Gambling skills topic

[sierra]

Seems like quite a lot of you fuckers fancy yourselves as keen gamblers, let's put this to the test.

Level 01, Warm Up: I offer to play a game with you, where I will throw two fair dice and pay you $X, where X is the product of the two numbers on the dice. I will charge you a price $P to play the game. Your profit is, of course, $(X - P). For example, if I roll two 6s, you will receive 6 * 6 = $36, and if I charged you $20 to play, your profit is 36 - 20 = $16.

Question: What is the maximum price, denoted $P`, that you would pay to play this game?

[Grace]

Well consider all 21 different Possible Outcomes.

1 * 1 - -$19
1 * 2 - -$18
1 * 3 - -$17
1 * 4 - -$16
1 * 5 - -$15
1 * 6 - -$14
2 * 2 - -$16
2 * 3 - -$14
2 * 4 - -$12
2 * 5 - -$10
2 * 6 - -$8
3 * 3 - -$11
3 * 4 - -$8
3 * 5 - -$5
3 * 6 - -$2
4 * 4 - -$4
4 * 5 - Neutral
4 * 6 - $4 Profit
5 * 5 - $5 Profit
5 * 6 - $10 Profit
6 * 6 - $16 Profit

This means you have a 1/12 Chance of Profiting, and at max your profit is only 80% extra, so guaranteed once you win the Adrenaline will make you play again, your still below your Starting Money.

I Wouldn't Play.

[sierra]

Well consider all 21 different Possible Outcomes.

1 * 1 - -$19
1 * 2 - -$18
1 * 3 - -$17
1 * 4 - -$16
1 * 5 - -$15
1 * 6 - -$14
2 * 2 - -$16
2 * 3 - -$14
2 * 4 - -$12
2 * 5 - -$10
2 * 6 - -$8
3 * 3 - -$11
3 * 4 - -$8
3 * 5 - -$5
3 * 6 - -$2
4 * 4 - -$4
4 * 5 - Neutral
4 * 6 - $4 Profit
5 * 5 - $5 Profit
5 * 6 - $10 Profit
6 * 6 - $16 Profit

This means you have a 1/12 Chance of Profiting, and at max your profit is only 80% extra, so guaranteed once you win the Adrenaline will make you play again, your still below your Starting Money.

I Wouldn't Play.

No, the price of $20 was just an example; it can take any value. My question is what is the maximum price I could charge at which you would still agree to bet? $5? $10? $25.70?

Hint: there is only one correct answer.

[A.K.B.]

$0

obvious

[Scruffy the janitor]

$11 says i. or near that atleast

[sierra]

$0

obvious

Obviously wrong. Clearly if I charge you $1, you are still virtually guaranteed a profit (with the exception of rolling two 1s). So by cutting yourself off at $0, or indeed at too low a price in general, you are limiting your profit-making ability.

[sierra]

$11 says i. or near that atleast

Interesting choice, what makes you say that?

[milagros]

12.25

[jaytea]

$12.25 obviously

ps. come on msn

[Xiphias]

ofcourse as human I'd pay as little as possible

but I guess it could be 12.66666666666666

because in the long term this would in average make the profit to 0$

maybe I'm thinking to simple here, hehe.. haven't learned "proposition" math yet so.. and not so good with these things.. but what ever =D

Code: Select all

Dice  Outcome: x	$(x-p)
1*1		1	        -11.67
1*2		2	        -10.67
1*3		3	        -9.67
1*4		4	        -8.67
1*5		5	        -7.67
1*6		6	        -6.67
2*2		4	        -8.67
2*3		6	        -6.67
2*4		8	        -4.67
2*5		10	        -2.67
2*6		12	        -0.67
3*3		9	        -3.67
3*4		12	        -0.67
3*5		15	        2.33
3*6		18	        5.33
4*4		16	        3.33
4*5		20	        7.33
4*6		24	        11.33
5*5		25	        12.33
5*6		30	        17.33
6*6		36	        23.33
Overall	  266	       0.00


Average: p		12.66666667	

could be nice with some explanation with the other guesses: mila and jt
or would that ruin the quiz?

[jaytea]

expected return is [(6+1)/2] * [(6+1)/2] = 3.5^2 = 12.25

and your little table is incorrect. 2 * 1 is not the same as 1 * 2 because you're using 2 different dice. if you did it right you'd get a total sum of 441, with 36 possibilites. 441 / 36 = 12.25

haven't learned "proposition" math yet

this doesnt have anything to do with the other thread (propositional logic/calculus)

[Scruffy the janitor]

Question: What is the maximum price, denoted $P`, that you would pay to play this game?

the question should be more accurate, although i assumed sierra wants the amount where you break even in endless amount of dice throws. 12.25 might be the value where you break even but no gambler would play the game with just the chance of breaking even, thus the $ maximum should be considerably lower than 12.25

[jaytea]

Question: What is the maximum price, denoted $P`, that you would pay to play this game?

the question should be more accurate, although i assumed sierra wants the amount where you break even in endless amount of dice throws. 12.25 might be the value where you break even but no gambler would play the game with just the chance of breaking even, thus the $ maximum should be considerably lower than 12.25

the optimal amount to play with is 0$, thats obvious. but his question is perfectly accurate, it's just the situation is unrealistic, no gambler would ever be faced with this situation in practice.. but you'd use similar math to calculate odds in other more practical situations. so the point was clearly to find the break even value

[sierra]

$12.25 is incorrect, and I don't know how you calculated this. It is slightly too high. Please show your expected value calculations, that I may laugh hysterically at your shortcomings.

[Zweq]

I do not know answer to this question because I do not want to read 5 line question/introduction in exams nor here because I do have hurry to go play elma which matters just as less as this question

[Igge]

I would have done it like 441/36=12,25 then nabed around and got 9.33333 also, but probably even further away from the corect answer.

[sierra]

The shameful fact about this pathetic topic is that Scruffy The Janitor is the closest so far to the correct answer. Members of Mopolauta, come on, essay to correct this horrific state of affairs.

[sierra]

Question: What is the maximum price, denoted $P`, that you would pay to play this game?

the question should be more accurate, although i assumed sierra wants the amount where you break even in endless amount of dice throws. 12.25 might be the value where you break even but no gambler would play the game with just the chance of breaking even, thus the $ maximum should be considerably lower than 12.25

the optimal amount to play with is 0$, thats obvious. but his question is perfectly accurate, it's just the situation is unrealistic, no gambler would ever be faced with this situation in practice.. but you'd use similar math to calculate odds in other more practical situations. so the point was clearly to find the break even value

Why should no gambler ne faced with this situation in practice? I can quite easily imagine being in Vegas, with some red-faced hick bellowing, "Come on come all, for just $15 I will pay you whatever number appears on this here dice roll", and one would have to instantaneously calculate whether one was getting a good or a bad deal. I think you wrote this as a result of the more fundamental character deficiency of you being of the category of men who like to physically love another man.

[milagros]

$12.25 is incorrect, and I don't know how you calculated this. It is slightly too high. Please show your expected value calculations, that I may laugh hysterically at your shortcomings.

sierra pls
if you dont know fuck about math, dont open topic like this (or gay jaytea) one

a few diff solutions :
1. for totally uncorrelated X and Y, E(XY) = E(X)E(Y) = 3.5^2 = 12.25

2. all possible incomes divided by total nuber of possibiliites :
(1*2 + 1*3 + ...6 * 6) / (6^2) = (1 + 2 +... + 6) * (1 + 2 + ... + 6) / (6^2) = 21^2 / 6 ^ 2 = 12.25

[A.K.B.]

please what the fuck this isn't highschool maths class, shut the fuck up sierra and stick with english.

[sierra]

$12.25 is incorrect, and I don't know how you calculated this. It is slightly too high. Please show your expected value calculations, that I may laugh hysterically at your shortcomings.

sierra pls
if you dont know fuck about math, dont open topic like this (or gay jaytea) one

a few diff solutions :
1. for totally uncorrelated X and Y, E(XY) = E(X)E(Y) = 3.5^2 = 12.25

2. all possible incomes divided by total nuber of possibiliites :
(1*2 + 1*3 + ...6 * 6) / (6^2) = (1 + 2 +... + 6) * (1 + 2 + ... + 6) / (6^2) = 21^2 / 6 ^ 2 = 12.25

Dude I was joking, of course $12.25 is the right answer.

[nony]

12,25 is wrong because there are 15 possibilities to throw the dices with bigger amount and 21 with low r. since i'm in the car waiting for someone I find it difficult to give u exacr ansWer but i'd say ~11,3.

EDIT: didn't see sierra's post. hmmm, really? the calculation for 12,25 is correct, but still, as a gambler, i'd want to be sure i'm in the middle, with 18 throws win. anyway...

[milagros]

12,25 is wrong because there are 15 possibilities to throw the dices with bigger amount and 21 with low r. since i'm in the car waiting for someone I find it difficult to give u exacr ansWer but i'd say ~11,3.

i want to play roulette with you
if i guess the number right, i will get 10000000000000x more from you
you know, there is 1 number where i earn and 36(or 37 in usa roulette) where i loose
of course we can repeat it over and over again

[sierra]

It's important to note that even though $12.25 is the expected return, to say that you should pay it assumes risk-neutrality. In reality most people are risk-averse, meaning they will in fact gamble less than the expected value. It is also possible for some people to be risk-loving; being prepared to pay above $12.25 simply because they love the gamble. Technically everyone who gambles in casinos is risk-loving, because all the games have a negative expected return. So when I said earlier that 'there is only one answer', that was only true under the assumption of risk-neutrality.

[milagros]

lev02?

[sierra]

Lev 02 - Flat Track:

As the winner of a competition, I offer you one of three prizes -

a) $100,000 now
b) $19,000 for each of the next 10 years
c) $6,500 next year and increasing thereafter by 5% a year forever

The interest rate is 12%. Which prize should you take?

[Scruffy the janitor]

C sounds like the best

[sierra]

To give a convincing answer you obviously have to provide some kind of reason.

[teajay]

As I need money NOW, I will choose A. Can you pm me?

[milagros]

Lev 02 - Flat Track:

As the winner of a competition, I offer you one of three prizes -

a) $100,000 now
b) $19,000 for each of the next 10 years
c) $6,500 next year and increasing thereafter by 5% a year forever

The interest rate is 12%. Which prize should you take?

of course c) because
lim (t->inf) a/c = 0
lim (t->inf) b/c = 0

that question is not good set anyway because if you give me $100,000, the bank can have higher interest that 5% and that one may be better, same for b). Depends on what can I do with that money I have atm

[milagros]

oh i havent noticed that 12% at the bottom, so let me calculate:)
that c) is meatn that next year 1'll get 6500, year after 6500*1.05, year after 6500*1.05^2, ...?

[milagros]

with a) you will have 310585 after 10 years
with b) you will have 333425 after 10 years
so b > a
but however c) is meant, no matter how interest is calculated, the limit to infinity is higher

[teajay]

You have some convincing answers milagros.

[jaytea]

mila' answer didn't convince me, and he seems to have missed the point of the question. it's not just a "which gives you more money", which is simple to calculate (but then again, sierra's first question was max simple too) but theres probably some economic principles to consider

~6,000 every year isnt going to feel like much, especially once you start earning a salary. you're likely to appreciate an immediate 100,000 a lot more. then you need to think about how much you could earn if you invested the money properly

[teajay]

The only reason why I chose for option A, is the reason that I get the money now and not in 2009.

[sierra]

milagros has indeed misunderstood the question. You don't earn any interest on the money. In b) for example, you will only get the nominal sum of $19,000 every year.

that c) is meatn that next year 1'll get 6500, year after 6500*1.05, year after 6500*1.05^2, ...?

Correct. In nominal terms.

I realized you needed one extra bit of information: the inflation rate is assumed to be 0% forever.

then you need to think about how much you could earn if you invested the money properly

Well I told you in the question, the interest rate is 12%. Maybe I should explain it a little clearer: 12% is the (annual) interest rate, that is, the rate you could earn on risk-free assets such as bank deposits or government bonds. There is no interest paid on the prize money, so rather than you earning 12%, you are in fact foregoing 12% every year. Perhaps this well-known finance motto will give you a clue; "A dollar today is worth more than a dollar tomorrow"...

P.S.:

it's not just a "which gives you more money"

On the contrary, that is precisely the relevant calculation.

[nony]

not gambling, but bumped into this recently:
i have an empty retail space on 5th avenue, similar to the ones close to me(as surface, traffic, finishing etc). hence i know the rent to ask. i want to make a gimmick though, in order to convince a retailer: i want to receive 85% of the normal rent/sqm/month in the 1st year, 90% of the normal rent/sqm/month in the 2nd year, 95% in the 3rd and 100% in the 4th and 5th. still, i don't want to lose anything, compared to what i should get when having 100% the whole 5 years - the duration of the contract.
How much more rent should i ask?

ps: if previous wasn't answered then do both.

[sierra]

Lev 02 - Flat Track:

As the winner of a competition, I offer you one of three prizes -

a) $100,000 now
b) $19,000 for each of the next 10 years
c) $6,500 next year and increasing thereafter by 5% a year forever

The interest rate is 12%. Which prize should you take?

Might as well provide the solution. The method is to convert all future cash flows into present value. It's no use learning that you will receive $5,000 in six years' time if you don't know how much you can buy with $5,000 by then, hence one way to get around this is to convert the $5,000 into present day terms, by discounting every future cash flow in every time period by the relevant discount rate. In these questions the annual discount rate is 12%, because the annual interest rate is 12%. To see this more clearly, consider how the value of $1 will change over the course of a year:

Time=0 Time=1
--------- ---------

$1 -> $1*(1.12) = $1.12

Using this relationship, it is straightforward to calculate how much $1.12 received in 1 year is worth in present day terms: $1.12/(1.12) = $1. Similarly, $50 received in 1 year's time equals $50/(1.12) = $44.64 in present value. If this idea seems odd to you, remember that it is only so because one can earn 12% in bank deposits/government bonds for zero risk. If the interest rate was 0%, then $50 in 1 year would be no different to $50 today.

So, back to the problem. I'll calculate the present value of those cash flows.

a) PV[$100,000] = $100,000

b) PV[$19,000 for each of the next 10 years] = {19000/(1.12) + 19000/(1.12)^2 + ... + 19000/(1.12)^10} = {19000/(0.12) - (19000/[0.12])*(1/[1.12]^10)} = $107,354.24

c) PV[$6,500 next year and increasing thereafter by 5% a year forever] = 6500/1.12 + (6500*1.05)/[(1.12)^2] + ... = 6500/(0.12 - 0.05) = $92,857.14

Hence, b) is the most valuable prize.

[teajay]

Still I'd stick with option A.

[sierra]

Still I'd stick with option A.

You're a dumbass then!

[Zweq]

or d) something you cant measure in money or matter. like I got this teddybaer from childhood, man it's more than 100k$ anyday

[teajay]

Sierra, the doctor diagnosed that I'm terminally ill. If I die in six months, what's money worth then next year?

[voidak]

ye fuck the rest!

gimme one hundred thousands bucks now!

[sierra]

Sierra, the doctor diagnosed that I'm terminally ill. If I die in six months, what's money worth then next year?

Prize B is always worth more, regardless of how much one may have received of it at any given point in time. Your argument is like preferring to win a $10 lottery prize tomorrow over a $1,000,000 lottery prize a week later.

Of course I see the point you were trying to make, but this is a very short-sighted approach to investment, and a source of a lot of poor financial management in real life. A prime example is R&D (research and development); a company probably won't see the returns to R&D investment for a long time, and to a naiive observer they will appear to be pouring money down the drain, but one day they stumble upon the iPod, or a cure for arthritis, or a fuel without greenhouse gas emissions, and then the payoff becomes very apparent.

[teajay]

Suar, but the monies you made us too choose out didn't differ much. As I'm a very inpatient individual, I want to have money now, if the difference is within 10%, it doesn't really matter.

[nony]

in theory sierra's calculation is correct, no doubt about it. it's much wiser and better financially to take b option.
though theory's not good everywhere. for exemple, in countries with falling/emerging economy, taking 100k now is far from being the best choice.
eg: zimbabwe has a crashing economy where a brick now has the price of what used to be a house few years ago. of course, if one would take the money he'd... flee.
eg2: emerging countries with high yields. in romania 100k now will easy be 150k by next january. considering a slight yearly drop of 10% from that 50% increase, though less likely, i'd still be close to millionaire in 10yrs. the same with many other eastern european neighbours.
so, if u ask me, it would take me a little more than 5 seconds to ask you for 100k.
but then again, in theory, 19k/yr is perfectly accurate.

[Scruffy the janitor]

i would take the 100k right now and shove it up my ass for no reason

[Ky.Jelly]

there should be a sports betting thread, give tips etc, Im gambling all the time would good to see what you pimps think as well