MichaelBluejay
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December 10th, 2010 at 1:43:33 AM permalink
Okay, we all know that one should refuse even money on blackjacks, because even money is the wrong play. But exactly how wrong? Doubling on 18 and standing on 16 v 10 are both wrong, but the former is *very* wrong while the latter is only a tiny bit wrong. There are certainly different degrees of wrong! So how wrong is it to take even money on blackjacks? The answer: not very.

If your bet is $1, then the expected value of even money is $1. That's easy.

If you refuse the even money, then you've got a ~9/13 chance of winning your hand, because of the 13 hole cards the dealer could have, 9 of them mean a win for you (A-9) and 4 of them mean a loss for you (10, J, Q K). So the expected value of your hand is 9/13 x $1.50 = $1.04 (actually 1.03846154, but let's not split hairs).

So for a $100 bet, the average penalty for taking even money is around $4. But how often do you have the opportunity take even money? According to the Wizard's EV table, the probability of 10,A vs. A in a six-deck game is 0.00244016. That's one out of every 410 hands. If you play 100 hands an hour, then you could take even money less than once every four hours on average. So for a $100 bettor, the cost of taking even money is less than a dollar an hour.

So I think taking even money falls into the category of "wrong, but not *that* wrong".

Here's another way to look at it. The typical edge in a 6-deck, H17, DAS game is -0.42622%. The penalty for taking even money is 3.8646154% x 0.00244016 (from the numbers above), or 0.00943%. So that increases the edge from -0.42622% to -0.43565%. Meaning, it increases the edge only just barely.

So, if you like taking even money on blackjack, you can rest assured that even though it's "wrong", it's not *that* wrong.
Last edited by: MichaelBluejay on Jan 27, 2018
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FleaStiff
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December 10th, 2010 at 4:08:07 AM permalink
Wrong, but not that wrong.
Yes. Many things in blackjack will evoke great emotion from players, almost all of it excessive. Even splitting tens can be not all that bad, but try escaping the criticism if you do it. Basic Strategy indicates what is optimal and quite often the next best option is not all that much worse.
I've taken even money not really knowing what I'm doing and its worked out ... often.
I've even hit hard 18 and had it work out... though I sure would not recommend that to anyone. Its wrong and its definitely that wrong.
Headlock
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December 10th, 2010 at 7:18:05 AM permalink
I disagree with your calculation. Say you're playing a single deck game, and you have blackjack, dealer shows an ace. There are 49 cards left, 36 of which make you a winner. 36 divided by 49 times $1.50 is $1.10. In a six deck game, it would be 216 divided by 309 times $1.50, or $1.0485.
Wizard
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December 10th, 2010 at 8:02:44 AM permalink
Quote: MichaelBluejay

According to the Wizard's EV table, the probability of 10,A vs. A in a six-deck game is 0.00244016.



My blackjack appendix 9 assumes the dealer has already peeked for blackjack, and doesn't have one. So that 0.00244016 probability is for the player having a blackjack, the dealer has an ace up, and the hole card isn't a 10. However, let's forget that and do this from scratch. To keep the math simple, let's assume an infinite deck.

Pr(player BJ) = 2*pr(10)*pr(A) = 2*(4/13)*(1/13)=4.73%. (You multiply by 2 because the 10 and ace can be in either or order).
Pr(dealer ace up)=1/13=7.69%.
Pr(player BJ and dealer ace up) = 4.73% * 7.69% = 0.36%.

Expected win in that situation by refusing insurance = pr(no 10 in the hole)*1.5 + pr(dealer 10 in the hole)*0 = (9/13)*1.5 + (4/13)*0 = 1.0385. So taking even money costs the player 0.0385 units.

So habitually taking even money lowers the players expected return by 0.36%*0.0385=0.014%.

Regardless how minimal the cost, any mistake should be viewed as polluting a perfect game. If I played perfect basic strategy except taking even money on blackjacks it would be like climbing Mt. Everest, but turning around voluntarily 10 feet from the top.

To draw another example, suppose I like to hit hard 21 when it is composed of three suited sevens. Would that not be foolish despite it rarely happening? I'm sure the cost of that error would be less than taking even money. Or how about every leap day I celebrate by burning a $100 bill. It wouldn't cost much, but I'd sure look like a fool once every four years.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
teddys
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December 10th, 2010 at 8:26:50 AM permalink
Quote: Wizard

Regardless how minimal the cost, any mistake should be viewed as polluting a perfect game. If I played perfect basic strategy except taking even money on blackjacks it would be like climbing Mt. Everest, but turning around voluntarily 10 feet from the top.

To draw another example, suppose I like to hit hard 21 when it is composed of three suited sevens. Would that not be foolish despite it rarely happening? I'm sure the cost of that error would be less than taking even money. Or how about every leap day I celebrate by burning a $100 bill. It wouldn't cost much, but I'd sure look like a fool once every four years.

LOL! Wiz FTW.
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Mosca
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December 10th, 2010 at 11:36:01 AM permalink
Quote: Wizard

Or how about every leap day I celebrate by burning a $100 bill. It wouldn't cost much, but I'd sure look like a fool once every four years.




But think of the fun you'll have doing this!
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MathExtremist
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December 10th, 2010 at 11:57:22 AM permalink
Quote: Wizard

Or how about every leap day I celebrate by burning a $100 bill. It wouldn't cost much, but I'd sure look like a fool once every four years.



In a similar vein to your eBay posts, you could charge $1 as a pay-per-view fee for a webcam feed of you burning the $100 bill in a ceremonious fashion, and I'd guess you'd have far more than 100 viewers if you publicized it right. Of course, destruction of U.S. currency is a federal offense:

Quote: 18 U.S.C. 17 § 333. Mutilation of national bank obligations


Whoever mutilates, cuts, defaces, disfigures, or perforates, or unites or cements together, or does any other thing to any bank bill, draft, note, or other evidence of debt issued by any national banking association, or Federal Reserve bank, or the Federal Reserve System, with intent to render such bank bill, draft, note, or other evidence of debt unfit to be reissued, shall be fined under this title or imprisoned not more than six months, or both.



Interestingly, that appears to apply to any currency, not just U.S. notes. Maybe it even applies to these:

"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
MichaelBluejay
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December 10th, 2010 at 12:11:09 PM permalink
Quote: Wizard

Taking even money costs the player 0.0385 units. ... Regardless how minimal the cost, any mistake should be viewed as polluting a perfect game. If I played perfect basic strategy except taking even money on blackjacks it would be like climbing Mt. Everest, but turning around voluntarily 10 feet from the top. To draw another example, suppose I like to hit hard 21 when it is composed of three suited sevens. Would that not be foolish despite it rarely happening? I'm sure the cost of that error would be less than taking even money. Or how about every leap day I celebrate by burning a $100 bill. It wouldn't cost much, but I'd sure look like a fool once every four years.



Okay, so I figured a 3.846154% penalty instead of 3.85%. I was pretty close.

As for the rest, I disagree strongly. What the proper play is is not subjective, but whether you *should* do something is certainly subjective. It depends on what your goals are. I'm going to presume that the reason most people gamble is for fun. If a $5 better enjoys the game more by taking even money at a cost of only 7¢ an hour, I argue that they can get their money's worth for that 7¢. All the analogies given are really poor. Hitting three suited sevens is different because the penalty there is close to 100%, while the penalty for taking even money is only <4%. Climbing Mt. Everest is different because it's a process with a pinnacle goal -- it's completely apples and oranges. Burning a $100 bill is different because the raw penalty is much higher for the same amount of time (unless you play a phenomenal amount of blackjack). Still, in all these cases, if someone felt that their enjoyment was enhanced by the deviation, then deviating is valid (from a pleasure perspective, not a financial one). After all, if it's wrong to ever take the action with the lower EV, then no one should ever gamble at all. Because the EV of gambling vs. not gambling is lower -- a *lot* lower. The penalty for gambling vs. not gambling is phenomenally higher than the penalty for taking even money on blackjacks. We might as well say that anyone who gambles at all is doing the equivalent of hitting three suited sevens or burning a $100 bill periodically. The analogy is a lot closer there.
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benbakdoff
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December 10th, 2010 at 2:20:30 PM permalink
Good points on both sides. A recreational player most likely will have different goals than the serious player or the AP.

If I ran a casino, I would want everyone to take even money every time.
odiousgambit
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December 10th, 2010 at 2:27:19 PM permalink
The WoO does not brook much opposition, perhaps Mr. Bluejay can get away with a continued discussion [g]. I do wonder in this case if there is a hard-to-value [mathematically] reduction in variance. In other words, if it is marginally more expensive in EV, but reduces variance, might be worth it.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
Wizard
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December 10th, 2010 at 3:01:10 PM permalink
I stand by my analogies. Of course some mistakes are worse than others, but I view them all in the same light. For example if one person burned a $1 bill and another burned a $100 bill I would think both are fools. I wouldn't view the second person as a 100x greater fool.

To make another example, I would compare taking even money on blackjack as putting a little pebble poop in a punch bowl, and hitting hard 21 as a taking a massive dump in a different punch bowl. In both cases the punch is contaminated.

However, you make a valid point about playing at all. If your goal is to lose as little as possible, then you shouldn't play in the first place. That isn't my goal. I play in part for the love of gambling and the study of the game. Once in a while I make an accidental mistake, and beat myself up for it very hard when I do. I'm not saying everyone has to play for the same reasons I do. I am just saying how I see it. Nobody is required to agree.

About the destroying of money, I think the government should encourage it. When you burn $1 it increases the value of every other dollar. Now I could see the reason to forbid defacing a dollar, and then putting it back in circulation. Also, what about all those devices that flatten pennies to make a souvenir? Aren't those in violation of that law?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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December 10th, 2010 at 5:09:59 PM permalink
I split off the posts about putting coins on railroad tracks to Putting coins on railroad tracks.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MichaelBluejay
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December 10th, 2010 at 5:25:04 PM permalink
Quote: Wizard

I stand by my analogies.... To make another example, I would compare taking even money on blackjack as putting a little pebble poop in a punch bowl, and hitting hard 21 as a taking a massive dump in a different punch bowl. In both cases the punch is contaminated.



These analogies are terrible. Taking even money affects only the person who takes even money. Contaminating a punch bowl affects others.

I wonder if the Wizard thinks that betting the Pass Line instead of Don't Pass is equivalent to burning a $100 bill, pooping in a punch bowl, or quitting near the top of Mt. Everest.
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Wizard
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December 10th, 2010 at 5:51:25 PM permalink
Quote: MichaelBluejay

These analogies are terrible. Taking even money affects only the person who takes even money. Contaminating a punch bowl affects others.



Oh my! If the punch bowl analogy was not clear then what was wrong with the $1/$100 one?

Quote: MichaelBluejay

I wonder if the Wizard thinks that betting the Pass Line instead of Don't Pass is equivalent to burning a $100 bill, pooping in a punch bowl, or quitting near the top of Mt. Everest.



He would say no, that there is beauty in playing a game well. He would probably make a terrible analogy that it would be better to play a $100 violin well than a $1,000,000 violin badly.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MichaelBluejay
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December 10th, 2010 at 6:11:59 PM permalink
Quote: Wizard

What was wrong with the $1/$100 analogy?



The analogy is good but the conclusion is subjective. You said, "For example if one person burned a $1 bill and another burned a $100 bill I would think both are fools." I disagree. If someone gets at least $1's worth of pleasure out of burning a $1 bill, then I don't think that burning the bill is foolish. Ditto for a $100 bill. It's no different from spending money on any other kind of entertainment.
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pacomartin
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December 10th, 2010 at 6:20:25 PM permalink
Michael,

I am not sure what your point is. I think most of us understand that decision theory results in a decision. That is the part under our control. What we can't control is how much advantage we will get by our decision.

If we are dealt a 9, 7 against a dealer 10, then we get only the slightest advantage by hitting vs standing. But why choose stand because the advantage is small. Splitting 8's against a dealer 10 produces a very small increase in EV.

To me "even money" is two bets. One is the side bet called "insurance", the second is playing out the hand. In the case of "even money" the second bet resolves itself immediately. But the first bet is just as stupid, or just as smart, as taking "insurance" against any other dealer up card. Why would it be smart to take insurance against an ace and smart to not take insurance against another card? The probability is the same either way.
Switch
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December 10th, 2010 at 6:45:41 PM permalink
I'm sure I've read reports before on how counters, who take 'Even Money', when just their big bets are out (i.e. the count is high so 'Even Money' is the correct decision) can stand out and induce 'heat' from the pit.

Most casino pit personnel know that 'Even Money' is not the correct play and is taken by recreational players.

So, to put a different slant on it, if a counter takes 'Even Money' all the time then he/she will be incorrect (in taking it) when their small bets are out and correct when their big bets are out (So, the overall reduction in player ev will also be diminished). The fact that they ALWAYS take 'Even Money' may reduce the heat and therefore prolong the playing time of a player. So, the question becomes "Is taking 'Even Money' at all times worth the extended playing time that it gives?".

The same arguement could be made for 16 vs 10 if a counter always stands then the correct play will be made when the big bets are out.

I suppose it's difficult to measure slight incorrect plays and their respective overall value in allowing the counter to continue playing at the same casino but it does shed some purposeful reason for considering the play under certain conditions.
MichaelBluejay
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December 10th, 2010 at 7:07:53 PM permalink
Obviously we're not talking about card counting. That couldn't be farther afield. The point is simply that players who take even money get routinely blasted by the experts (e.g., in this thread they're called "foolish" and equated to those who would turn back from the top of Mt. Everest), while in reality the penalty is tiny and of little *practical* consequence.
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Wizard
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December 10th, 2010 at 8:54:44 PM permalink
Quote: MichaelBluejay

The point is simply that players who take even money get routinely blasted by the experts.



Those annoying experts! So self-righteous and judgmental.

On another topic, you might be interested in this discussion.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
benbakdoff
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December 11th, 2010 at 4:37:12 AM permalink
Quote: MichaelBluejay

Obviously we're not talking about card counting. That couldn't be farther afield. The point is simply that players who take even money get routinely blasted by the experts (e.g., in this thread they're called "foolish" and equated to those who would turn back from the top of Mt. Everest), while in reality the penalty is tiny and of little *practical* consequence.



Just as common are the experts getting routinely blasted by the ploppies. Such is the game of blackjack.

Most experts who really understand the game do not berate fellow players.
odiousgambit
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December 11th, 2010 at 7:50:13 AM permalink
The WoO in BJ is OK with simple strategy as opposed to basic strategy, but on a different basis: he concedes a perfect strategy will elude the beginner. But to make a play at any disadvantage, when you know better, cannot be justified, in his book. So discussions like this are the ultimate challenge to the WoO's approach to gambling: lowest HE to the nth degree only, whereas we can see certain respectable individuals of some clout do not exactly agree. This is a bigger deal than someone like me disagreeing [g]. I still wonder if getting reduced variance can have a certain value that is not found in a WoO formula.


Quote: Wizard

... you make a valid point about playing at all. If your goal is to lose as little as possible, then you shouldn't play in the first place.




Is this in fact the WoO view about going for reduced variance at little expense?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
Switch
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December 11th, 2010 at 8:02:39 AM permalink
Quote: benbakdoff

Just as common are the experts getting routinely blasted by the ploppies. Such is the game of blackjack.

Most experts who really understand the game do not berate fellow players.



Very true. Sitting at 3rd base, when hitting 'Soft 18' or splitting 9's goes wrong, you should hear the amount of 'experts' giving you advice on how you should really have played the hand :-)

If counting is not considered then taking 'Even Money' against a dealer Ace is the wrong decision but I don't think that players should get berated for it. However, on similar lines, players regularly:-

Stand on some 16's
Don't double all soft totals
Don't hit 12 vs 2 or 3
Don't hit 'soft 18' vs 9, 10, A
Don't double 11 vs 10 & 10 vs 9

All these close 'wrong' plays add up and the more the player makes then the higher the ev is against him/her. Taking 'Even Money' just adds another piece to the pile.
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December 11th, 2010 at 8:09:14 AM permalink
Quote: Switch

... However, on similar lines, players regularly:-

Stand on some 16's
Don't double all soft totals
...

All these close 'wrong' plays add up and ....

I assume that someone will explain why these plays may actually be the correct ones even for the player who is not counting cards. I don't think I want to get into the details myself.
MichaelBluejay
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December 11th, 2010 at 2:43:22 PM permalink
Quote: odiousgambit

So discussions like this are the ultimate challenge to the WoO's approach to gambling: lowest HE to the nth degree only, whereas we can see certain respectable individuals of some clout do not exactly agree. This is a bigger deal than someone like me disagreeing [g].



If you're talking about me, then thanks, but really I'm just some guy with a website. Anyone can start a website and look like an authority. It's my big secret. :)

And for the record, on gaming math issues, there's no more authority than the Wizard. I mean, he *is* the Wizard. But when we talk about personal preferences, that's subjective so I don't think anyone can be an authority, so I think it's fair game for anyone to have an opinion. I'm with the Wizard in that I want people to have the best information so they have the opportunity to make the best decisions. I think where we disagree is he thinks it's foolish to ever choose a play with a lower EV, whereas I think it's personal preference, and of no practical consequence when the cost of the "wrong" play is very low.
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CoolMike
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December 11th, 2010 at 4:22:32 PM permalink
One thing that mathematically changes this discussion is when we bring the element of risk into the equation. Taking even money on a blackjack is a much lower variance play than not taking even money. This means that if your goal is to maximize your personal utility taking even money is probably still a bad idea, however, it gets ever so slightly closer to being a good idea when you factor in the risk of making the correct play versus the loss in equity of taking the lower variance option.

If however, you have made a poor decision and placed a large percentage of your bankroll on one hand, and then recieve a blackjack, it can be mathematically correct to take the lower equity play. It all depends on how you want to set up the equations. Obviously, the fact that it is lower risk doesn't change the fact that you give away a few penies on the dollar every time you make the play. Instead, we must change the way we look at the game. We should start by thinking that the goal of your play is to maximize your personal happiness. Now we can postulate that our happiness is related to the amount of money we win, but not linearly so. If this is true, than there are certain bets that our average overall happiness is maximized by taking the path that leads to a smaller average win.

As a thought experiment, think about what you would do if you literally bet the farm on a hand of blackjack. To your great pleasure you recieve a blackjack. To your horror the dealer has an ace showing. Now, I would submit that you would have to be a fool to give up the sure win here and risk losing the farm in order to improve your result from a double up to a double-and-a-half up. I also would concede, however, that you'd be a fool here no matter what choice you made, becuase you should not be betting the farm if you can't afford to lose it!

I'm certain that I am not covering new ground here, as I know that the wizard and many others have studies this effect a great deal. In fact, if I recall correctly the wizard himself posted some risk averse plays on the main website in the past?

Well, I just thought i'd advance the discussion with a little thought experiment. I'm sorry for not having time to do it in a more vigorous manner.
MichaelBluejay
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December 11th, 2010 at 4:30:01 PM permalink
Thanks, CoolMike, this is straight to the point of what I was suggesting, that the goal of our play is to maximize personal happiness, and making the play with the highest EV doesn't always support that goal. I like your example of betting the farm. I'll give another one, which is a lot more possible (i.e., a lot less hypothetical): Let's say it's your last hand of the night, or of your trip. You have the opportunity to take even money. If you do, then you'll have a profit for the trip. If you don't, then you risk walking away a loser. You know that the feeling of walking away a winner is important to your happiness. It's a lot more pleasant to feel like a winner than a loser. By taking even money you can ensure that you had a win for the day (or for the trip). So here's a case where making the "wrong" play meets your goals.
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Wizard
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December 11th, 2010 at 7:44:37 PM permalink
It is absolutely true that advantage gamblers should sometimes make a less than optimal EV play to lower variance. As I explained in my Sep. 20, 2007 Ask the Wizard column, video poker players below a certain bankroll relative to bet size, when playing full pay deuces wild, should keep five 22233, although keeping the deuces only results in a higher EV.

My basic point is that players, in general, should not deliberately make bad plays. It doesn't bother me when somebody makes a error out of ignorance. Do I know every penalty card exception to the video poker games I play? No, and I make no apologies for it. As I said before, what rubs me the wrong way is deliberately making an error. However, MB's example of someone playing his last hand is a situation where I could see their motive. Habitually taking even money is still something I have a hard time with and can't condone.
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mkl654321
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December 11th, 2010 at 8:20:52 PM permalink
Quote: MichaelBluejay

Okay, we all know that one should refuse even money on blackjacks, because even money is the wrong play. But exactly how wrong? Doubling on 18 and standing on 16 v 10 are both wrong, but the former is *very* wrong while the latter is only a tiny bit wrong. There are certainly different degrees of wrong! So how wrong is it to take even money on blackjacks? The answer: not very.

If your bet is $1, then the expected value of even money is $1. That's easy.

If you refuse the even money, then you've got a ~9/13 chance of winning your hand, because of the 13 hole cards the dealer could have, 9 of them mean a win for you (A-9) and 4 of them mean a loss for you (10, J, Q K). So the expected value of your hand is 9/13 x $1.50 = $1.04 (actually 1.03846154, but let's not split hairs).
.



This is utterly incorrect, and very surprising coming from MBJ. Of course, the initial bet has ABSOLUTELY NOTHING to do with the insurance bet. If you win your so-called "insurance" bet, you still lose your original bet if you didn't have a blackjack, and push if you did! Nothing has changed in that regard.

So the only real question is, should you or should you not take insurance, REGARDLESS OF YOUR HAND. And the answer is, "no". You suffer an 8% house edge.

The fact that many people only "insure" when they have a blackjack is neither here nor there. It's a blunder to make that bet, whatever hand you hold. Of course, I see the point that it's an INFREQUENT blunder, but I don't see it as having a negligible effect. Every time you take insurance, you pay the same house edge as in EIGHT bets off the top in a four-deck shoe with decent rules. That's a LOT of HE to fade.
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
MichaelBluejay
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December 11th, 2010 at 10:47:49 PM permalink
Quote: mkl654321

Of course, the initial bet has ABSOLUTELY NOTHING to do with the insurance bet.



Sure it does. The size of the insurance bet is limited by the amount of the initial bet.

Quote:

If you win your so-called "insurance" bet, you still lose your original bet if you didn't have a blackjack, and push if you did! Nothing has changed in that regard.



Your point being?

Quote:

So the only real question is, should you or should you not take insurance, REGARDLESS OF YOUR HAND. And the answer is, "no". You suffer an 8% house edge.



See, here's where I think folks are assigning objective conclusions to a subjective concept. Is taking even money the lower-EV play? Yes, that's objective. Does that mean the player "should" refuse the even money? That's subjective, and it's for the player to decide. We've identified a few reasons that it might be worth it to the player to forego a few pennies -- lowering variance, coming out a winner at the end of a session/weekend, or just because it's more fun.

Quote:

The fact that many people only "insure" when they have a blackjack is neither here nor there.



Sure it is, because that's the situation we're discussing. The title of this thread is "Vindication for taking even money ON BLACKJACKS". It's precisely that play that we're talking about.

Quote:

Of course, I see the point that it's an INFREQUENT blunder, but I don't see it as having a negligible effect. Every time you take insurance, you pay the same house edge as in EIGHT bets off the top in a four-deck shoe with decent rules. That's a LOT of HE to fade.



Not-uh. For a $25 bettor playing 80 rounds an hour, the cost is 28¢ an hour. I can't agree that that's a "lot" of house edge to fade.

By the way, the Wizard and mkl54321's responses show why I started this thread: some folks are just so insistent on making the mathematically-correct under all circumstances, they go crazy at the thought that someone might willingly choose a suboptimal play simply because he prefers it -- even when the difference in expected value is negligible. That kind of devotion to a principle is almost like religious fervor.
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pacomartin
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December 12th, 2010 at 1:10:25 AM permalink
The correct move with a Ace, 7 against a dealer 2 is to Double. However, it is only a very small increase in EV over the second best move, to stand.

If you have a lot of money on the table, I could understand the player's reluctance to double. But I wouldn't start a thread about how I was vindicated by making this move.
odiousgambit
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December 12th, 2010 at 5:48:17 AM permalink
Quote: pacomartin

I wouldn't start a thread about how I was vindicated by making this move.



Oh, come on, I think this thread is quite interesting. I won't say who I think has made the best points, I am kind of on the fence. What makes it interesting [to me] is that the cost of the bad play seems at first too high, but then there is the factor of how infrequently it comes up. Does that squelch the opposite argument, or not? Is it how many angels on the head of a pin again? Havent decided yet.

But I will say it is a bit rare for the WoO to not just diss these arguments. Of course he has to deal with a lot of idiotic questions and dubious claims, I appreciate that. But this is a good thread.

edited
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
DorothyGale
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December 12th, 2010 at 7:50:39 AM permalink
Quote: Wizard

Regardless how minimal the cost, any mistake should be viewed as polluting a perfect game. If I played perfect basic strategy except taking even money on blackjacks it would be like climbing Mt. Everest, but turning around voluntarily 10 feet from the top.

29029*(.00014) = 4.1 feet (in elevation), and that assumes climbing it from sea level. If the slope at the end of the climb is 40%, then stopping 10 feet of travel distance from the top is about right.

--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"
mkl654321
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December 13th, 2010 at 8:22:19 PM permalink
Quote: MichaelBluejay

Sure it does. The size of the insurance bet is limited by the amount of the initial bet.
Your point being?
Not-uh. For a $25 bettor playing 80 rounds an hour, the cost is 28¢ an hour. I can't agree that that's a "lot" of house edge to fade.

By the way, the Wizard and mkl54321's responses show why I started this thread: some folks are just so insistent on making the mathematically-correct under all circumstances, they go crazy at the thought that someone might willingly choose a suboptimal play simply because he prefers it -- even when the difference in expected value is negligible. That kind of devotion to a principle is almost like religious fervor.



My point was that the initial bet will win or lose regardless of whether you take insurance or not. Therefore, that bet, and its outcome, should NOT affect your decision to make or not to make the insurance bet.

Where your thinking goes off the rails is in considering the original bet AND the insurance bet as some kind of organically melded whole. The simple fact is that the two bets ARE ENTIRELY SEPARATE, and therefore should be considered separately. The illusion, and delusion, is that because the outcomes of the bets are partly related, that the two bets are interdependent. They are NOT. (You can lose the "insurance" bet, and still lose the original bet.)

So once again, the ONLY, SOLE consideration is, should you make a side bet that has an 8% house edge? Obviously not. You can call the reluctance to make a bet with that kind of house edge "religious fervor" if you wish.

And if you're betting so much that the dealer's Ace can blackmail you into accepting less than the EV you deserve on your blackjack, then you are pretty much by definition betting too much in the first place.
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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December 13th, 2010 at 8:53:55 PM permalink
By the way, somebody challenged me about this in my Feb. 13, 2004 Ask the Wizard column.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MathExtremist
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December 13th, 2010 at 10:31:45 PM permalink
Quote: mkl654321

So once again, the ONLY, SOLE consideration is, should you make a side bet that has an 8% house edge? Obviously not. You can call the reluctance to make a bet with that kind of house edge "religious fervor" if you wish.



I disagree, and I think the "enormous bet" scenario illustrates this case perfectly. Once you've got a meaningful amount of money on the line, the variance of that single wager entirely dominates the EV considerations (which are realized only over a large number of hands). It's like investing your 401(k) funds - you can take the "conservative" option with a broader asset diversity, lower 10-year annualized return, and lower risk, or the "aggressive" option which is mostly small-cap equities. The small cap equities have a much higher 10-year annualized return, but a wide range of annual returns including often negative. In other words, the EV is higher (often by a lot) for the aggressive investing strategy, but if you're one year from retirement you'd be a fool to put all your money into small-caps. Why? The EV doesn't matter if you only get to make one bet. That's true for any kind of investing, and it's just as true if you're overbetting your bankroll in a -EV game.

Let's put it this way: if you were forced to withdraw your entire life savings and put it on a single hand of blackjack, and the dealer dealt you A,J and showed an A upcard, are you actually suggesting that you'd skip the even-money payout?
"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
mkl654321
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December 13th, 2010 at 11:00:13 PM permalink
Quote: MathExtremist

I disagree, and I think the "enormous bet" scenario illustrates this case perfectly. Once you've got a meaningful amount of money on the line, the variance of that single wager entirely dominates the EV considerations (which are realized only over a large number of hands). It's like investing your 401(k) funds - you can take the "conservative" option with a broader asset diversity, lower 10-year annualized return, and lower risk, or the "aggressive" option which is mostly small-cap equities. The small cap equities have a much higher 10-year annualized return, but a wide range of annual returns including often negative. In other words, the EV is higher (often by a lot) for the aggressive investing strategy, but if you're one year from retirement you'd be a fool to put all your money into small-caps. Why? The EV doesn't matter if you only get to make one bet. That's true for any kind of investing, and it's just as true if you're overbetting your bankroll in a -EV game.

Let's put it this way: if you were forced to withdraw your entire life savings and put it on a single hand of blackjack, and the dealer dealt you A,J and showed an A upcard, are you actually suggesting that you'd skip the even-money payout?



That this is an apocryphal situation illustrates the point I was trying to make. You would never do that voluntarily, precisely because you would be facing a situation where variance trumps EV considerations. And that leads to bad financial decisions. For instance, buying any kind of insurance is making a -EV bet because you feel blackmailed by variance.

In your hypothetical situation, would I take even money? Absolutely not. After all, I will still get my life savings back, no matter what. And the loss of EV by taking insurance would be not trivial---a year's earnings or so.
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
MichaelBluejay
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December 14th, 2010 at 2:07:52 AM permalink
Quote: mkl654321

Where your thinking goes off the rails is in considering the original bet AND the insurance bet as some kind of organically melded whole. The simple fact is that the two bets ARE ENTIRELY SEPARATE, and therefore should be considered separately.



Sorry, I call bullshit. When you take Even Money that effectively consolidates the two separate bets into one. If you take even money then you know exactly what you're getting. There is no practical advantage to thinking of those bets separately. Sure, there are actually two different bets in play, but so what? If the player knows there's a ~3.5% penalty by taking even money, that's all they need to know. The idea of forcing regimented thinking about the bets as separate isn't helpful, and certainly isn't of any practical value.
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weaselman
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December 14th, 2010 at 9:08:57 AM permalink
Quote: MichaelBluejay

All the analogies given are really poor. Hitting three suited sevens is different because the penalty there is close to 100%, while the penalty for taking even money is only <4%. Climbing Mt. Everest is different because it's a process with a pinnacle goal -- it's completely apples and oranges. Burning a $100 bill is different because the raw penalty is much higher for the same amount of time (unless you play a phenomenal amount of blackjack). Still, in all these cases, if someone felt that their enjoyment was enhanced by the deviation, then deviating is valid (from a pleasure perspective, not a financial one).



The first sentence says the analogies are poor, and the last one essentially establishes, that they are good :)
Personally, I found Wizard's examples right on.

Sure, if somebody finds enjoyment in throwing money away, there is nothing "invalid" about it, but it does look kinda foolish upon an examination.

Having said that, the same logic applies to playing BJ (or any casino game for that matter) to begin with. If one thinks throwing money away is a foolish way to spend time, one should not set foot a casino. So, it is pretty much a given, that everyone at that BJ table is wasting their money anyway (except for the card counters, who are wasting their time instead).
From this perspective, it doesn't really matter what sucker bet you are going to make, be it insurance or match the dealer ... It's not a rational decision, but if you only decided rationally, you would not be playing at all.
"When two people always agree one of them is unnecessary"
MichaelBluejay
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December 14th, 2010 at 12:06:22 PM permalink
Quote: weaselman

The first sentence says the analogies are poor, and the last one essentially establishes, that they are good :)



The analogies are indeed poor, and the last sentence doesn't contradict that. The point of the last sentence is that even *if* we take the bad analogies as valid (which they're not), then those bad analogies can still be argued against.

Quote:

Having said that, the same logic applies to playing BJ (or any casino game for that matter) to begin with. ... So, it is pretty much a given, that everyone at that BJ table is wasting their money anyway (except for the card counters, who are wasting their time instead). From this perspective, it doesn't really matter what sucker bet you are going to make, be it insurance or match the dealer ... It's not a rational decision, but if you only decided rationally, you would not be playing at all.



Amen! If taking even money is foolish, then so is playing blackjack in the first place. Even more so.
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mkl654321
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December 15th, 2010 at 12:12:41 AM permalink
Quote: MichaelBluejay

Sorry, I call bullshit. When you take Even Money that effectively consolidates the two separate bets into one. If you take even money then you know exactly what you're getting. There is no practical advantage to thinking of those bets separately. Sure, there are actually two different bets in play, but so what? If the player knows there's a ~3.5% penalty by taking even money, that's all they need to know. The idea of forcing regimented thinking about the bets as separate isn't helpful, and certainly isn't of any practical value.



"Taking even money" is MAKING AN INSURANCE BET. Therefore, there are no two bets to "consolidate into one" at the time you make that second bet. AND, the two bets are STILL separate bets and have separate outcomes. The house saves itself time by awarding the total payoff that will result in either case, BUT THERE ARE ACTUALLY TWO SEPARATE BETS BEING RESOLVED at that point.

The point I've been trying so hard to get across to you is that the only decision point is "do I or do I not" make an insurance bet. What on earth does the insurance bet have to do with the PLAYER'S hand???????????? It's a bet on the DEALER'S hand!!!

The practical value of realizing these are separate bets is IMMENSE: it gets the player away from the false impression that the bet "insures" anything (it doesn't), and it gets the player away from making a bad EV bet just to "prevent" his blackjack from pushing (it doesn't). The true genius of the person who concocted the bet in the first place was calling it the false "INSURANCE". If it was called "feedly fiddly foo" instead of "insurance", that would be more accurate (at least it wouldn't be a lie that way), and less people would sucker for it.
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
mkl654321
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December 15th, 2010 at 12:15:19 AM permalink
Quote: MichaelBluejay

Amen! If taking even money is foolish, then so is playing blackjack in the first place. Even more so.



Playing BJ has a house edge of less than 1%. Taking even money (making an insurance bet) has a house edge of 8%. How is playing BJ "even more so" foolish?
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
weaselman
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December 15th, 2010 at 5:12:22 AM permalink
Quote: mkl654321

Playing BJ has a house edge of less than 1%. Taking even money (making an insurance bet) has a house edge of 8%. How is playing BJ "even more so" foolish?


I guess, you could say it's more foolish in a sense that (in absolute numbers) you lose more money playing BJ, than taking insurance.

Personally, I think, it is equally equally foolish, because I don't believe there is a good way to quantify foolishness to begin with. Something either is foolish or it isn't. If you think that throwing money away without getting anything tangible in return is foolish, then you'd be a fool to play BJ. And if it is established that somebody is a fool, then whether or not he habitually takes insurance while playing is irrelevant.

Disclaimer: I am NOT saying that everybody who plays BJ is a fool :) FWIW, I love going to casino, and BJ is the only game I play there.
I never take insurance, because I find my enjoyment in playing a perfect game, but I cannot claim I am less foolish or more rational than the next guy, who just loves that terrible match the dealer bet - yes, he loses more money than I do, but he, probably, enjoys it more too (or, maybe, he just has more money to lose to begin with).
"When two people always agree one of them is unnecessary"
Ibeatyouraces
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December 15th, 2010 at 7:55:14 AM permalink
deleted
DUHHIIIIIIIII HEARD THAT!
MichaelBluejay
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December 22nd, 2010 at 9:00:36 PM permalink
Quote: mkl654321

The practical value of realizing these are separate bets is IMMENSE: it gets the player away from the false impression that the bet "insures" anything (it doesn't), and it gets the player away from making a bad EV bet just to "prevent" his blackjack from pushing (it doesn't). The true genius of the person who concocted the bet in the first place was calling it the false "INSURANCE".



Sorry, I call bullshit again. The insurance bet effectively *does* act like insurance. In the real world, insurance is paying a fraction of the value you want to insure, to compensate you for a loss of that value. Blackjack insurance works the same way.

Let's take insurance on your house:

NO INSURANCE: Your value is at risk.
INSURANCE + NO PERIL: You're out the cost of the insurance.
INSURANCE + PERIL: You're compensated for your loss of value.

And insurance in blackjack effectively works the same way. You pay a fraction of the original value, and if disaster strikes, then you don't lose your original value immediately.

In the case of even money, you never lose your insured value, so the insurance covers everything. For non-BJ hands, you could buy insurance and still lose your hand later, but that's because the insurance doesn't cover everything. The only covered loss for an insurance bet is the dealer having BJ; blackjack insurance doesn't cover a later loss of the hand, just like my homeowner's policy doesn't cover acts of terrorism.
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EvenBob
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December 22nd, 2010 at 9:28:28 PM permalink
Quote: MichaelBluejay

Sorry, I call bullshit again. .



Mr Bluejay, apparently you aren't aware that MKL, by his own admission, has an IQ of 190. Perhaps you should rephrase that..
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mkl654321
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December 22nd, 2010 at 11:28:10 PM permalink
Quote: MichaelBluejay

Sorry, I call bullshit again. The insurance bet effectively *does* act like insurance. In the real world, insurance is paying a fraction of the value you want to insure, to compensate you for a loss of that value. Blackjack insurance works the same way.

Let's take insurance on your house:

NO INSURANCE: Your value is at risk.
INSURANCE + NO PERIL: You're out the cost of the insurance.
INSURANCE + PERIL: You're compensated for your loss of value.

And insurance in blackjack effectively works the same way. You pay a fraction of the original value, and if disaster strikes, then you don't lose your original value immediately.

In the case of even money, you never lose your insured value, so the insurance covers everything. For non-BJ hands, you could buy insurance and still lose your hand later, but that's because the insurance doesn't cover everything. The only covered loss for an insurance bet is the dealer having BJ; blackjack insurance doesn't cover a later loss of the hand, just like my homeowner's policy doesn't cover acts of terrorism.



Counter-bullshit. What you are describing is "compensation for", not "insurance against".

In any case, my central point was that a so-called "insurance" bet is a SIDE bet on the DEALER's hand ONLY, and has NOTHING to do with the original bet or original hand, in that it is a separate decision with a separate outcome. I'm sure you can find some way to disagree, or "call bullshit", with that, too, but let's drop it.
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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December 23rd, 2010 at 12:32:57 AM permalink
Quote: mkl654321

In any case, my central point was that a so-called "insurance" bet is a SIDE bet on the DEALER's hand ONLY, and has NOTHING to do with the original bet or original hand, in that it is a separate decision with a separate outcome.



The outcome of the insurance bet is highly negatively correlated to the outcome of the blackjack bet itself. That is why they call it insurance. When I try to explain why insurance is a lousy bet, I look at it separately from the blackjack bet. I would say it should be analyzed separately, but I wouldn't say it has nothing to do with the blackjack wager, just to be technically safe. In a blackjack tournament the negative correlation can be critical, and must be considered in some end-game situations.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
bjgod
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December 23rd, 2010 at 12:36:09 AM permalink
Quote: Wizard

The outcome of the insurance bet is highly negatively correlated to the outcome of the blackjack bet itself. That is why they call it insurance. When I try to explain why insurance is a lousy bet, I look at it separately from the blackjack bet. I would say it should be analyzed separately, but I wouldn't say it has nothing to do with the blackjack wager, just to be technically safe. In a blackjack tournament the negative correlation can be critical, and must be considered in some end-game situations.



Would you mind giving your two cents on my blackjack system.. The sims cant lie I would just appreciate someone of your stature commenting
I am a blackjack machine programed to take in cards and shit out money!
MichaelBluejay
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December 23rd, 2010 at 1:20:06 AM permalink
Well, if anything, I think this thread has demonstrated that some folks have such a deeply religious-like attachment to expected value, to the point that they can't put it into perspective, and start foaming at the mouth when anyone suggests that EV isn't the be-all and end-all. I know, because I used to be in that camp. I'm glad I finally realized that, from a *practical* perspective, there are times where it just really does not matter.
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odiousgambit
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December 23rd, 2010 at 4:06:05 AM permalink
I have been wondering if I would ever take "even money" , it almost seems like you'd want to pick some other time to take insurance if you had any desire to do so. With 16 vs dealer Ace it is better to surrender it seems, but with 15 or 14 vs that Ace it has to be marginal to hit as instructed as opposed to surrender, so how about buying insurance then, instead of when you hold Blackjack?

I may be missing something obvious here.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
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