Lotto - Positive EV?
Quote: TheNightflyRob, 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.
I agree I am a video poker guru. I am also, however, the only "guru" in this field that does not sell a strategy. Surely, even Goldilocks would understand why.
If you purport to have such a stern knowledge of my site, you'd have known that my play strategy is grounded in math, ie, optimal play. What you also missed is that I found out, from being an AP for over 6 years prior, that optimal play alone is simply playing directly into the hands of the casinos, who thrive by the math. This is the reason why approx. 5% of my plays differ from how AP's would play the hands.
Where you are fooling yourself about having "the edge" on a certain play is that first, that is exactly how the casino wants you to think, and that is how they make much of their vp profits. There's a reason for there being seemingly non-stop promos all over LV, and it entirely has to do with a plethora of AP's being sucked into play them. Next, while a 104% theoretical play may be enticing, it is only so if the player is in it for the long run. No promotion goes on that long, so all any player can hope for is to get lucky and get lucky fast. To say that anyone actually played with a 4% advantage today is ludicrous.
What strategy do I recommend? Well, between my single-play strategy, RTT, & ARTT I've won that figure stated above in a decade, and I've won at over an 80% rate. People are so hung up on saying "if you play a +EV game all the time you will likely win, and if you play a -EV game over time you WILL lose". But that's just not the case. It's the simpleton's theoretical way out of reality. And just the fact that you stumbled thru trying to explain how my strategy works tells me you would never be able to understand the true complexities that went into its development. In fact, I've gotten that same story from the most notable of names over the years, and STILL, no one wants to delve into what it is I actually do. I can only guess that they will not be able to handle the resulting sense of it all. After all, you know how neurotic math AP's are.....
Quote: AyecarumbaTonight's jackpot now $312 million. Does that make my dollar wager woth a little more than a dollar now?
The annuity is $312MM, but the cash option is about $190MM. I think the cash needs to be over $260MM in order for the game to be +EV.
Quote: rdw4potusThe annuity is $312MM, but the cash option is about $190MM. I think the cash needs to be over $260MM in order for the game to be +EV.
No. The website I linked before breaks it down. When the cash value is ~ $154MM, it goes positive. It's at about $198MM cash now.
Oregon: Lotto 6/48. 50 cents per play, 2 plays per $1 ticket. Jackpot $20,700,000 - $10,350,000 cash value. Odds of winning 1 in 12,271,152. Average tickets sold (based on past month 4/6 and 5/6 number of winners) - 800,000. Poisson true worth (accounting for split jackpots) ~ $9,900,000. EV of other prizes (per Oregon Lottery regulations - 5.9 cents.) Expected value - $0.90 per 50 cent play.
Ohio: Lotto 6/49. Jackpot $38,800,000 - $19,400,000 cash value. Odds of winning 1 in 13,983,816. Doesn't publish breakdowns, but given the fact that this jackpot has rolled over for a full year, but only grown by $200,000 and $300,000 increments, I expect that this is positive EV, but with very low sales.
California: Super Lotto Plus. Cash value $36,100,000. Odds of winning 1 in 41,416,353. Tickets sold ~ 5,600,000. Poisson true worth $33,700,000. EV of other prizes (per CA lottery regulations and breakdown) - 19.25 cents. EV = $1.00.
Florida: Florida Lotto. Jackpot $28,000,000 - Cash value ~ $16,000,000. Odds of winning 1 in 22,957,480. Tickets sold ~ 4,000,000. Poisson true worth ~ $14,600,000. EV of other prizes (per Wikipedia article) = 18.25 cents. EV ~ 81 cents.
The law of large numbers obviously comes into play, but there is definitely a lack of interest in medium sized jackpots in other states. In California, when Fantasy 5 (1 in 575,757 odds of jackpot) hits $400,000, you see routinely over a million tickets sold (number of winners over 110,000 for a game with 1 in 9 total odds). In CA Mega Millions with a lower jackpot than Super Lotto Plus still manages to get 3 million tickets sold, despite 4 times worse odds than SLP. People are drawn to the multi state games, but unless you are playing with a group, $200,000,000 annuity or $100,000,000 cash is way too much for me to even contemplate. Powerball is going to go to $2 plays next year, but will up the jackpot amounts so they grow faster. However, the odds are not getting appreciably better, so this is another group play.
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!
I am under the impression that, in MegaMillions, non-jackpot prizes in California are pari-mutuel (based solely on the number of tickets purchased in California), while other states have fixed payouts.
One thing I didn't notice in this discussion; when calculating EV, you have to take into account the number of tickets bought, since this can affect the amount you would win if you won the jackpot. (If I calculated this correctly, the most likely number of winners of a jackpot = (the number of tickets + 1) / the number of possible combinations, rounded down (if this is already an integer, this value and the number - 1 are equally likely). You are much more likely to win, say, $300 million from a $300 million jackpot if there are only 25 million tickets bought than if there are 250 million (with the additional 225 million chances that somebody else has "your" numbers so your prize is "only" $150 million).)
Somebody check these numbers to see if I missed something:
Let P be the probability of winning the jackpot (= 1 / the number of combinations)
Q = the probability of not winning the jackpot = 1 - P
N = the number of tickets
The EV of the number of winners is the sum of:
1 * N * P * QN-1
2 * N * (N-1) / 2 * P2 * QN-2
3 * N * (N-1) * (N-2) / 6 * P3 * QN-3
4 * N * (N-1) * (N-2) * (N-3) / 24 * P4 * QN-4
...
N * PN
This equals N * P * the sum of the following:
Q(N-1)
(N-1) * P * Q(N-1)-1
(N-1) * (N-2) / 2 * P2 * Q(N-1)-2
(N-1) * (N-2) * (N-3) / 6 * P3 * Q(N-1)-2
...
PN-1
By the binomial theorem, the sum = (P + Q)N-1; since P + Q = 1, the sum = 1, so the value is N * P * 1 = N * P
= the number of tickets * the probability of hitting the jackpot
= the number of tickets / the number of combinations
The EV of the jackpot = the jackpot amount / the EV of the number of winners
= the jackpot amount / (the number of tickets / the number of combinations)
= the jackpot amount * the number of combinations / the number of tickets
-When it did get to 360 Million, there were 200 Million tickets sold for one drawing.
-Assuming that you win, you should also expect, on average, another 1.14 players to win, so the real prize is Jackpot/2.14
-Then, you apply a 4% discount rate for 26 years and you get a lump sum payment of about 61% of the prize. Real Prize = Jackpot/2.14*.61
-Then, assume you live in a state where there is no state income tax, such as TX. Your tax rate on this amount will be 35%. Real Prize = Jackpot/2.14*.61*(1-.35)
-All said and done, the Real Prize = Jackpot * 0.18528
-EV from Jackpot = Jackpot * 0.18528 / 175,711,536
-EV from the rest of the game (accounting for tax of 15% for 10,000 prize and 25% for 250,000 prize) = 0.1638
So, even at 360,000,000 jackpot, EV = 360,000,000 * 0.18528 / 175,711,536 + 0.1638 = 0.54.
If the prize does get higher than that, expect the number of tickets sold to increase at least in proportion to the jackpot.
Quote: buzzpaffWhat is the +EV of the dream of winning, even if you only invest in 1 ticket ?
That's worth a buck every once in a while.
Quote: CrystalMathMega Millions will ever be +EV.
-When it did get to 360 Million, there were 200 Million tickets sold for one drawing.
-Assuming that you win, you should also expect, on average, another 1.14 players to win, so the real prize is Jackpot/2.14
-Then, you apply a 4% discount rate for 26 years and you get a lump sum payment of about 61% of the prize. Real Prize = Jackpot/2.14*.61
-Then, assume you live in a state where there is no state income tax, such as TX. Your tax rate on this amount will be 35%. Real Prize = Jackpot/2.14*.61*(1-.35)
-All said and done, the Real Prize = Jackpot * 0.18528
-EV from Jackpot = Jackpot * 0.18528 / 175,711,536
-EV from the rest of the game (accounting for tax of 15% for 10,000 prize and 25% for 250,000 prize) = 0.1638
So, even at 360,000,000 jackpot, EV = 360,000,000 * 0.18528 / 175,711,536 + 0.1638 = 0.54.
If the prize does get higher than that, expect the number of tickets sold to increase at least in proportion to the jackpot.
I looked into this a little more, because I wasn't satisfied with my simple handling of the 1.14 additional winners. After further analysis, with 200 Million tickets sold, the expected value of the jackpot is 59.7% of the total jackpot. Given this, the value of the jackpot is Jackpot*0.597*0.61*(1-0.35) = Jackpot * 0.237 (and not 0.18528 like previously stated).
With these changes, the EV of a 360 million dollar jackpot is 360,000,000 * 0.237 /175,711,536 + 0.1638 = 0.649.
