When I would take Even Money
Suppose someone were to give you a million dollars as a wager. The condition is that you must bet it all, right now, on one hand (Edit: win lose or push) of blackjack at a SD, 3:2 table where the shuffle has just occurred. You don't keep the bet if you win, you only keep the winnings. You place the million into the betting circle and the cards are delt. The dealer's up-card is an ace, and you are dealt a blackjack. Even money is offered. Do you take it?
If you take even money you walk with a million. If you don't take even money you will push 30.612245% of the time, and get paid $1,500,000 69.3877% of the time, for an average win of $1,040,815. Of course, there is no average win if you don't take even money. You either win $1,500,000 or you win nothing.
Your odds are better by not taking even money, and you win $40,815 more, on average, if you don't. But I would take even money. That's because a million dollars 100% of the time is worth more to me than taking a 30.612245 % chance of winning nothing, and a 69.3877% chance of winning $1,500,000.
This is an absurd scenario which would never happen, but it makes an important point. We may accept a lower EV and variance if the win is big enough. How big is relative to the individual bettor.
Interesting note this doesn't actually solve the St. Petersbrug Paradox since we can rephrase that problem to have a quicker growing payout schedule.
Quote: TortoiseMy biggest problem with utility theory is that it usually ignores repetition over time. I think we'd all take the million dollars if this were a once in a lifetime opportunity, but if you were presented with the same situation every day you'd almost certainly make more over the course of a year declining even money. In the short run insurance decreases your financial risk but in the long run it increases it. This leads to the counter intuitive conclusion that if you have an edge then in the long run it's riskier not to gamble.
That's fair utility theory is really only good for these once in a life time scenarios.
Quote: GreasyjohnSometimes, we may not make the "correct" play in blackjack. Sometimes a play that has a +EV is better than a play that has an even better EV. The following example is strictly hypothetical but brings home the point that we may accept a smaller win if that win is very substantial.
Suppose someone were to give you a million dollars as a wager. The condition is that you must bet it all, right now, on one hand of blackjack at a SD, 3:2 table where the shuffle has just occurred. You don't keep the bet if you win, you only keep the winnings. You place the million into the betting circle and the cards are delt. The dealer's up-card is an ace, and you are dealt a blackjack. Even money is allowed. Do you take it?
If you take even money you walk with a million. If you don't take even money you will push 30.612245% of the time, and get paid $1,500,000 69.3877% of the time, for an average win of $1,040,815. Of course, there is no average win if you don't take even money. You either win $1,500,000 or you win nothing.
Your odds are better by not taking even money, and you win $40,815 more, on average, if you don't. But I would take even money. That's because a million dollars 100% of the time is worth more to me than taking a 30.612245 % chance of winning nothing, and a 69.3877% chance of winning $1,500,000.
This is an absurd scenario which would never happen, but it makes an important point. We may accept a lower EV and variance if the win is big enough. How big is relative to the individual bettor.
How about the same example, but the dealer up card is a 10, and the casino gives you the option to take even money
Quote: michael99000How about the same example, but the dealer up card is a 10, and the casino gives you the option to take even money
The dealer would have a blackjack about 6% of the time. So roughly 94% of the time you'd win 3:2. I'd like to think about it. I know it's more exciting to be gallant. Well, I'm not gallant. The decision is made thoughtfully not boldly. I think I'll take my chances and see if my blackjack holds up. To someone that needs the money the right decision could be different.
Edit: I'm still thinking...
Edit: Honestly, I could live with it either way, but a sure million is worth more to me than a 94% chance at winning 1.5 million with a 6% chance of winning nothing. (That's after 26 minutes of thinking.)
Please don't remove an ace from the deck and torture me.
Quote:Thou Shalt Not Hedge Thy Bets
However, he makes an exception for life-changing money. I look at taking EM as essentially a hedge, so because that is life-changing money for me, I feel justified in taking it...and not just because the Wizard says so.
Hell, if you offered me 50-75% I'd probably take it. Anything less than a guaranteed +500K is when I'd have something to start thinking about.
Howabout this scenario - same win/lose rules with the money, and a deal from a fresh deck every time, but:
100 hands at $10,000 a hand
Dealer up card is ALWAYS an ace
You could take even money each of the 100 times for a guaranteed million. Would you?
Quote: michael99000How about the same example, but the dealer up card is a 10, and the casino gives you the option to take even money
My life would be positively changed if I won $1m right now.
Given the option to take even money 36% of the time (vs A or X), or 1.5x win outright the other 64% of the time, sure.
The terms implied this was a one shot deal, and you only get to keep the payout - not the original wager. Something is a whole lot better than nothing.
Quote: Dalex64Yeah, several factors there affecting someone's choice - life changing money, once in a lifetime opportunity. I'd take the money.
Howabout this scenario - same win/lose rules with the money, and a deal from a fresh deck every time, but:
100 hands at $10,000 a hand
Dealer up card is ALWAYS an ace
You could take even money each of the 100 times for a guaranteed million. Would you?
1,050,000 expected v. 1,000,000 guaranteed hmmmmmmmm…?
But you should never be wagering so much money at a time where you'd have to make this kind of a play.
If you're ever in that situation, you are either:
1) Really f****** stupid for betting that much money (relatively / compared to BR)
or
2) Really f****** lucky for ending up in a ridiculous situation like that. (or if someone does a $1000 don't-pass bet, the point becomes 4, the player says "hey that's all you, you can have it i'm leaving the table").
Although, I don't like the way you've phrased this thread. Ultimately, if it's life-changing (or a huge amount that's not quite life changing but significantly bank-roll changing), then you hedge / take lower variance / etc. But still, the original post (to me) makes it seem like you're giving off the impression that hedging or taking the lesser EV is better sometimes.
I'd rather it had been worded in a way, like, "NEVER hedge / take even money / etc. NEVER ever EVER!!!! * ....... *unless it's a life changing amount".
Quote: mcallister3200In a pitch game or deeply dealt game fairly late in the deck and the TC dropped significantly during round, is under but close to the insurance threshold, and your current bet would be overbetting if the round were to start now. Could always insure for less too, but that has a better than 50% of confusing the dealer and floor being called over.
What're ya talking about!? Dealers totally know what to do when a player insures a blackjack for less! I've never had any issues with it, at least...... ;)
Quote: aceofspades1,050,000 expected v. 1,000,000 guaranteed hmmmmmmmm…?
That's only the long run expected value (if you were to do this a million times that would be your 'average' win each time). If you boil it down to a binary decision then it's 1,500,000 vs 1,000,000...
Quote: RomesThat's only the long run expected value (if you were to do this a million times that would be your 'average' win each time). If you boil it down to a binary decision then it's 1,500,000 vs 1,000,000...
Which is where Certainty Equivalency comes into play.
I think working off of a Certainty Equivalent is fine for long term, repetitive wagers since your risk tolerance is going to be captured by your Kelly number.
Quote: RomesThat's only the long run expected value (if you were to do this a million times that would be your 'average' win each time). If you boil it down to a binary decision then it's 1,500,000 vs 1,000,000...
But the question was changed to 100 hands of 10k each
Quote: GreasyjohnSometimes, we may not make the "correct" play in blackjack. Sometimes a play that has a +EV is better than a play that has an even better EV. The following example is strictly hypothetical but brings home the point that we may accept a smaller win if that win is very substantial.
Suppose someone were to give you a million dollars as a wager. The condition is that you must bet it all, right now, on one hand of blackjack at a SD, 3:2 table where the shuffle has just occurred. You don't keep the bet if you win, you only keep the winnings. You place the million into the betting circle and the cards are delt. The dealer's up-card is an ace, and you are dealt a blackjack. Even money is offered. Do you take it?
If you take even money you walk with a million. If you don't take even money you will push 30.612245% of the time, and get paid $1,500,000 69.3877% of the time, for an average win of $1,040,815. Of course, there is no average win if you don't take even money. You either win $1,500,000 or you win nothing.
Your odds are better by not taking even money, and you win $40,815 more, on average, if you don't. But I would take even money. That's because a million dollars 100% of the time is worth more to me than taking a 30.612245 % chance of winning nothing, and a 69.3877% chance of winning $1,500,000.
This is an absurd scenario which would never happen, but it makes an important point. We may accept a lower EV and variance if the win is big enough. How big is relative to the individual bettor.
I understand your point but I would like to quibble. In your scenario, if the dealer does have blackjack then I push and have to play the money again on another hand, right? And when I play that hand I will not have another $1,000,000 to double or split, right? So the effective house edge on the next hand that I am obligated to play is around 2%, meaning that the average hand value decreases by about $20,000 if you reject even money.
Quote: bigfoot66I understand your point but I would like to quibble. In your scenario, if the dealer does have blackjack then I push and have to play the money again on another hand, right? And when I play that hand I will not have another $1,000,000 to double or split, right? So the effective house edge on the next hand that I am obligated to play is around 2%, meaning that the average hand value decreases by about $20,000 if you reject even money.
I should have said in my post: One hand, win, lose or push. And yes, the whole million on the initial wager.
Quote: aceofspadesBut the question was changed to 100 hands of 10k each
For the original question, I would take even money... Understanding that I now have a $500,000 bankroll and let's think of the EV that could come from that =D.
For the newly changed question, where it's over 100 hands 10k each... I would never take even money (assuming fresh deal each time). After 100 hands your chances of being ahead more than the even money EV are very good.
Quote: RomesFor the original question, I would take even money... Understanding that I now have a $500,000 bankroll and let's think of the EV that could come from that =D.
For the newly changed question, where it's over 100 hands 10k each... I would never take even money (assuming fresh deal each time). After 100 hands your chances of being ahead more than the even money EV are very good.
I thought other people would think that, too.
It is really interesting. So there is a line out there, a decision point, somewhere, between taking a guaranteed amount, vs making the "best" decision, mathematically speaking.
Quote: Dalex64I thought other people would think that, too.
It is really interesting. So there is a line out there, a decision point, somewhere, between taking a guaranteed amount, vs making the "best" decision, mathematically speaking.
I would argue that with numbers this big, the EV of the game probabilities does not capture "real life EV". It is more than just a utility of money argument, but it is also an understanding that having $1,000,000 allows you to take advantage of other money saving opportunities. For example if I have a $400,000 4% mortgage with 20 years left I could save about $180,000 by paying it off today with that $1,000,000. If I had to calculate the additional mortgage interest into the cost of losing the wager then I am clearly better off taking even money because the saved interest dwarfs the difference in EV.
Quote: Mission146Wizard says:
However, he makes an exception for life-changing money. I look at taking EM as essentially a hedge, so because that is life-changing money for me, I feel justified in taking it...and not just because the Wizard says so.
Hell, if you offered me 50-75% I'd probably take it. Anything less than a guaranteed +500K is when I'd have something to start thinking about.
I was just about to quote the Wizard's 7th commandment of gambling without reading the rest of the thread. Figured I'd better check someone didn't beat me to it!
I would take even money. $1MM is life-changing to me.
Quote: TortoiseMy biggest problem with utility theory is that it usually ignores repetition over time. I think we'd all take the million dollars if this were a once in a lifetime opportunity, but if you were presented with the same situation every day you'd almost certainly make more over the course of a year declining even money.
I don't think it's a problem to utility theory itself. Utility is just the way you measure the efficiency of your decisions. Of course it boils down what utility to apply.
The log-utility arises from the goal to maximize your wealth's growth rate. The basic concept is, with greater wealth you can make equally larger-scale decisions. Thus with each opportunity offered, you try to maximally exploit it by growing wealth before it. Same applies if you lose some of your +EV bets, the log utility basically guarantees that you are not underfunded and can still continue to exploit upcoming opportunities.
Having said that, one should always chose the log-utility decision. It gets you best of both worlds: for single decisions and also for multiple repetitions. The log utility is conservative if you face serious decisions (like your million dollar blackjack hand vs. dealers A). But it also applies for the repetitive game: once you have a large amount of wealth (and you should get them fast, getting these kind of opportunities) the log-utility effectively becomes the EV-utility where you eventually don't take even money anymore.
Personally I find the log-utiltiy as it unites conservative and exploitive play in a very beautiful play. As it's been said it doesn't solve the mentioned St.Petersburg paradox. I think this is because at really really large amounts, even log-utility does not represent reality. If you can buy all of the world, there is no further use of dollars in your wallet.
Often I do it to get closer to Kelly, and other times I do it just because I don't want to deal with the high variance mentally.
If you had a 3k roll and could take a 100 dollar bet with an EV of 197 dollars and a variance of 4000 or you could take a 100 bet with an EV of 92 bucks and a Variance of 800 dollars which would you take? I could be mistaken, but I'm pretty sure only one of those two bets fits under Kelly, with the former getting kind of close. Honestly even if it was at full Kelly I'd probably go under a little for the sake of my sanity.
I roughly made up the numbers but I had been faced with similar decisions in the past. And I usually took the line with less variance because the less often you downswing the more opportunity you have to keep making +EV plays.
This discussion reminds me of Tournament Hold-Em players as the tourney field shrinks close to the money bubble. Most players, particularly non-wealthy players, will tighten up and play more conservatively so that they can "make the money," even though utility theory suggests to play aggressively and accept a higher risk of not making the money in order to increase your chance of finishing first in the tournament.
Quote: Greasyjohn
Suppose someone were to give you a million dollars as a wager. The condition is that you must bet it all, right now, on one hand (Edit: win lose or push) of blackjack at a SD, 3:2 table where the shuffle has just occurred. You don't keep the bet if you win, you only keep the winnings. You place the million into the betting circle and the cards are delt. The dealer's up-card is an ace, and you are dealt a blackjack. Even money is offered. Do you take it?
This is an absurd scenario which would never happen, but it makes an important point. We may accept a lower EV and variance if the win is big enough. How big is relative to the individual bettor.
IF you are sitting at a table with AoS you would be the dumbest person on earth not to take even money on that. Guaranteed the dealer has it.
Quote: surrender88sI think this is important for amateur or aspiring advantage players. Pros, who have been in these situations hundreds of times, know to take the +EV play, every time(sorry, sort of sidetracking the one-in-a-lifetime scenario of the OP). But for an amateur with a limited bankroll, in a high variance situation, taking the lower variance can mean longevity. +0 vs +150% is a big difference.
I understand where you're coming from about longevity, but if you're going to reference your comment towards aspiring advantage players I would think it's more important for them to learn to do the right play every time, regardless of anything else.
Quote: bigplayerI take even money on a BJ whenever I have more than a minimum bet out. This works out to +3 Zen instead of the usual +5. This has more to do for reasons of cover than anything else. If your house was worth $1 you wouldn't buy fire insurance, likewise, nobody takes even money when betting the table minimum.
You are correct If my house was worth $1 I would not buy fire insurance... I would light it on fire.
ploppies take even money all the time whilst min betting. :)
Quote: rainmanYou are correct If my house was worth $1 I would not buy fire insurance... I would light it on fire.
ploppies take even money all the time whilst min betting. :)
The other day at the table, player BJ vs Ace. Dealer asks even money/insurance, player's like "Nah that's stupid". Another player has a questionable look on his face, the guy with the BJ then flips over his cards, " HAH, I ain't no fool -- of course I'll take even money every time!!"
It's basically just even money, but, it pays 10% less.
