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Wait, I don't understand why that couple's timing could benefit them in winning the smaller prizes where they match less than 5 numbers. I understand that the $2.5M limit to the big payoff is then redistributed to the lower numbered matching winners, but does that mean the odds of those smaller wins truly become greater than 100%? Doesn't that defeat the purpose of a lottery? And why couldn't they buy all those tickets early as well? Also, I'm assuming this couple is buying "quick picks" with random numbers instead of the Virginia lottery scheme where they were trying to cover all the numbers... which would have the the Mass. couple LOSE all the money they were "investing" right? It seems this couple's strategy side-steps the logistical hassles of covering all the numbers because quick picks are much faster/easier if you are buying hundreds of thousands of dollars worth. It's ingenious, but I'm not sure why it worked so well for them.
Wait, I don't understand why that couple's timing could benefit them in winning the smaller prizes where they match less than 5 numbers. I understand that the $2.5M limit to the big payoff is then redistributed to the lower numbered matching winners, but does that mean the odds of those smaller wins truly become greater than 100%? Doesn't that defeat the purpose of a lottery? And why couldn't they buy all those tickets early as well? Also, I'm assuming this couple is buying "quick picks" with random numbers instead of the Virginia lottery scheme where they were trying to cover all the numbers... which would have the the Mass. couple LOSE all the money they were "investing" right? It seems this couple's strategy side-steps the logistical hassles of covering all the numbers because quick picks are much faster/easier if you are buying hundreds of thousands of dollars worth. It's ingenious, but I'm not sure why it worked so well for them.
LV2ndHome! Come give me another math lesson! :-)
The way I read the article, it appears the odds of winning the smaller prizes did not change, only the amounts of the prizes. And that amount apparently went up enough to turn the bet positive, much like a progressive climbing high enough to become positive which was previously discussed.
The nice thing about this is the odds of winning a smaller prize are much better than the top prize, which means variance (risk) is lower, i.e. you get into the "long run" averages quicker. This is why the article described it as having little risk.
I understand the logic about higher prizes for smaller wins, but the're is something else that bothers me:
The article (and supporting links in the article) also mention that the odds work in their favor (74% chance of winning) if they buy 100,000 tickets and even better odds with more tickets purchased. That doesn't make sense to me. If all of the lower numbered matches have the same payouts and all are quickly given an expected return of over 100% given the $2.5M jackpot limit being reached, then why would if make a difference in the number of tickets the couple buys? I have just as much chance of turning a profit with a $5000 purchase as they do with a $500,000 purchase right? It's just relative in terms of % return.
In fact, wouldn't their strategy work against them with more tickets since they are essentially "paying themselves" in winnings with the higher number of tickets bought? I can imagine that they themselves make up a significant percentage of the total revenue for the drawing.
What other states have similar lotteries with the same rules? Hmmmm...
Here's another one for you. At Palace Station, there is a progressive VP bank, dollars, that is now up to 150K for a royal in ascending or descending order. I've never gotten one in order.
What are the odds of that happening? I think I read once upon a time the odds of just hitting a royal in random order are pretty astronomical. Is it time to play this one?
Here's another one for you. At Palace Station, there is a progressive VP bank, dollars, that is now up to 150K for a royal in ascending or descending order. I've never gotten one in order.
What are the odds of that happening? I think I read once upon a time the odds of just hitting a royal in random order are pretty astronomical. Is it time to play this one?
One in 280,687,680...If I did it right. That is the odds of winning the jackpot...Not of winning.
and I probably did it right. The particular one is easy to calculate.
I understand the logic about higher prizes for smaller wins, but the're is something else that bothers me:
The article (and supporting links in the article) also mention that the odds work in their favor (74% chance of winning) if they buy 100,000 tickets and even better odds with more tickets purchased. That doesn't make sense to me. If all of the lower numbered matches have the same payouts and all are quickly given an expected return of over 100% given the $2.5M jackpot limit being reached, then why would if make a difference in the number of tickets the couple buys?
You are confusing Expected Value (EV), which is what a ticket will return on avg, with variance, which is what most people call the "luck" factor. It doesn't matter if you buy 1 ticket or or a million tickets, the value per ticket is the same, other than potentially having to split the top prize if there are duplicate winners. But the top prize (1 in over 9MM probability) contributes a fairly small amount to the EV, the odds of having to split it are very slim, so ignore the effects of a potential top prize split for simplicity since it is not significant to the avg value of a ticket and is not the focus of the play. We are focused on getting the numerous small pays that have been increased.
Quote:
Originally Posted by logline
I have just as much chance of turning a profit with a $5000 purchase as they do with a $500,000 purchase right? It's just relative in terms of % return.
No. Your EV per ticket will be the same as theirs, but you are much more at risk to variance, i.e. "bad luck". Their actual results will almost certainly be close to EV, while you will have a much higher chance of your actual results being much higher or much lower than EV. Most people prefer a near 100% chance of winning $100k than say to have a 50% chance of winning $500k coupled with a 50% chance of losing $300k. Both have same EV (avg value), but one has much more variance.
Let's illustrate with a coin flip game. You pay $10 on each loss and receive $11 on each win... obviously a good game for you to play. But suppose you choose to only play 4 times. EV is to win 2 and lose 2 for a total profit of $2, which is an EV of +50 cents per flip. There are 16 possible win/loss combinations for 4 flips. The odds of losing or winning 4 in a row is 1 in 16 for each. The odds of going 1-3 or 3-1 is 4 in 16 for each. The odds of having 2 wins and 2 losses is 6 in 16, or only 37.5%. It's obvious these outcomes avg a 50% win rate, but you only have 37.5% chance of actually being at 50% with only 4 total plays. You have over 31% chance of being a loser through 4 flips even though you are playing with an edge (and likewise over 31% of winning substantially more than EV). The $2 in EV is not enough to safely overcome the variance, so you are far from being able to say you are almost certain to end up ahead.
Now the next guy comes in and plays a million flips instead of 4. He has the same 50 cents per flip in EV as you, or $500k in total EV. It's easy to lose 4 flips in a row, but virtually impossible to lose a million in a row. His actual results will be very close to 50% wins due to the law of large numbers. Even if he lost 52% due to negative variance (bad luck), meaning he's lost 40,000 more flips than he's won, he's still made money. We can thus be much more highly certain he will make money. Here's a link for more info: Law of large numbers - Wikipedia, the free encyclopedia
Quote:
Originally Posted by logline
In fact, wouldn't their strategy work against them with more tickets since they are essentially "paying themselves" in winnings with the higher number of tickets bought? I can imagine that they themselves make up a significant percentage of the total revenue for the drawing.
I'm not sure I follow. The payoffs on all the smaller prizes are fixed amounts as linked below and are the amounts one would use for the computations. Any amount that their play contributed is factored in by using those amounts. What's wrong with "paying yourself" to some degree? That's not a loss, and it doesn't change the size of the initial pool we are targeting. If you are winning back say 50 cents of your own money per ticket, it simply means the ticket is costing you $1.50 instead of $2.00 as another way of looking at it, so your share of the initial pool (other people's contributions) only has to cover $1.50 instead of $2.
Here's the lottery payoffs (look at the July 14 row in the chart), and the probabilities can be found further down under the "How to Win" tab:
The amounts of increase really stick out. They only have to match 2 of 6 to get their money back. 3 of 6 paid $26 instead of $5. 4 of 6 paid $802 instead of $150. 5 of 6 paid $19.5k instead of $4k, and had 1 in 39k odds, meaning they would likely have hit a few of those which would help get close to avg.
Your $5k buys 2500 tickets. If you hit the 1 in 39k prize you are way ahead of EV, if you miss you end up way behind. You don't have a high degree of certainty of being ahead because the law of large numbers don't apply to your small number of trials.
Another key point which I'm sure they took into account is different numbers should be played to the greatest extent possible to reduce variance (google correlation coefficient) at no cost in EV. They could have selected 1-2-3-4-5-6 on all the tickets and would have the same EV, but they are really at risk (it's like playing 1 ticket, but with a higher face value). You want to avoid playing 1-2-3-4-5-6 and 1-2-3-4-5-7 as another example of high correlation (5 of the 6 picks being the same). A very high percentage of the time one wins [loses], the other will also win [lose], so you still largely have all your eggs in one basket and don't get into the law of large numbers. Remember that only 2 matches out of 6 picks is still worthwhile to us, and we'd rather our actual results be guaranteed to end up close to the middle (close to EV) instead of likely being on one extreme end or the other.
Quote:
Originally Posted by logline
What other states have similar lotteries with the same rules? Hmmmm...
They haven't ended the opportunity on this one yet that I can tell unless I missed something. They took a stab at it by limiting each store to $5k in sales per day, which changes nothing except advantage players now have to spread out their purchases over more stores.
Here's another one for you. At Palace Station, there is a progressive VP bank, dollars, that is now up to 150K for a royal in ascending or descending order. I've never gotten one in order.
What are the odds of that happening? I think I read once upon a time the odds of just hitting a royal in random order are pretty astronomical. Is it time to play this one?
Quote:
Originally Posted by olecapt
One in 280,687,680...If I did it right. That is the odds of winning the jackpot...Not of winning.
and I probably did it right. The particular one is easy to calculate.
Sorry but not even close. It depends a little on game version and on the size of the progressive, but it's around 1 in 2.4MM. Using optimal strategy on 9/6 Jacks or Better with the usual 4000 coin RF payoff, the RF occurs roughly once every 40k hands. There are 120 permutations of the 5 cards making a RF, 2 of which earn the jackpot (making it 1 in 60 of the RFs on avg will be ascending or descending). So 60 x 40k = 2.4MM.
Note that when chasing high progressives, optimal strategy changes as the progressive grows, though granted this effect is minimal in this case since the progressive doesn't apply to all RFs. For example, at some point it becomes higher EV to throw away a high pair in favor of holding 3RF due to the huge RF payoff, essentially giving up a sure single for a shot at the home run. This can shorten the RF cycle substantially on progressives. On the other hand, if the game is something like Double Double Bonus, optimal strategy assuming the typical game parameters provide for a RF roughly every 48k hands instead of every 40k, so the ascending/descending jackpot odds would be closer to 1 in 3MM than 2.4MM.
Sorry but not even close. It depends a little on game version and on the size of the progressive, but it's around 1 in 2.4MM. Using optimal strategy on 9/6 Jacks or Better with the usual 4000 coin RF payoff, the RF occurs roughly once every 40k hands. There are 120 permutations of the 5 cards making a RF, 2 of which earn the jackpot (making it 1 in 60 of the RFs on avg will be ascending or descending). So 60 x 40k = 2.4MM.
Note that when chasing high progressives, optimal strategy changes as the progressive grows, though granted this effect is minimal in this case since the progressive doesn't apply to all RFs. For example, at some point it becomes higher EV to throw away a high pair in favor of holding 3RF due to the huge RF payoff, essentially giving up a sure single for a shot at the home run. This can shorten the RF cycle substantially on progressives. On the other hand, if the game is something like Double Double Bonus, optimal strategy assuming the typical game parameters provide for a RF roughly every 48k hands instead of every 40k, so the ascending/descending jackpot odds would be closer to 1 in 3MM than 2.4MM.
Yeah lv2nd is correct or at least more so than I am. I calculated the odds of a naturally dealt hand without hitting it. And that is wrong here as of course you can replace one set of cards. I also like his analysis and agree to the 2 out of 120 of royal flushes. So 2.4 Million.
Now however there is an interesting side thing...could you make it better? I expect so but only at the cost of missing other royals or winners. You only hold a lead in sequence that fits the up down sequence. Got to change the odds a lot in favor of an up down sequence...but at the cost of other losses. I wonder if it can be calculated. Easily simulated but complex to calculate.
I calculated the odds of a naturally dealt hand without hitting it.
The odds of a dealt RF in VP (or 5 card stud, Caribbean Stud, etc) is well known to be about 1 in 650k. Times 1 in 60 for ascending/descending gives about 1 in 39MM... still way off your 280MM+. Still way off even if you figured for only one specific suit. Not sure how you arrived at 280MM since you didnt provide your work.
Quote:
Originally Posted by olecapt
Now however there is an interesting side thing...could you make it better? I expect so but only at the cost of missing other royals or winners. You only hold a lead in sequence that fits the up down sequence. Got to change the odds a lot in favor of an up down sequence...but at the cost of other losses. I wonder if it can be calculated. Easily simulated but complex to calculate.
There are several "off the shelf" softwares available for this that are able to give the EV, variance, and optimal play strategy for most any VP parameters. They aren't that expensive (starting at ~$50 or so I think... haven't priced any in a very long time. I'm still using software I bought 20 yrs ago), and they also double as practice software. You play VP on your computer and you can have it alert you to play errors, the costs of those errors, track how many hands per hr you playing, etc. A must have for anyone intending to play much, as it will pay for itself very quickly over intuitive play.
For a quick example, a common 9/6 Jacks or Better game with 4k coin RF has an EV of 99.54% and variance of 19.6, and a RF cycle of just over 40k hands. Just by changing the RF to 8000 coins, the EV jumps to 101.86%, variance jumps to 81.8 , and RF cycle drops to 32,743 hands. It also gives the correct strategy, but it's easy to see from these numbers that you are tossing away small winners (or a good chance at them) to go for the grand daddy, and your actual results are thus more likely to either strike it big or strike out than to end up somewhere in the middle of the road compared to the game with typical payouts.
The ascending/descending progressive doesn't cause as radical of change from the base game because the bonus is so limited. You not only need 3RF for example, but they have to be in the right positions before you change strategy from the base strategy. If 9/6 JOB is available for this particular ascending/descending progressive, the return is 100.95% with the progressive at $150k. But usually on progressives, if JOB is offered, it's at 8/5 or less. If it's 8/5, the return is only 98.68%. The OP didn't state what game versions were available and the pay tables, but he did say they were $1 machines.
I gotta say, that reading all these posts, Is like watching two people make love, and the members of CD making observations;
one user: "Go baby, go"
Another user: "His style is sloppy, and at this rate, he will finish, way before she is satisfied, odds are she will leave him in 2.5 months"
Another user: "I will give it a try, just for fun"
Another user: "I disagree, at the percentage of stroke vs thrust, given the body temperature and outside air temperature, he can satisfy her in 2,111 more strokes, based on 1,000 strokes per hour"
How about just the FUN of MAYBE hitting a machine that may (or may not) be ripe.
wouldn't it be cool if its one of us?
Jonathan
+1. Can't rep basically anyone coz I got greedy earlier, but totally agree ^
Even if it wasnt me or anyone I personally know, to actually hear on here that is was one of us, AMAZING
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, and RF cycle drops to 32,743 hands. It also gives the correct strategy, but it's easy to see from these numbers that you are tossing away small winners (or a good chance at them) to go for the grand daddy, and your actual results are thus more likely to either strike it big or strike out than to end up somewhere in the middle of the road compared to the game with typical payouts.
