Lotto - Positive EV?
Currently Mega Millions is at $290M (~$183M instant payout). I consider the instant payout to be the most accurate since all annuities do is lower the current value of your future payment. For this problem let's ignore taxes (although I believe taxes need to be considered because they're equivalent to a vig in the player's eyes).
Mega Millions is played with a field of 5 numbers ranging from 1-56 that cannot be repeated and their order does not matter. In addition, you must also hit the Mega Ball number that ranges from 1-46. I have a couple of questions:
1. How do you calculate the odds of hitting the jackpot ONLY? Please go into details, I'm getting something way off.
2. The Washington (and Mega Millions) websites say that there is a 1:175,711,536 chance of hitting the jackpot. To reference the previous question, I get well over 400 million to 1 when just counting the 5 numbers from 1-56. If it is 1:175,711,536 - does that mean it would be advantageous for some millionaire to buy one ticket of every combination if he knew nobody else would hit the jackpot (This could lead to a -real- discussion since the chance of someone else hitting the jackpot is something you need to consider)? If it is not 1:175,711,536 - how are they getting that number?
Reference for advertised odds: Mega Millions Official Website
46 * 56*55*54*53*52/(5*4*3*2*1) = 175,711,536Quote: ahiromu...1:175,711,536 ...
There are 56*55*54*53*52 = 458,377,920 permutations for picking five numbers from 1-56. However, the order of the five numbers does not matter, so 458,377,920 must be divided by 5*4*3*2*1 to find the number of combinations for picking 5 numbers from 1-56.Quote:... I get well over 400 million to 1 when just counting the 5 numbers from 1-56...
Here is a discussion of having to share a lottery jackpot with other winners: https://wizardofvegas.com/forum/off-topic/off-topic/2447-split-lottery-jackpot-winners/
Of course, this presumes that you can generate 700 tickets per second. ;^)
The biggest monkey wrench to the whole problem, is the possibility of sharing the prize with multiple winners. I believe the team waited for the prize to be 2.5 times the cost.
FYI: Taxes aren't as big of an issue as you may think. Lottery losses get deducted right off the top. Since you'll have all those losing tickets, only the profit is taxed.
ME, I am going to make the assumption that you did not make the mistake of looking at the lump sum amount, calculating how much you could turn it into after twenty years (actually 25 for Mega-Millions and 29 for Powerball), and comparing it to the advertised payout amount. That would be an inappropriate comparison, because the advertised figure is the annuity amount (payouts all along the way) and not an end-of-investment figure. Many people make that mistake in doing the comparison, but I doubt that you would.Quote: MathExtremist... First off, you always want to take the lump sum payout, but that's only about 1/2 the pot. They just use it to buy a 20-year annuity to double the money, but doubling your money in 20 years is a suboptimal investment - you can do better on your own. ....
However, have you taken into account the tax deferral aspect of the annuity? I think that is where a jackpot winner draws the big benefit of not taking the lump sum. By letting the lottery corporation make the investment, you allow them to invest pre-tax dollars, which is a much larger sum than you can invest yourself with the lump-sum, after-tax amount. To do better, you would need to obtain substantially higher returns than the annuity rate.
Also, as for "you can do better on your own", are you referring to risk-free investments, or do you discount your expected returns based on the risk to which you expose the principal? The lottery annuity funds not only are substantially invested in federal government securities, but the jackpot winner also has a binding contract with the state to pay the annuity proceeds even if the lottery corporation's investment does not pay out as expected. I think that's about as risk-free an approach as is available these days.
If I were actually to win one of those mega-jackpots, I would have an additional, non-mathematical reason for preferring the annuity. Considering the level of wealth I have personal experience managing, I would be well over my head trying to manage hundreds of millions of dollars. I think it would be a tremendous hassle to do that, and if I had that kind of personal wealth, the last thing I would want is added hassle in my life. Yes, of course I could hire a professional financial adviser, perhaps someone who would turn out to be (ethically) a second cousin of Bernie Madoff. Personally, I'd prefer the ease of just having the checks come in on a very-reliable, annual basis while I enjoyed my hassle-free life.
Quote: DocIf I were actually to win one of those mega-jackpots, I would have an additional, non-mathematical reason for preferring the annuity. Considering the level of wealth I have personal experience managing, I would be well over my head trying to manage hundreds of millions of dollars. I think it would be a tremendous hassle to do that, and if I had that kind of personal wealth, the last thing I would want is added hassle in my life. Yes, of course I could hire a professional financial adviser, perhaps someone who would turn out to be (ethically) a second cousin of Bernie Madoff. Personally, I'd prefer the ease of just having the checks come in on a very-reliable, annual basis while I enjoyed my hassle-free life.
I would imagine at $290 million even using the annuity would require a financial planner of some sort.
Your other points are totally valid, though. Why do most people seem to take the lump sum, then? Greed? They don't trust the lottery?
Quote: ElectricDreamsWhy do most people seem to take the lump sum, then? Greed? They don't trust the lottery?
Probably because the state encourages it.
I have a buddy that works for the NJ Lottery. Here, (and presumably elsewhere), if you win, and have selected the annuity, you are given the chance to change your mind. If you selected cash when purchasing the ticket, you can not change. They have trained the ticket agents to automatically hit the cash button rather than ask, when a customer doesn't specify a choice.
Why?
Because, as shocking as it is, people with million dollar annuities sometimes move without leaving a forwarding address. The headaches it causes the Lottery Commission are so great that they prefer people take the cash option.
A $290 million jackpot for MegaMillions, taken as an annuity, would mean annual payments of about $11 million minus the federal and state taxes withheld. Yes, a financial adviser could be useful -- I would think more in terms of needing a good attorney for tax and estate planning.Quote: ElectricDreamsI would imagine at $290 million even using the annuity would require a financial planner of some sort.
Your other points are totally valid, though. Why do most people seem to take the lump sum, then? Greed? They don't trust the lottery?
In my own case, I don't really expect to live long enough that I would see all those annuity payments if I actually were such a jackpot winner. If I mismanaged the $11 million minus taxes one year, then what the heck, just wait for next year's check. Surely even with my limited competence I could manage the funds well enough not to go broke while the checks were still coming in. If I took the lump sum, it might vanish (see earlier reference to Bernie Madoff.)
I don't know why "people seem to take the lump sum" or if that is even true. The annuity option is the default, and you must explicitly choose the cash option within a time limit in order for that to happen.
As I pointed out, in NJ at least, the default is cash, and if you chose annuity, you're allowed and encouraged to change your mind.Quote: DocThe annuity option is the default, and you must explicitly choose the cash option within a time limit in order for that to happen.
Upon thinking about it, I'd be surprised to learn that NJ is alone, or a minority, in this line of thinking.
Quote: DocI don't know why "people seem to take the lump sum" or if that is even true. The annuity option is the default, and you must explicitly choose the cash option within a time limit in order for that to happen.
Okay, I'll admit that I only made that claim just from personal observation. I can't seem to find a statistic for annuities vs. lump sums after some Google searching, either, though :-\
Quote: ahiromumy weakness is throwing a few bucks on the lotto when the jackpot gets up there (Powerball/Mega Millions 100+ million).
Mega Millions Official Website
... because when the jackpot is over 100$ million you are more likely to win it. :)
haha just breaking ur balls a little bit
Quote: DJTeddyBearAs I pointed out, in NJ at least, the default is cash, and if you chose annuity, you're allowed and encouraged to change your mind.
Upon thinking about it, I'd be surprised to learn that NJ is alone, or a minority, in this line of thinking.
In California, the winner may choose either, AFTER the win is verified, you don't need to pick cash or annuity when purchasing the ticket.
Also, in California, the annuity is not a straight line amount. After a larger initial payment, the remainder is distributed in varying percentages that grow over the remaining payout period.
Quote: AyecarumbaIn California, the winner may choose either, AFTER the win is verified, you don't need to pick cash or annuity when purchasing the ticket.Quote: DJTeddyBearAs I pointed out, in NJ at least, the default is cash, and if you chose annuity, you're allowed and encouraged to change your mind.
Upon thinking about it, I'd be surprised to learn that NJ is alone, or a minority, in this line of thinking.
Also, in California, the annuity is not a straight line amount. After a larger initial payment, the remainder is distributed in varying percentages that grow over the remaining payout period.
To DJTeddyBear:
Yes, different states handle things differently. As you say, a choice of lump-sum is non-reversable, while an initial choice of the annuity option may be changed to lump sum if you do it quickly enough. I read the NJ rules, and a player can choose "cash option" at the time of ticket purchase or for up to 60 days after being declared a winner. After that, the annuity automatically goes into effect. I view that as meaning that the annuity is the default, with the player being given ample opportunity to choose the cash alternative. If they actually do train their retail agents to make the decision for the player, I would consider that approaching fraud, or at least theft of the player's control of his options.
To Ayecarumba:
Are you sure that those varying payouts apply to MegaMillions? That is the way that PowerBall works (geometric-growth annuity with 4%/year increase, I think), but I believe that MegaMillions is a uniform-payment annuity in all states.
To all:
At present, the MegaMillions advertised jackpot has risen to $330 million, or $208 million for the cash option.
Quote: Doc
To Ayecarumba:
Are you sure that those varying payouts apply to MegaMillions? That is the way that PowerBall works (geometric-growth annuity with 4%/year increase, I think), but I believe that MegaMillions is a uniform-payment annuity in all states.
I stand corrected. According to the California Lottery website, the Mega jackpot is paide in 26 equal annual payments. This is the default setting when you buy a ticket. If you win, you have 60 days to change to "lump sum".
California runs another large lottery known as SuperLotto Plus. This jackjpot is paid in 26 annual graduated payments, 2.5% of the jackpot for the first, then slowly growing to 5.1% of the jackpot for the 26th. Sorry for the confusion.
Note that California does not require state income tax from their lottery proceeds for California residents.
Quote: DocAt present, the MegaMillions advertised jackpot has risen to $330 million, or $208 million for the cash option.
What discount rate does this imply if the payout is 25 years (I think that's right)? I'm blanking on the formula and can't find a table handy.
Anyway, FWIW, I always ballpark the cash payout after discounting and taxes at about 40% of the published jackpot. So, for $330 million, the payout after discounting and taxes would be about $132 million.
That's about right, +/- 5%, isn't it?
Quote: Doc
To all:
At present, the MegaMillions advertised jackpot has risen to $330 million, or $208 million for the cash option.
With a 47% total taxrate, the MM breaks even with a cash-option jackpot of about $302,000,000. At the current rate of escalation, that'll be crossed on the drawing on 1/15/11 (maybe on 1/11/11 if the rate increases slightly). If the jackpot is not won beforehand, all hell will break loose on Friday, 1/15. It's the second Friday of the month, and it's the 15th. The vast majority of American workers will have a nice fresh paycheck to invest in the lottery on that day.
Sorry that I overlooked your post earlier.Quote: ItsCalledSoccerWhat discount rate does this imply if the payout is 25 years (I think that's right)? I'm blanking on the formula and can't find a table handy.
Since the MegaMillions jackpot annuity payout involves one payment when the claim is approved followed by 25 additional and equal annual payments, it is a 26-year, beginning-of-period annuity, also known as an annuity-due. A formula is provided at this Wikipedia link. Unfortunately, that formula is for the future value of the annuity rather than the present value. I think you get the present value by dividing by (1+i)^n. Alternately, you can use the formula for present value for an end-of-period annuity (available at this Wikipedia link and multiply by (1+i) to adjust for the payments starting immediately. Confusing enough? (I'm too lazy to try to compose and post full, clear equations here myself. It's late here on the east coast.)
Calculations are "left to the reader."
Quote: ItsCalledSoccerWhat discount rate does this imply if the payout is 25 years (I think that's right)? I'm blanking on the formula and can't find a table handy.
Anyway, FWIW, I always ballpark the cash payout after discounting and taxes at about 40% of the published jackpot. So, for $330 million, the payout after discounting and taxes would be about $132 million.
That's about right, +/- 5%, isn't it?
Using my 47% total tax here in MN (for income over $250,000 - I'm assuming for simplicity that the top rate applies to the entirity of each distribution), I get an NPV of about $125MM on the annuity and about $110MM on the cash option. It looks like the annuity's discount rate is about 2.79%.
If you assume that you can either take the cash and invest it safely at 5% for 25 years or take the annuity and re-invest the annuity payments at that same 5%, then 25 years from now you'd have about $373MM from the cash option and $349 from the annuity. (note, out of laziness I'm applying regular income tax on the initial distributions but ignoring any investment-related tax implications)
Given the relative proximity of those numbers and the safety of the annuity stream, I'd have to be pretty damn sure of myself to take the cash option. I'm almost certain that I'd take the annuity if it came to it. Though, the victory celebration in Vegas with y'all would eat up most of the year 0 distribution...
Quote: wildqatAs far as cornering the market goes, yes, if you buy one of every ticket combination, then you'd be spending $175,711,356, and you would need to win at least $175,711,357 to have a positive EV. Since you would win $31,979,120 from the smaller prizes, you would need to win at least $143,732,417 from the jackpot to be +EV. This would need to be after taxes, splits, tips on the hand pay, etc., and doesn't take the Megaplier into account at all (but the jackpot would need to be much larger, even at ×4).
Of course, this presumes that you can generate 700 tickets per second. ;^)
I doubt you'd get the full $31,979,120 from the smaller prizes, either. They'd go parimutuel with too many winners and you'd receive less for them. The jackpot would have to be astronomical to even consider buying all the numbers, and anyone with ~176 million in cash to blow on lottery tickets should be smart enough to figure out even one other winner would ruin the whole thing.
Edit to add: It just jumped to $355 million. That's worth wasting a few bucks on!
The states want you to take the "cash" option becasue MORE money moves to the state THAT year, then waiting 26 to 29 years to get it.
Lets say you win $100 million on the cash option. NJ would get about $7 million in that year. Assume a 7% state tax rate.
But if you take the annuity, you get (to make the math easy) a win of $225 million paid over 26 years, or $8,654k the first year. NJ would only get $599,480 in that year, and presuming every year afterwards. You still pay, even if you move out... ;)
I have already put my $5.00 in.
Personnally, I would take the annuity.
Some states do use parimutuel payouts for the lesser prizes, but most states have fixed payouts. This factor depends upon where you bought your gazillion tickets.Quote: FarFromVegasI doubt you'd get the full $31,979,120 from the smaller prizes, either. They'd go parimutuel with too many winners and you'd receive less for them. ...
Quote: DocSome states do use parimutuel payouts for the lesser prizes, but most states have fixed payouts. This factor depends upon where you bought your gazillion tickets.
Is that really done on a state-by-state basis for a multi-state lottery game? If you and I both hit 5 white balls tonight, I can get the whole prize and you might get a smaller payout? That doesn't seem fair - not that it has to be - but that really doesn't seem fair!
Quote: DJTeddyBear
Because, as shocking as it is, people with million dollar annuities sometimes move without leaving a forwarding address. The headaches it causes the Lottery Commission are so great that they prefer people take the cash option.
the lottery is mailing out million dollar checks????
Quote: rdw4potusUsing my 47% total tax here in MN (for income over $250,000 - I'm assuming for simplicity that the top rate applies to the entirity of each distribution), I get an NPV of about $125MM on the annuity and about $110MM on the cash option. It looks like the annuity's discount rate is about 2.79%.
Really? Just 2.79%? Doesn't that seem incredibly low?
Anyway, I would take the one cash payment. That may be based more on ignorance than any financial and actuarial calculations, but the lingering question I have is ...
1. I'm pretty sure you can't sell the annuity, so that's out if you select it. But ... who owns the annuity upon your death? Can it convey AT ALL?
2. While my EV on remaining life exceeds 26 years, you never know.
3. There's no god-given right to not having runaway inflation here in the USA. And, to add further concern, with an unpayable debt and no apparent political will to slow it down, the current environment seems as likely as we've ever had to experience this. Yes, it would also affect a cash payout, but you'd have the money in hand.
4. If the state goes bankrupt, or there's a severe sudden change in the law, or the lottery commission goes under, I'm not sure the payments would continue in the amounts promised.
I'm gonna run some numbers and see if I can't BFFI my way to figuring out the discount rate. 2.79% just sounds too low to me.
Quote: rdw4potusIs that really done on a state-by-state basis for a multi-state lottery game? If you and I both hit 5 white balls tonight, I can get the whole prize and you might get a smaller payout? That doesn't seem fair - not that it has to be - but that really doesn't seem fair!
Apparently California is the only place that is different -- that seems to be a trend there. Here's what it says here on the MegaMillions site, which seems to be bogged down this evening. ;-)
Quote: MegaMillionsWhat if you win the jackpot?
Annuity option: Provides 26 annual payments. For every $1,000,000 in the jackpot, you will receive approximately $38,500 per year before taxes.
Cash option: A one-time, lump-sum payment that is equal to all the cash in the Mega Millions jackpot prize pool.
In addition to the jackpot, there are other prizes ranging from $2 to $250,000*.
* In California all prizes are pari-mutuel, meaning payouts are based on sales and the number of winners. All other Mega Millions states set the 2nd through 9th prizes at pre-determined amounts.
**Some states use a Megaplier feature to increase non-jackpot prizes by 2, 3 or 4 times. To find out if your state participates, and to get Megaplier results, visit the lottery web site in the state in which you played.
So the discount might be tied to the 20-yr + 200, at least that's the roundest number of the few indexes I mentioned. Could be anything ... 400 above target? 200 above 20-yr? 100 above prime?
Is this discount published anywhere?
Anyway, 4.14% still seems low. I thought it would be in the 8% - 10% range, but oh well. Interesting.
Quote: NicksGamingStuffI have an odds question, since the mega numbers are 1-46, wouldnt the odds of picking the mega number be 1:46? But according to the NJ website it says odds of winning the Mega only are 1:75, http://www.state.nj.us/lottery/games/1-1-1_mega_millions.shtml im sure this has something to do with the fact you pick 5 plus the mega, but I would think for mega alone it should be 1:46, any thoughts?
The NJ form says "How to win Megamillions - Match 0 White Balls + Megaball, Mega Million prize $2, Mega Million odds 1:75." That means to win $2, you must match exactly zero numbers out of 56 numbers and pick the megaball. The number of ways to do that is: 51*50*49*48*47/(5*4*3*2*1) * 1 = 2,349,060. The total number of choices is 56*55*54*53*52/(5*4*3*2*1) *46 = 175,711,536. And 2,349,060/175,711,536 = 1/74.8.
Quote: DocSome states do use parimutuel payouts for the lesser prizes, but most states have fixed payouts. This factor depends upon where you bought your gazillion tickets.
From the Virginia Lottery site:
Quote:Jackpot prizes are pari-mutuel. All other prizes are "fixed" prizes. If prize liability exceeds the prize-pool funding for fixed prizes, these prizes may be paid on a pari-mutuel basis and could be lower than these published prize levels.
Had you played the numbers from Lost, you'd have matched 3 plus the MegaBall for this drawing. I wouldn't be surprised to see an overabundance of $150 winners. With the Megaplier, it would be $600.
If the Virginia lottery actually expressed it that concisely, they must use a much smaller army of lawyers than some other states to obfuscate their game rules. From earlier discussions on this thread, I downloaded the MegaMillions rules as published by both the North Carolina and New Jersey lotteries. They have different wordings of how to deal with those situations when there are too many lower-tier winners in a drawing for the funds available. They both make it complex. The NC rules run five paragraphs totaling 26 lines on how to handle this. The NJ version covers it in one 11-line paragraph, but it goes on for another page and a half covering the details of other problems with divvying up the money pool.Quote: FarFromVegasFrom the Virginia Lottery site:
...Quote:Jackpot prizes are pari-mutuel. All other prizes are "fixed" prizes. If prize liability exceeds the prize-pool funding for fixed prizes, these prizes may be paid on a pari-mutuel basis and could be lower than these published prize levels.
By the way, I did not win the jackpot this time.
Quote: DocIf the Virginia lottery actually expressed it that concisely, they must use a much smaller army of lawyers than some other states to obfuscate their game rules. From earlier discussions on this thread, I downloaded the MegaMillions rules as published by both the North Carolina and New Jersey lotteries. They have different wordings of how to deal with those situations when there are too many lower-tier winners in a drawing for the funds available. They both make it complex. The NC rules run five paragraphs totaling 26 lines on how to handle this. The NJ version covers it in one 11-line paragraph, but it goes on for another page and a half covering the details of other problems with divvying up the money pool.
By the way, I did not win the jackpot this time.
Virginia usually keeps to the point of "If it's fun, then it's most likely illegal." But we have the lottery with its lousy odds to keep us amused between trips to Vegas or Atlantic City. I guess they found a part-time lawyer to write a rule or two.
I didn't win, but I didn't drop an awful lot on tickets, either.
Quote: ElectricDreamsNo jackpot for me! Worst $5 spent ever...
You've obviously never eaten at White Castle...;-)
Quote: rdw4potusYou've obviously never eaten at White Castle...;-)
Hey now - White Castle is delicious! Of course, the nearest one is two or more hours away. Which is sad :-(
Their chicken rings are a little weird, though, have to admit.
Project website
So the EV gets positive somewhere around the $260 million mark. Not like the odds will ever be in your favor, though.
Quote: dmWhy won't they be in your favor if 260 gets reached?
Your odds are still 1 in 176 million. But the expected value of your $1 ticket will be $1. It makes it look like a bit less of a sucker bet at that point, but I still consider it a sucker bet. It's the only game in town around here, though, and I can afford to blow a dollar on the chance lightning will strike.
Quote: FarFromVegasI had remembered a group of students in San Antonio had done a project on the expected value of lottery tickets, and it looks like they started it back up a year ago.
This professor and his students got the Texas Lottery Commission to change the wording on scratch off tickets to include pushes, e.g., instead of odds of winning = 1:4.61, odds of winning or breaking even = 1:4.61.
Now he's analyzing his employer's use of a lottery system to determine pay for summer school teachers Teacher Lotto.
Quote: AyecarumbaTonight's jackpot now $312 million. Does that make my dollar wager woth a little more than a dollar now?
Mathematically, about $1.30. Realistically, it's a dollar you can afford to lose, I hope. :)
I got Chinese food tonight, and my fortune was about Lotto for the first time I can ever remember! So I put it on my ticket for luck. Maybe Lady Variance likes lo mein noodles.
Quote: AyecarumbaTonight's jackpot now $312 million. Does that make my dollar wager woth a little more than a dollar now?
So does this mean that if everyone purchased one $1 ticket they'd all have a +EV bet?
Quote: FarFromVegasMathematically, about $1.30. Realistically, it's a dollar you can afford to lose
That's being honest, but the video poker gurus have a different tale to spin when they come face-to-face with a +EV game. If they had a 30% "edge" then after putting $10,000 in play thru the machine and losing $400, they'd proclaim to the world that they just came out ahead by $3000....in phantom bucks of course, but I'm the only one who's ever exposed them for the BS they spew to so many unsuspecting players.
Quote: RobSingerThat's being honest, but the video poker gurus have a different tale to spin when they come face-to-face with a +EV game. If they had a 30% "edge" then after putting $10,000 in play thru the machine and losing $400, they'd proclaim to the world that they just came out ahead by $3000....in phantom bucks of course, but I'm the only one who's ever exposed them for the BS they spew to so many unsuspecting players.
Rob, for someone who purports to have devised a scheme that has won upwards of $900,000 at video poker and has a website dedicated to the proseletization of this "fact", no one here (or elsewhere I imagine) could be more aptly named a "video poker guru" than you. To poo-poo advantage play the way you do is simply showing that you either don't have any concept of the concept or that you just like to be abrasive by pretending to be thick headed.
If I have a 101-sided die and 50 sides are red and 51 sides are blue, if we place a $1 wager on the roll of the die and I win if a blue side comes up, I have the advantage over you. Even you MUST be able to see that. Now, what kind of fool would EVER take that wager by betting red? Sure, betting blue I might lose 20 rolls in a row and I might be down $20 but I would STILL have an advantage over you on each and every roll, regardless of the outcome.
So, if I was to find a +EV VP machine and play perfect strategy and run $10,000 through it and end up losing $400, I'd say that I'd lost $400, been the victim of variance and know that I played the game with an advantage regardless of what the outcome may have been. I'd play the same game again and still have that advantage tomorrow or the next day and forever.
That's advantage play Rob.
On the other hand, looking at the 101-sided die analogy, if we rolled the die 10,000 times and I permitted to to vary your bet as you pleased (always at even money) and you came out ahead after the trial, it by no means would suggest that you either had an advantage over me or that you have used some special system or method to beat me. It simply would have meant that you overcame the 1.071% advantage I'd had playing against you by luck/variance. Nothing more.
So, feel free to sneer at those advantage players and make up stories about how the only way to win is to know when to walk away... you are still playing at a disadvantage and you will not be a long-term winner at any game with any strategy.
What strategy do you recommend? Walking away any time I'm ahead, which does no more good than going to the crapper or watching a football game and coming back... the machine doesn't know I've left and returned and it's still a -EV game. You telling someone to walk away from a -EV game when they're ahead and then putting more money into another -EV game... until they're ahead again is simply foolishness. Who says they're always going to be ahead at any point? You? Telling them to set a stop-loss and then putting more money into a -EV game to win back that money and then win more... is that the best you've got? Oh, I'm sorry, I forgot your special plays. Take a -EV game and then take a situation where you are at a disadvantage and put yourself at a GREATER disadvantage because that sneaky little ol' Royal Flush just might be hiding where you least expect it! Oh, I almost forgot the important one... find the HOT game that's paying out.
Do advantage players win every time they play? Certainly not. Do you? Certainly not. But all you've done is take the red side of the die and made up a story about how you can win money even when you're behind from the start. Anyone who has any understanding of math (about grade 4 level I'd say) will see you for what you are... a story teller whose tale belongs in the same league as Goldilocks, Br'er Rabbit and all those e-mails I get that promise to enlarge my penis.
