tickets or chances per draw 10 possible combos of 5/39 numbers = 575757 MATCHES ODDS WINNING COMBOS EXPECTED WINNERS 5/5 1 : 575757 1 0.0000173684 4/5 1 : 3387 170 0.0029526345 3/5 1 : 103 5610 0.0974369395 2/5 1 : 10 59840 1.0393273551 _______________________________________________________________________ overall odds are 1 : 8.7 1.1397340000 total expected winners

True, adding a few more decimal places would change the results and show no differences in the two betting scenarios but usually 2 decimal places is close enough for my purposes. As JADE said that's not the right way to prove it so I'll wait for The Mathematical Alpha Geek to post his calculations. Thanks for the head-ups.

RJOh

The chart proves by betting the $10 one time, the player can expect to match 2 numbers and because they should, it sightly increases the chances of matching 3, 4, or 5 numbers. However while the chances are slightly better, they still can only expect to get one 2 number match.

I'm assuming the intentions of the players are to win the jackpot so if the $10 better craps out on the first drawing, the $1 better still has 9 more chances to win. If the number of threads on "how I'll spend the winnings" are any indication, betting $1 ten times will probably win this poll.

If mathematically one method is better than the other, I'll defer to the Alpha Geeks too.

NY United States Member #23835 October 16, 2005 3475 Posts Offline

Posted: April 7, 2011, 7:48 pm - IP Logged

Quote: Originally posted by mayhem on April 5, 2011

It is all about time. You can buy 1000 Pick 3 Tickets for one draw or you can buy 1000 and play for 1000 draws (quite a long time). One of them your going to win. The other you have the chance of winning 1000 times....or never. lol. To increase odds you always bet more on a single game. Even though each ticket has the same single chance of winning (1:1000) your chances have increased because you hold more than one ticket.

I guess that was a logical deduction. I don't know how to write out a formula, but I'm sure it's a simple one.

That's one way to figure it out as a simple exercise in logic. If you play all 1000 possibilities you've got a 100% chance of winning. If you play 1 possibility 1000 times your chance of losing is .999 raised to the 1000th power, which is .3677, or 36.774%. meaning your chnce of winning is only 63.23%.

Here's another way to think about it without doing the math. It's obvious that playing a single ticket in multiple games gives you a chance of winning multiple times. There's no such thing as a free lunch, so what does the chance of winning multiple times cost? The cost is a reduced chance of winning even once.

Let's start small and play pick 1, a game that would have odds of 1 in 10 if anybody actually offered it, with two tickets. If you buy one ticket for each of two games you've got a 90% chance of losing each time. That means the chance of losing both times is .9 * .9 = .81, so your chance of winning is .19 or 19%. Your chance of winning both times is .1 * .1 = .01. When you play 2 tickets on a single game you've got 2 chances in 10 to win, which is 20%. You can't win twice, but you're 5% more likely to win. Of course that better chance of winning gets smaller as the odds of the game increase, but you'll always be trading the chance of winning multiple times for a slightly better chance of winning at all.

Just for fun, what happens after you find that your first of two pick 1 tickets is a loser? Doesn't that second ticket now gives you odds of 1 in 9? That's an 11% improvement over the 1 in 10 chance you'd have if that 2nd ticket was for a different drawing.

West Concord, MN United States Member #21 December 7, 2001 3675 Posts Online

Posted: April 7, 2011, 10:26 pm - IP Logged

First, we have to calculate the Probability of M - matching numbers from P - played quantity in D – drawn quantity within an N - Numbers pool. Below is a diagram of how this looks graphically. M is how many individual combination numbers played match the drawn numbers. P is how many numbers you are playing per combination. D is the quantity of numbers being selected for a draw. N is the quantity of numbered balls in the bin for the drawing.

The probability of matching is, where C(?, ?) is the Combination function:

The total combinations of P – Play quantity that can be taken in the possible ways of M –Matching numbers.

C(P, M)

Times, the total combinations of the remaining N – Numbers pool minus the P – Played quantity taken by the remaining D – Drawn quantity minus the M – Matching quantity.

C(N - P, D - M)

Divided by the total possible combinations of N – Numbers in the pool taken in D – Drawn ways.

C(N, D)

The probability of matching M numbers between a Play and a Draw is (C(P, M) * C(N – P, D – M)) / C(N, D).

To find the Probability of matching numbers between a Q – Quantity of plays and a Draw is (Q * C(P, M) * C(N – P, D – M)) / C(N, D).

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

West Concord, MN United States Member #21 December 7, 2001 3675 Posts Online

Posted: April 7, 2011, 11:53 pm - IP Logged

Ok, now this gets a bit more abstract.

When we posted the poll, we could have said, “What’s the better bet? – 1 Wingdebing / 10 Zibdo or 10 Wingdebing / 1 Zibdo”

In that, could you say for absolute certainty that a Wingdebing is or really determine what a Zibdo is?

I could have reversed the order from what you may think it is.

Ultimately, you can’t say what they mean, and I won’t say either because I don’t speak Jibber-Jab.

To that end, when we look at the probability, (Q * C(R, M) * C(N – R, R – M)) / C(N, R), the Q variable is not Associated with anything.

It can not, by the very essence of Quantum Mechanics, be Associated with any value of P and D, because, behold, we removed them and replaced it with R.

Now, can you say for absolute certainty what value R is only Associated with, P or D; I’d say not.

We can then say that in this state as an unsolved probability the Q value is in an Indeterminate Association.

It is only when we apply the probability that Q’s association is determined, and if P = D = R, then we could with the pervious Play-Draw Symmetry assign Q to the D value.

This means the Q - Quantity of D - Draws as it relates to finding the Probability of matching a single P – Play is the same as finding the Probability relating to the Q – Quantity of Plays matching a single D – Draw.

The best we could say is finding the probability of multiple Q – Quantity of some selection A from N items taken R at a time matching a single selection B from a similar set of N items taken R at a time is (Q * C(R, M) * C(N – R, R – M)) / C(N, R).

In that, we now have a generalized probability where A selection could be Plays or Draws and B selection could be a Draw or a Play, respectively.

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

mid-Ohio United States Member #9 March 24, 2001 19831 Posts Offline

Posted: April 8, 2011, 8:49 am - IP Logged

Now I'm more confused. How would you use that formula to evaluate taking 10 random shots at an invisible target all at once verses taking 10 random shots one at a time at an invisible target that changes position after each shot?

* you don't need to buy more tickets, just buy a winning ticket *

Now I'm more confused. How would you use that formula to evaluate taking 10 random shots at an invisible target all at once verses taking 10 random shots one at a time at an invisible target that changes position after each shot?

That's an intersting anecdotal summary of confusion.

In order to clear up the confusion, we need a common frame of reference.

So, please relate the following key words to the posts we made: shots, invisible, position.

How do you quantify or equate those to our post?

shots = ?, invisible = ?, position = ?

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

mid-Ohio United States Member #9 March 24, 2001 19831 Posts Offline

Posted: April 8, 2011, 12:35 pm - IP Logged

Quote: Originally posted by JADELottery on April 8, 2011

That's an intersting anecdotal summary of confusion.

In order to clear up the confusion, we need a common frame of reference.

So, please relate the following key words to the posts we made: shots, invisible, position.

How do you quantify or equate those to our post?

shots = ?, invisible = ?, position = ?

shots = picking lottery combinations to play

invisible = combination will be from any of 575,757 possible combinations but unknown at the time

position = combination different each drawing thus it's new/has positional change each time

Playing lottery is similar to trying to shoot a moving target in the dark. Using a gun that can cover the whole area with a burst of unlimited fire power will hit the target for sure but if you only get ten shots, is it a better strategy to have a burst of ten shots or take one shot at a time? If you don't know what you're trying to hit, does it make any differences?

* you don't need to buy more tickets, just buy a winning ticket *

invisible = combination will be from any of 575,757 possible combinations but unknown at the time

position = combination different each drawing thus it's new/has positional change each time

Playing lottery is similar to trying to shoot a moving target in the dark. Using a gun that can cover the whole area with a burst of unlimited fire power will hit the target for sure but if you only get ten shots, is it a better strategy to have a burst of ten shots or take one shot at a time? If you don't know what you're trying to hit, does it make any differences?

Well, we are almost there.

We have something to go on.

We're getting something ready, so it may be a bit.

Hopefully, we can make a better understand of what we've shown as proof.

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

Now I'm more confused. How would you use that formula to evaluate taking 10 random shots at an invisible target all at once verses taking 10 random shots one at a time at an invisible target that changes position after each shot?

Alright, using your example of hitting a target we’ll setup a simple expression of what we are proving by generalizing a similarity.

First, we have the target shown below. The target is the total possible outcomes for a lottery of N numbers taken R at a time.

Next we have an arrow that represents a selection that is to be made from that total possible set of outcomes. The selection could be a Play or it could be a Draw; either way, they are the same R selections from N numbers.

When it hits the target, it selects an outcome that can be expressed as a smaller area around the arrow shown below. That area represents one of the possible outcomes or the R selections from N pool of numbers.

When two arrows have overlapping areas there is said to be a match between the two selections. The following image shows what this looks like on our target.

We can setup an example of our two different types of strategies of playing 10 bucks. Below are the two different examples.

From those two examples, can you tell me which is which; Either 10 Plays / 1 Draw or 1 Play / 10 Draws?

You could not say exactly which is which based on those hits shown. That’s what the probability, (Q * C(R, M) * C(N – R, R – M)) / C(N, R), is generalizing and it is equally applicable to both examples of 1 Play / 10 Draws and 10 Plays / 1 Draw.

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer