility of Money (if it sucks worse to lose 10k than 5k, then quadruple rather than double if you have huge utility at 30k (+20k))

3) Something that I didn't consider before tonight, if you actually enjoy gambling, then it would be best for you to double twice. However, I'm not 100% sure, but I think that this is the type of person who would gamble at -EV recreationally in order to gain the utility of gambling. Anyways, I cut this possibility out by saying hero didn't particularly like to gamble.

[DavidC]

Cheater! [img]/images/graemlins/smile.gif[/img]

[crovax4444]

cheating how? Remember, I have no friggen idea wtf your talking about mathmatically 1/2 the time. I simply picked the responce that I agreed with most :-p In essence, I plagerized Eeegah's responce.

Crovax

[AdamL]

What's the utility of 10k vs the utility of 5k here Dave? *cough*

(innocent, stupid look)

[DavidC]

[ QUOTE ]
What's the utility of 10k vs the utility of 5k here Dave? *cough*

(innocent, stupid look)

[/ QUOTE ]

[ QUOTE ]
You care just slightly about money between $10k and $30k, but you care about $30k A LOT.

[/ QUOTE ]

[DavidC]

[ QUOTE ]
You care just slightly about money between $10k and $30k, but you care about $30k A LOT.

[/ QUOTE ]

The numbers don't quite match up my personal circumstances, but it pretty much sums up what I'm going through right now (with the exception of the $5k royal [img]/images/graemlins/cool.gif[/img]).

I've found that it APPEARS as though I have some utility of money, even though I don't really spend a ton of money or anything. I've called this marginal utility of money that I don't spend "utility of income". Meaning that on a daily/weekly basis I like to see a growth in my assets regardless of whether or not I have any spending goals, regardless of if I'm way over-rolled for my current limit and I've got the "Miller 3-months" behind me.

This is pretty weird, but seems to be general human nature.

Thus, your utility of 10k is higher than 5k, even if you aren't planning on spending the $10k or the $5k...

It was stated in the original question, though. Everything was there from the hero's perspective.

Anyways, enjoy your day, sir. I'm off to bed. [img]/images/graemlins/smile.gif[/img]

[AdamL]

You knew this, because you ruled it out in your original post, but normally 5k in the hand is worth more than 50% of 10k *even* if you have a strangely shaped utility function (as you've described.) The reason of course is that the 5k has the ability to make money, even if nothing more than simple interest. You have two options which each have equal EV, but only one of them is guaranteed to be "playable".

Any surefire permanent addition to your roll is worth more than a 50% neutral EV shot at the same thing. There is no opportunity cost to keeping the 5k.

I hope that makes sense. "Well, if you had 10k you'd have twice as much opportunity to collect interest". True, but if you lose you'd have zero interest.

Given that interest and other bankroll-related activities are *compound* activities, a 100% 5000 is worth more than a 50% 10,000. The loss in compounded interest when you lose the double out-weighs the extra interest you'd have with 10k.

5k at 10% interest = 5500 ev, plus guaranteed compound interest.

50% x 10k at 10% interest = 5500 ev, but when you lose, you cost yourself in time-interset accumulation.


This is very similar to my suggestion that there are real costs to downswings, if they prevent you from doing things in real life which would make you money or prevent you from spending it on unprofitable outcomes.

If you rent for an extra 6 months due to a downswing in a booming real estate market, you lose a lot more than you would have if you had an upswing or stuck near EV. The "Sklansky Bucks" may be equal, but the real dollars won or lost are far from equal.

Likewise, if some individual were planning on buying a big money-pit, pain-in-the-ass, somewhat uneccessary, depreciating asset if they had an upswing, then they would actually prefer from a utility standpoint to NOT have an upswing. The upswing has "excess baggage" beyond the neutrality of the sklansky bucks that the individual shouldn't, from a strictly financial standpoint, wish to incur.

Of course, some people just want to have their toys. *COUGH*. [img]/images/graemlins/laugh.gif[/img] [img]/images/graemlins/laugh.gif[/img] [img]/images/graemlins/wink.gif[/img]

I switch doors, I remember reading about it in my discrete math textbook. [img]/images/graemlins/tongue.gif[/img]

I seem to recall that was in a Marilyn vos Savant column once. She was adamant about the answer despite many readers serious objections. I can't recall the dang details.

[mojobluesman]

I'm not sure which is correct in the theoretical world, but I can tell you which is correct in the real world because I've probably been gambling for longer than most of you are alive.

If getting to 30K is really important, then go for the quadruple immediately. Otherwise, after winning the first bet in a double up, the decision on whether or not to continue will be agonizing and a loss will put you on a 3 week drinking bender. [img]/images/graemlins/blush.gif[/img]

If the 30K is not really that important, then go for the double up because the probability of winning is higher and it will give you a chance to re-evaluate your feelings and priorities after you are ahead the 10K.