Variance tolerance straw poll

[Nate tha' Great]

Please read carefully before responding.

Suppose a benefactor knocks on your door this morning and offers you the choice of several proposition wagers. Each wager involves flipping a coin. If the coin comes up heads, you will win a certain amount of money, and if the coin comes up tails, you will win or lose a certain amount of money as is specified ahead of time. The amount that you win or lose will be based on the size a big bet (BB) in the highest limit poker game that you play regularly.

Which of the following offers would you take? Amounts are provided in BB. The numbers in parenthesis represent the monetary value for a player whose highest regular game is 15/30.

[SmileyEH]

I'm way overbankrolled for the limit I play, so I went with the largest wager.

-SmileyEH

[bunky9590]

Nate, so much involved in this is a bankroll issue. As far as the limit I regularly play online, I have 1500 BB. With that in mind, IF thats what you're saying, Id have to take something in the 110-115 EV range.

[mmcd]

I'm no statistician, but what are the chances you come out behind after 100 flips getting laid 3-2. Intuitively, I'm pretty sure it's less than 5% and may even be less than 2%.

I'm too busy/lazy to do the math, anyone know the answer offhand?

I chose the last option.

P.S. Do you pay/get paid per/flip or settle up at the end?

[pudley4]

I've only got ~900 BB in my bankroll and no way to replace it, so I chose the 2nd highest variance/payout; otherwise it would have been the highest.

[DMBFan23]

I find it interesting that I chose

[ QUOTE ]
Heads: Win 220 BB ($880); Tails: Win/Lose 0 BB ($0)

(dollars converted to 2/4)


[/ QUOTE ]

when, every time I play 100 hands, I'm taking a SD/EV ratio larger than your highest variance option. perhaps this is due to the fact that I can "flip the coin" playing poker an arbitrarily large number of times.

[stoxtrader]

can i choose win 9k BB / lose 6k BB? or whatever the progression goes to?

[sfer]

A very good friend of mine used to use nearly this exact example to explain risk-neutral probabilities and cashflow discounting to people. He also played poker.

[Piz0wn0reD!!!!!!]

0 risk is clearly the way to go.

[sfer]

[ QUOTE ]
0 risk is clearly the way to go.

[/ QUOTE ]

Not if your goal is to maximize your EV.

[bobbyi]

[ QUOTE ]
0 risk is clearly the way to go.

[/ QUOTE ]
So you're quitting poker?

[B Dids]

I went with "Heads: Win 400 BB ($12,000); Tails: Lose 150 BB (-$4,500)"

400 moves me up, and has a lot of impact. 150 sucks, but it doesn't move me down and I can cope.

[BottlesOf]

I went with the second riskiest. I just can't swing a 50% chance of losing in the last example.

[Knoler]

Assuming I can flip the coin as many times as I want, why would I ever take an option that wasn't the "no-risk, highest amount per average flip" option?

Regards,
-Brian

[mmcd]

Is there really a 50% chance that 67(or more)/100 flips will come up tails?

Nevermind, I didn't read the post carefully and thought the game involved 100 flips.

[sfer]

I interpret Nate's poll as being offered a single flip, and you get to select what you can win/lose on that one flip.

[Schneids]

I'm a risk-averse puss. I took the 100BB guaranteed.

[theghost]

I took one of the least popular:
[ QUOTE ]
Heads: Win 160 BB ($4,800); Tails: Win 50 BB ($1,500)

[/ QUOTE ]
I didn't go for max EV because you only get one flip, I like the guaranteed win. Why not take the 100/100 guarantee? Pure psychology, it's found money either way so I'll take a chance with some of it to get slightly more.

Unlimited flips and I'll go for max EV every time.

[diddle]

no [censored]

[MicroBob]

If you got 100 flips or as many flips as you wanted then I would think that taking the zero-loss flops would be kind of obvious.

I also assumed it was just 1 flip.

[jaybee_70]

Awesome poll. I just jumped a level so I chose the second option.

Joe

[MicroBob]

for only 1 flip I chose the sure thing (win 100, win 1000.


In poker you can always step down in limits when things go badly...or take 'calculated' shots at the next highest level. And you can play thousands and thousands of hands.


with this single-flip I'm taking the sure thing.



I don't know why I think of this....but if it was a choice between 100% chance of $1-million or a 50/50 chance between $2.1-mil or $0 I would DEFINITELY be taking the sure $1-mil.



What's curious is that i generally consider myself to be a little too risk-tolerant and agressive with my poker playing and bankroll. But, for some reason, I am an ultra-conservative wimp on this one.

Maybe it's because I haven't had enough coffee yet.

[Schneids]

I wonder if people who primarily play limit are answering in a different general way than people who primarily play NL?

[theghost]

[ QUOTE ]
no [censored]

[/ QUOTE ]

bankroll

[stoxtrader]

[ QUOTE ]
I don't know why I think of this....but if it was a choice between 100% chance of $1-million or a 50/50 chance between $2.1-mil or $0 I would DEFINITELY be taking the sure $1-mil.


[/ QUOTE ]
this is because your marginal utility/dollar decreases as your dollars grow. everyone experiences this to varying extent.

in other words, you get much more use/enjoyment (utility) out of the first 1 million than out of your 2nd million. basically just a corollary of risk aversion.

[Bluffoon]

I don't think the EV increases enough to offset the risk. I am taking the sure 100BB.

[Danenania]

I took win 400/lose 150 since 150 bb's isn't too significant to me but I could do a lot with 400. I'm too scurred to go higher.

[detruncate]

Great question. This is going to seem ridiculously involved, but I've been thinking a lot about my reaction to variance lately and I find it helps me to write my way through things. Might as well post the result.

I have a very low risk tolerance for going broke, hence a minimum 1000 BB bankroll. I'm also in the run-up to a level change, and have ~1500 BB on hand at my current level. The loss of 300 BB still leaves me comfortably over-rolled, and it wouldn't take too long to get myself back on track re. moving up preparations. In other words, losing 300 BB would have a fairly minimal impact on me.

A 600 BB loss would be too much relative to my (somewhat surprising) indifference to the increased $ -- I'm happy with a significant amount of unexpected money, but the difference between the top two levels isn't sufficient to make me willing to risk a bigger loss.

Reducing the amount at risk to 150 BB doesn't seem worth it at first glance. Losing 150 BB is not sufficiently better than losing 300 BB relative to my total roll size. However, the moving between 400/150 and 570/300 involves doubling the amount of chips at risk to increase my potential win by 30%, and now that I think more about it, I'm not sure the difference between the $ figures is sufficiently attractive.

My initial reaction was "yes", but I was looking more at the potential loss than the potential gain, figuring that any amount of extra money is good, so it came down to how much I was willing to lose relative to the size of my roll. I'm still playing very small limits, so the actual $ figures involved might be playing into this -- though they're all clearly significant to me given my current lifestyle.

I voted for 570/300, and could still see myself following through with it. However, risking 50% as much to win 70% (400/150) would almost certainly be the way I'd go if I wasn't so over-rolled.

[MicroBob]

Yes...but to me it feels the same at the lower level.


"Hey...$1k is nice....or I could do the $2.2k or Zero option. Well....am I really going to be able to do THAT much more with $2.2k than I can with $1k. Not really. The sure-thing $1k sounds good to me."


Again...this is only if it's one flip.

$1k vs. nothing is a bigger difference to me than $2.2k to $1k is.

Thus I take the sure $1k.


I believe I would use the same logic for $100 at 100% vs. $220 at 50%.

[Zetack]

I didn't read carefully, I thought he showed up every day. Obviously you take the highest wager your bankroll can stand and I was trying to figure that out.

With one flip I take the guaranteed money and go +160 or +50.

Heck what can I say, I love free money.


And outside of poker I don't enjoy gambling.


--Zetack

[slogger]

I would think that if you could flip 100 times, even more risk averse people would take the highest wager option because over 100 tries, the likelihood of coming out worse than the guaranteed money on every flip option would be very small.

[Chris Daddy Cool]

this is mainly a bankroll risk issue. i think anybody who can afford to lose it should take the biggest bet. for me i chose the 400bb,-150bb bet.

[Awesemo]

I never win coinflips. I choose option 1.

[sfer]

[ QUOTE ]
this is mainly a bankroll risk issue. i think anybody who can afford to lose it should take the biggest bet.

[/ QUOTE ]

That's sort of the question. How much can you psychologically handle losing from your bankroll all at once, except that here you actually have to give up EV if you forgo a larger bet.

[fnord_too]

I picked the biggest bet, because the money is still within my comfort level and I think the greatest EV is the way to go here. I liked the bit with two having the same EV, but one having more variance, and am surprised a bit to see between those two the higher variance one winning.

One thing I am probably weird for thinking about: I look at all these as really being less the actual pay offs in each direction due to taxes, so all of the choices are scaled down.

[gmanko]

I'd invite him in for coffeee, and then roll him.

[bakku]

[ QUOTE ]
this is mainly a bankroll risk issue. i think anybody who can afford to lose it should take the biggest bet. for me i chose the 400bb,-150bb bet.

[/ QUOTE ]

So instead of losing your whole roll in 4 months you'd lose it in 3?

[imported_transmitt]

I thought about this for while, and I decided that the answer depended on some simple variables. Nominally, the number of times that we can take the proposition and the health of our bankroll.

(1) Assume that you flip the coin once, and your bankroll is sufficiently large enough to sustain a loss of a given bet without its health being too adversely affected.

(2) Assume that you can flip the coin once, and your bankroll is not sufficiently large enough to sustain a loss of a given bet without its health being too adversely affected.

(3) Assume that you flip the coin a predetermined number of times, and your bankroll is sufficiently large enough to sustain the loss of a given bet without its health being too adversely affected.

(4) Assume that you flip the coin a predetermined number of times, and your bankroll is not sufficiently large enough to sustain the loss of a given bet without its health being too adversely affected.

In both cases (1) and (2), you are only able to flip the coin one time. Because of of this, the mathematical expectation of the proposition is irrelevant. This is because mathematical expectation is the amount a bet will average over the long run. In the case of one coin flip there is no long run, and so clearly the correct decision is the one where you win 160 BBs when the coin is heads, and win 50 BBs when it is tails. This is the wager that maximizes the BBs you can win while entailing no risk, and ensuring that you do in fact win something.

Cases (3) and (4) are more interesting. I believe that in case (3), as the predetermined number of coin flips increases in value, you should choose propositions with increased mathematical expectation, and thus with increased variance. This is because variance is obviously a factor only in the short term. Case (4) on the other hand, requires you to choose the proposition that affords you the highest mathematical expectation for the variance you can sustain.

Just my two cents.

- mitt

[Michael Davis]

If I lose the toss do I have to pay that amount of money right there? Can I keep a running tab? This would make the question too simple, I suppose.

Do I have options to take more tosses, or is this a one shot deal?

-Michael

[MicroBob]

[ QUOTE ]
I would think that if you could flip 100 times, even more risk averse people would take the highest wager option because over 100 tries, the likelihood of coming out worse than the guaranteed money on every flip option would be very small.

[/ QUOTE ]


Yes...this occured to me after I posted.

I was kind of waiting fore someone to blast me on this.