WizardofEngland
WizardofEngland
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November 2nd, 2010 at 5:28:51 AM permalink
Ok, my attempt at a question for the Wizard,

Mr Burns has taken his mental pills and as a result offers you these crazy ideas for your Christmas Bonus.

1) $10,000 cash, no questions asked.
2) $5,000 cash and 10 spins on a single zero roulette wheel with 1 extra 18 and 1 extra 19 on the wheel, but you can only place outside bets.
3) $5,000 cash and 20 hands of six-deck blackjack (standard rules) where blackjack pays 10-1 (including splits)
4) $5,000 cash and 20 hands of three card poker, dealer exposes one card.

Which offer would you take?
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
MathExtremist
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November 2nd, 2010 at 8:41:19 AM permalink
Quote: WizardofEngland

Ok, my attempt at a question for the Wizard,

Mr Burns has taken his mental pills and as a result offers you these crazy ideas for your Christmas Bonus.

1) $10,000 cash, no questions asked.
2) $5,000 cash and 10 spins on a single zero roulette wheel with 1 extra 18 and 1 extra 19 on the wheel, but you can only place outside bets.
3) $5,000 cash and 20 hands of six-deck blackjack (standard rules) where blackjack pays 10-1 (including splits)
4) $5,000 cash and 20 hands of three card poker, dealer exposes one card.

Which offer would you take?



Depends on the table limits and my bankroll. If I can bring more money to the table and bet big, #3 is the best bet. Blackjack pays 10-1 makes the game over 40% +EV, and if you include splits then you'd also split any pair of 10s and have a decent shot at hitting at least one blackjack in your 20 hands. If I'm stuck with the initial $5000, none of the other options have an EV of > 100% (and with no variance, to boot) so I pick #1.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
miplet
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November 2nd, 2010 at 8:58:10 AM permalink
Quote: MathExtremist

Depends on the table limits and my bankroll. If I can bring more money to the table and bet big, #3 is the best bet. Blackjack pays 10-1 makes the game over 40% +EV, and if you include splits then you'd also split any pair of 10s and have a decent shot at hitting at least one blackjack in your 20 hands. If I'm stuck with the initial $5000, none of the other options have an EV of > 100% (and with no variance, to boot) so I pick #1.


One card poker has a player advantage of 3.48% on the 5/4/1 paytable.
Option 2 has a player advange, but I've never seen a roulette wheel with 39 numbers.
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WizardofEngland
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November 2nd, 2010 at 10:29:43 AM permalink
Quote: MathExtremist

Depends on the table limits and my bankroll. If I can bring more money to the table and bet big, #3 is the best bet. Blackjack pays 10-1 makes the game over 40% +EV, and if you include splits then you'd also split any pair of 10s and have a decent shot at hitting at least one blackjack in your 20 hands. If I'm stuck with the initial $5000, none of the other options have an EV of > 100% (and with no variance, to boot) so I pick #1.



The limits would be $10,00 max per bet, but you can't bring your own money.
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
WizardofEngland
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November 2nd, 2010 at 10:30:20 AM permalink
Quote: miplet

One card poker has a player advantage of 3.48% on the 5/4/1 paytable.
Option 2 has a player advange, but I've never seen a roulette wheel with 39 numbers.



It is only a theoretical wheel...... ;-)
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
JerryLogan
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November 2nd, 2010 at 10:41:54 AM permalink
That's easy. The only true option is the $10,000 cash. All that other stuff is nonsense laced with fluff.
Wizard
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November 2nd, 2010 at 10:45:35 AM permalink
Quote: WizardofEngland


1) $10,000 cash, no questions asked.
2) $5,000 cash and 10 spins on a single zero roulette wheel with 1 extra 18 and 1 extra 19 on the wheel, but you can only place outside bets.
3) $5,000 cash and 20 hands of six-deck blackjack (standard rules) where blackjack pays 10-1 (including splits)
4) $5,000 cash and 20 hands of three card poker, dealer exposes one card.

Which offer would you take?



First, it should be noted that 18 and 19 are both red, making the probability of a winning red bet 20/39.

So the advantage on (2) would be 1/39 = 2.56%.

The probability of a winning blackjack is 4.53%. So 10-1 on a blackjack is worth an extra 8.5*0.0453 = 38.5%! I won't fuss with the rule about after splitting. Let's assume the normal house edge is 0.5%, so (3) is worth 38%.

(4) As I show in my page on flashing Three Card Poker dealers, the advantage seeing one card is 3.48%.

So I would go with option (3) for sure.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
WizardofEngland
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November 2nd, 2010 at 10:51:59 AM permalink
Quote: Wizard

First, it should be noted that 18 and 19 are both red, making the probability of a winning red bet 20/39.

So the advantage on (2) would be 1/39 = 2.56%.

The probability of a winning blackjack is 4.53%. So 10-1 on a blackjack is worth an extra 8.5*0.0453 = 38.5%! I won't fuss with the rule about after splitting. Let's assume the normal house edge is 0.5%, so (3) is worth 38%.

(4) As I show in my page on flashing Three Card Poker dealers, the advantage seeing one card is 3.48%.

So I would go with option (3) for sure.



what would you make the payout on blackjack be, so it falls somewhere around the 2.5-3.5% shown on the other bets?
how does element of risk effect these bets?
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
rdw4potus
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November 2nd, 2010 at 11:44:21 AM permalink
Quote: WizardofEngland

Quote: Wizard

First, it should be noted that 18 and 19 are both red, making the probability of a winning red bet 20/39.

So the advantage on (2) would be 1/39 = 2.56%.

The probability of a winning blackjack is 4.53%. So 10-1 on a blackjack is worth an extra 8.5*0.0453 = 38.5%! I won't fuss with the rule about after splitting. Let's assume the normal house edge is 0.5%, so (3) is worth 38%.

(4) As I show in my page on flashing Three Card Poker dealers, the advantage seeing one card is 3.48%.

So I would go with option (3) for sure.



what would you make the payout on blackjack be, so it falls somewhere around the 2.5-3.5% shown on the other bets?
how does element of risk effect these bets?



if X is the number of additional units that a BJ would need to pay,and you want the game to return 3.35% (.65% HA-4% PA adjustment= 3.35% PA), then X*.0453=4%, so X=3%/.0453, so X=.883 units. So 2.38:1 would result in a 3.35% player advantage. Maybe call it 2.5:1?
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
rdw4potus
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November 2nd, 2010 at 11:48:05 AM permalink
Quote: Wizard

First, it should be noted that 18 and 19 are both red, making the probability of a winning red bet 20/39.

So the advantage on (2) would be 1/39 = 2.56%.

The probability of a winning blackjack is 4.53%. So 10-1 on a blackjack is worth an extra 8.5*0.0453 = 38.5%! I won't fuss with the rule about after splitting. Let's assume the normal house edge is 0.5%, so (3) is worth 38%.

(4) As I show in my page on flashing Three Card Poker dealers, the advantage seeing one card is 3.48%.

So I would go with option (3) for sure.



You would take option 3 over option 1? I think that if you sat down with $5000 and played 20 hands of a game with a 3.48% PA, you'd have a $9911 expected bankroll after your session.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
WizardofEngland
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November 2nd, 2010 at 11:50:35 AM permalink
Quote: rdw4potus

Quote: Wizard

First, it should be noted that 18 and 19 are both red, making the probability of a winning red bet 20/39.

So the advantage on (2) would be 1/39 = 2.56%.

The probability of a winning blackjack is 4.53%. So 10-1 on a blackjack is worth an extra 8.5*0.0453 = 38.5%! I won't fuss with the rule about after splitting. Let's assume the normal house edge is 0.5%, so (3) is worth 38%.

(4) As I show in my page on flashing Three Card Poker dealers, the advantage seeing one card is 3.48%.

So I would go with option (3) for sure.



You would take option 3 over option 1? I think that if you sat down with $5000 and played 20 hands of a game with a 3.48% PA, you'd have a $9911 expected bankroll after your session.



Hmm, this is getting interesting. so option 1 is best? even with 10-1 payout?
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
rdw4potus
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November 2nd, 2010 at 11:55:16 AM permalink
Quote: WizardofEngland

Quote: rdw4potus

Quote: Wizard

First, it should be noted that 18 and 19 are both red, making the probability of a winning red bet 20/39.

So the advantage on (2) would be 1/39 = 2.56%.

The probability of a winning blackjack is 4.53%. So 10-1 on a blackjack is worth an extra 8.5*0.0453 = 38.5%! I won't fuss with the rule about after splitting. Let's assume the normal house edge is 0.5%, so (3) is worth 38%.

(4) As I show in my page on flashing Three Card Poker dealers, the advantage seeing one card is 3.48%.

So I would go with option (3) for sure.



You would take option 3 over option 1? I think that if you sat down with $5000 and played 20 hands of a game with a 3.48% PA, you'd have a $9911 expected bankroll after your session.





Hmm, this is getting interesting. so option 1 is best? even with 10-1 payout?




Well, ok. #3 as written is by far the best option, #3 as adjusted to fall in line with the other options is slightly inferior to option 1.

*edit* Also, these nesting quotes are awesome. Thanks, JB.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
DJTeddyBear
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November 2nd, 2010 at 12:20:18 PM permalink
Quote: Wizard

First, it should be noted that 18 and 19 are both red, making the probability of a winning red bet 20/39.

So the advantage on (2) would be 1/39 = 2.56%.

I would also go with option 3, but the Roulette table has a bet that's better than Red: Both 18 and 19 are in the middle dozen. Since you'll win 28 (14*2) for each 39 bet, and lose 25 out of 39, there's a 3/39 = 7.69% advantage when betting the middle dozen.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
DJTeddyBear
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November 2nd, 2010 at 12:21:43 PM permalink
Quote: WizardofEngland

Hmm, this is getting interesting. so option 1 is best? even with 10-1 payout?

Yeah, except if that's your attitude, you might as well cancel your plans to spend Christmas in Sin City....
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
mkl654321
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November 2nd, 2010 at 12:27:40 PM permalink
I'd take the ten grand and run, because if Mr. Burns owns the casino, the games are all rigged, and I'd lose every bet.

It's also interesting to seriously consider this question in the light of EV vs. utility. Sure, by taking the $5000+ +EV bets, your overall expected value is greater than $10,000, but is it worth the (considerable) risk of winding up with much less than $10,000, despite your advantage?

People make this decision all the time, but mostly in the reverse context, for example when they buy fire insurance. It is obviously -EV to buy it, but they are risk-averse (probably, rationally so). When Mr. Burns hands you the ten grand, and that will pay for that $9000 Lasik eye surgery you've wanted for years, you'd be crazy to risk that for a relatively small additional EV.

Risk-aversion and selecting a lower than maximal EV is an ongoing dynamic on "Deal or No Deal", where just about every deal offered by the banker is -EV.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
WizardofEngland
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November 2nd, 2010 at 12:34:50 PM permalink
Quote: DJTeddyBear

Yeah, except if that's your attitude, you might as well cancel your plans to spend Christmas in Sin City....



Was only a hypothetical question.....;-)
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
newbie49
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November 3rd, 2010 at 8:14:06 PM permalink
>>>It's also interesting to seriously consider this question in the light of EV vs. utility. Sure, by taking the $5000+ +EV bets, your overall expected value is greater than $10,000, but is it worth the (considerable) risk of winding up with much less than $10,000, despite your advantage?

If you lose early, you don't get a chance to bet the full number of rounds. Thus no +EV.
If you win early, you can bet the full rounds, but top bet is limited to 10k

To answer the question need do more math, or sims.
mkl654321
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November 3rd, 2010 at 9:16:35 PM permalink
Quote: newbie49

>>>It's also interesting to seriously consider this question in the light of EV vs. utility. Sure, by taking the $5000+ +EV bets, your overall expected value is greater than $10,000, but is it worth the (considerable) risk of winding up with much less than $10,000, despite your advantage?

If you lose early, you don't get a chance to bet the full number of rounds. Thus no +EV.
If you win early, you can bet the full rounds, but top bet is limited to 10k

To answer the question need do more math, or sims.



This is untrue. "Positive expectation" means that a bet is advantageous. Under the conditions you stated, all such bets would be advantageous to the player. Whether the individual bets are won or lost is irrelevant.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
Wizard
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November 3rd, 2010 at 10:45:07 PM permalink
Quote: DJTeddyBear

I would also go with option 3, but the Roulette table has a bet that's better than Red: Both 18 and 19 are in the middle dozen. Since you'll win 28 (14*2) for each 39 bet, and lose 25 out of 39, there's a 3/39 = 7.69% advantage when betting the middle dozen.



Good catch! I should have thought of that.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
JerryLogan
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November 4th, 2010 at 12:16:55 AM permalink
Man are you guys so totally confused. It's a Christmas Bonus, which means you get extra money to buy presents for everyone, or at least better presents than you were going to get. So what's all this crazy "advantage" talk for? Option #1 is the only option that gives you $10k. The others give you half that and make you risk the other half....which automatically means you're not going to stop there: you'll gamble the whole thing. And since most gamblers don't know when to stop, you'll probably end up with nothing. So unless you're a degenerate gambler and don't understand the value of a dollar, you take the $10,000 and STAY AWAY FROM THE CASINOS.

How hard is that?
WizardofEngland
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November 4th, 2010 at 3:31:51 AM permalink
So.. If I re-word the question to say blackjack pays 2.5-1

Which option is best?
Does risk come into it?
How likely would you be to get more than $10k
How likely would it be that lose the whole $5k?
Would the kelly bet apply here?
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
dwheatley
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November 4th, 2010 at 7:35:35 AM permalink
Quote: WizardofEngland

Would the kelly bet apply here?



If you were limited by the $5000 bankroll, certainly.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
Ibeatyouraces
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November 4th, 2010 at 8:01:08 AM permalink
deleted
DUHHIIIIIIIII HEARD THAT!
newbie49
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November 4th, 2010 at 8:50:42 PM permalink
>>> This is untrue. "Positive expectation" means that a bet is advantageous. Under the conditions you stated, all such bets would be advantageous to the player. Whether the individual bets are won or lost is irrelevant.

hmm, I think you mis-understood me. Sure every bet you make has + EV, even if you end up losing the bet.

I think you are responding to my comment "Thus no +EV." I meant no +EV for the bets you do not make.
For example, you bet as much cash you have, starting from the initial 5000, then capped at 10,000. And suppose you lose everything after 5 rounds, then you don't make any positive EV on your 6th to 20th bet because you did not bet them.

Suppose you start with 10,000 cash and the bet is capped at 10,000. And any bet you make has 10% edge. Then for 20 rounds, you can calculate the profit as 20 x 10,000 x 10%. But it is not accurate, because in some cases you will run out of money, and you don't get to bet the full 20 rounds.
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