not another demon problem (simple (sorta) April problem #2)

[EXTRAPOLATER]

Help!

A demon has invaded my life.
This bitch has given me one last opportunity to communicate with the outside world and I have chosen here as the problem that has been posed to me might best be tackled by those on this forum.
This foul creature has transformed my knees into lettuce. Not sure how but if you have ever had that happen to you then you know that lettuce-knees are excruciating.

Here is the deal this twisted necromancer has proposed to me...

If I can turn a profit in this beast's foul casino then I can retain my life. To break even will not do--I must turn a profit to proove my worth. I am told that every game available will have a negative house advantage but I must still beat these odds to retain my existence. I cannot decide what to do and pray that someone will help me to improve my chances for survival in this sick game.

Here is my bankroll: the beast has given me two foul-smelling amber chips, each worth a supposed 50 unholy units. I am told that each game has a minimum bet of 50 and a maximum bet of 100. I cannot bet any winnings so I am allowed to make either one or two bets to save my life.

A 52-card playing deck is used for each game.

The games are as follows:

A) pick a spade--pays +500

B) pick no spade--pays +100

C) pick a black card--pays +110

D) pick no face card--pays -110

E) pick no face or ace--pays +100


I must choose what to play and can stop at any time. I have two bets maximum which I can make.
Obviously, I must make at least one bet as I MUST turn a profit to live.

Breaking even will not do...I shall die more violently than if I lose, or so I am told by this lurker from the threshold.

I see that the odds are in my favour.
But, I must still beat these odds to save my soul.

What should I do in order to increase my chances of survival?

What should I play and what are my odds of living?

 

[smurphy]

Holy shit!

..ummmm. sounds like "no spade" for +100 is player advantage.:shrug:

Good luck. Don't ever play the devil unless you are a very good fiddler.

 

[MrChristo]

One of you bets has to be C) pick a black card--pays +110...

...given a "push" won't save your life!

Do you have to make both bets at once, or can you make one...nope never mind...

...BOTH bets have to be C) pick a black card--pays +110...

(Take those winning to the foul smelling cashier :142smilie )

 

[marine]

I'd go with Pick no face card for one unit.

if you can't do that you deserve to die.


That is the one bet that is most likely to hit for you. Forget the payouts, you need to turn any profit, which means you just need to win one bet.

If I lost that, then I would follow up with picking a black card.

 

[MadJack]

If I lost that, then I would follow up with picking a black card.

then you break even and die.

i would do this

B) pick no spade--pays +100

if i lose do this.

C) pick a black card--pays +110

 

[freelancc]

What should I do?

kurby kurby kurby

 

[SixFive]

:mj07: :scared :mj01: :00x10 :00x1 :00x25 :00x27 :00x32 :00x7

play don't pick a face card.

Extrapolator, u sure have a warped mind. Maybe u should write a book in the wee hours instead of coming up with these weird hypothetical problems? :shrug: I'm sure you'd do an excellent job in the Sci-Fi area.

 

[KotysDad]

Play D for 1 unit. If you win stop. If you lose play C for the other unit. Your chances of survival are 46/52 (.884)

The next best option is B followed by C if you lose. Your chances there are 7/8 (.875)

 

[marine]

then you break even and die.

i would do this

B) pick no spade--pays +100

if i lose do this.

C) pick a black card--pays +110

That's a big ole negative there old timer.

I am putting one unit on picking a black card and that pays +110.

Remember.. 1 chip = 50 units.
Which means in a 1 unit bet, I get back 55 units. right?

And on the that first bet I made I lost.. I lost 1 chip (50 units)

which means I profited 5 units... or, 1/10 of a chip.
And its a profit.
Did she turn your brain to lettuce just like your knees?

:mj07:

 

[EXTRAPOLATER]

Thank-you one and all!
With your help I was able to achieve nearly a 90% chance for survival, and with odds like those who needs no-juice Thursdays?!

The beast has fled back to whatever satanic hole she had crawled out of. My knees have been restored and I had salad for dinner.

I would like to respond in full to all who helped to save my life but I am currently rather wiped out by my encounter with the netherworld. Best I leave my responses until tomorrow as, in my current state, I don't even think I can take a coherent shot at tomorrow's baseball board.
(might be a first)
Perhaps they're all night games.
Regardless, my life has been saved by these responses.
One provided me an 87.5% chance of survival.
Another one, an 88.5% chance of survival (actually 88.46% but still slightly better).
I shall elaborate in the 'morrow.

Hendrix bless madjacksports.com!

Long live madjacksports.com!

:00hour :00hour :00x1 :00hour :00hour

 

[smurphy]

I am putting one unit on picking a black card and that pays +110.

Remember.. 1 chip = 50 units.
Which means in a 1 unit bet, I get back 55 units. right?

And on the that first bet I made I lost.. I lost 1 chip (50 units)

which means I profited 5 units... or, 1/10 of a chip.
And its a profit.

:00x33












:00x4

 

[marine]

i dont get it?

 

[EXTRAPOLATER]

Holy shit!

..ummmm. sounds like "no spade" for +100 is player advantage.:shrug:

Good luck. Don't ever play the devil unless you are a very good fiddler.

I'd sure play this one at the paradise casino.
75% chance of winning with a 50% break-even mark on the line.
However, D actually has a slightly better probability--77% (actually 76.92%). With the slightly better payout for "no spade" we've got a value problem that I've tried, unsuccessfully, to get some feedback on previously.

i.e.
B) "no spade" pays +100 with a 75% prob.
Gives a +25 "value indicator". 75-50=25.
D) "no face" pays -110 with a 77% prob.
Gives a +24 value indicator. 77-53(for -110's)=24.

Ignoring my original scenario, which is the better game?

ROI
===
B) 75 x +1 = 75
....25 x -1 = -25
============
for a 50% return on investment.

D) 77 x .91 = 70
....23 x -1 = -23
=============
for a 47% return on investment.

Is the reduced payout worth the greater probability?
Both my VI and the ROI suggest not, but I've posted other examples where the answer is far from clear, to me at least.

In the demon scenario, you could try this on the first play but if you lost then you would need to try a game with a better than even-money payout as breaking even would mean death.

Best I move on...
maybe to grab a brew first.

:toast:

 

[EXTRAPOLATER]

One of you bets has to be C) pick a black card--pays +110...

...given a "push" won't save your life!

Do you have to make both bets at once, or can you make one...nope never mind...

...BOTH bets have to be C) pick a black card--pays +110...

(Take those winning to the foul smelling cashier :142smilie )

You're right, in the sense that playing C is needed if you drop the first play. Only two options pay better than even money and the 50% probability sure beats the 25% on pick a spade.

Actually, if you had to decide what you were playing beforehand then two plays of C WOULD be your best chance for survival, or a 75% chance of survival. Having the option to stop after one play makes a couple of other options better though, again, C is the way to go if you lose the first bet.

To your health.
:toast:

 

[EXTRAPOLATER]

I'd go with Pick no face card for one unit.

if you can't do that you deserve to die.


That is the one bet that is most likely to hit for you. Forget the payouts, you need to turn any profit, which means you just need to win one bet.

If I lost that, then I would follow up with picking a black card.

Good work.
Despite the less-than even money odds, this is still the best chance for a hit. Slightly better than picking no spade.

A 77% chance of a win (10/13=76.92%) over the 75% chance for no spade. And, of course, if no win on this then you need BETTER than even-money on the next to turn a profit.

try 1: 77%
if loss then
try 2: 23% (lose first) x 50% (pick black) = 11.5%
for an overall 88.5% chance of survival.

My guess is that you're up.
Continued success.
:00x1

 

[EXTRAPOLATER]

then you break even and die.

i would do this

B) pick no spade--pays +100

if i lose do this.

C) pick a black card--pays +110

When I first formulated this problem there was only A to C, before adding D and E. This is the best option without D & E and also the second best option for survival.

75%
+ (25% x 50%)
=87.5% chance of survival.

If the first play was 55 to win 50 then you'd be right about marine's being a break-even proposition. Bet #1, on D, would only be a risk of 50 though (win 45), so the +110 on the second play still would mean survival.
I guess that marine already pointed that out.

Formulated slightly differently and this would, in fact, be the best odds.

Sure would like to make a Superbowl party someday.
I guess '09 means another opportunity.

Keep on Chooglin'
:toast:

 

[EXTRAPOLATER]

play don't pick a face card.

Extrapolator, u sure have a warped mind. Maybe u should write a book in the wee hours instead of coming up with these weird hypothetical problems? :shrug: I'm sure you'd do an excellent job in the Sci-Fi area.

Don't pick a face, again, is the best option for your first play. Losing that, however, you can't turn a plus by playing it a second time.

Appreciate the other words. Sorta a compliment, I guess.
Wrote some sci-fi about 10-15 years ago. Never submitted anything, though (just short stories). Still dreaming about writing a book someday.

peace
:toast:

 

[EXTRAPOLATER]

Play D for 1 unit. If you win stop. If you lose play C for the other unit. Your chances of survival are 46/52 (.884)

The next best option is B followed by C if you lose. Your chances there are 7/8 (.875)

Another life saver--right on, bro!
Only one to provide my chances of survival, as well.

May you shred your books.
:00x1

 

[EXTRAPOLATER]

I guess that closes this.
Might try, again, to get some idea of how others here assess value, but I think I might leave such brain-teasers alone in the future.

Unless, of course, she returns.:scared

Thanks for the responses.

:mj06:

 

[SixFive]

Don't pick a face, again, is the best option for your first play. Losing that, however, you can't turn a plus by playing it a second time.

Appreciate the other words. Sorta a compliment, I guess.Wrote some sci-fi about 10-15 years ago. Never submitted anything, though (just short stories). Still dreaming about writing a book someday.

peace
:toast:

definitely. You're way over my head, but I know you have talent.

I actually have a friend who has written and published some sci-fi. It's a tough business to get into even with talent. Good luck with it!