Money

How To Get the Winning Combination Using Mathematics

Ever fork out ten bucks for a raffle and have some old lady beat you after only investing a quarter? I have and it was ridiculously annoying. Imagine seeing a bucket filled almost entirely with your name deliver the only ticket not yours. Unlikely, right? After all, percentages and randomness determine a raffle, right? WRONG! Certain factors skew the randomness, making the conventional raffle more of a strategy game than a game of chance. Here are some tricks on how to win that basket raffle, explained by mathematics.

Buying Multiple Tickets

But, what if you have multiple tickets? How would your strategy change? What if the bowls are occluded and you can’t see how many entries were in each drawing (or there were sufficiently many that you could not estimate?)

Is it better to put all your eggs (tickets) into one basket (drawing), or distribute them over all the drawings?

Again, let’s make the assumption that you are agnostic as to the prize you win (because, if you only cared about one, and only one, of the prizes you would still put all your tickets into that drawing).

The question comes down to the tradeoff: Does having more ‘skin in the game’ (multiple chances in one drawing), outweigh having multiple attempts at winning prize. Let’s take a look.

  • Let’s assume there are N tickets in the lottery before you place in your tickets.
  • Let’s assume there are d parallel drawings (competitions to enter).
  • Let’s assume that you have t tickets to distribute.

As we have no other information to go on, let’s assume that the existing entries have been uniformly distributed through the drawings. So, before you determine what to do, the N tickets have been spread through the d bowls so that each bowl holds N/d tickets.

Patience Is the Key to Success

Sometimes when the tickets are being drawn, a person merely spins the tickets around and picks one off the top. This inefficient mixing method doesn’t actually mix the tickets at all. It just rotates the tickets in the bucket a few times, which makes whichever one on top more likely to be drawn. So if you’re only going to buy a ticket or two, you might want to wait towards the end of the selling period. You’ll be that much more likely to win the raffle if this is the case.

All eggs in one basket strategy

If you place all t of your tickets into one drawing, the probability of you winning is:

This is a simple calcuation. Before you added your tickets, there were N/d tickets in the bowl. You’ve just added t more, so now the total number of tickets in the bowl is t+(N/d). Out of these, t tickets will cause you to win the prize.

Let’s put some real numbers in there. Let’s imagine there are 1,000 other tickets out there (N=1,000), and that there are five raffles (d=5), and that you have five tickets (t=5).

If you place all your tickets in the same bowl, your chance of winning is 5/(5+(1000/5)) = 5/205 ≈ 2.439%

If you had ten tickets, your odds increase to 10/(10+(1000/5)) = 10/210 ≈ 4.762%, not quite double.

Spread the Love / Disperse Your Resources Strategy

Just like in the above method, inefficient mixing methods can very easily skew randomness. So what if the person drawing the tickets doesn’t thoroughly mix and simply moves clumps around? In that case, your huge stack of tickets might all be on the very bottom. In order to avoid this, try buying periodically throughout the buying window. That way, you know you’ll always have a chance in every raffle regardless of how the tickets are mixed.

Now let’s see what happens if we distribute our tickets through all the drawings.

To calculate the probability of at least one win, we need to find the probability of losing every single drawing and subtract this from 1 (certainty). We need to do this because, with a ‘spread the love’ strategy it’s possible to win more than one of the prizes.

If you have t tickets then distributing these evenly you will be putting t/d additional tickets in each bin which, before you placed in your tickets, held N/d tickets.

You lose a drawing if your ticket is not selected, and this happens N/d times out of (N/d + t/d) times. There are the total of d drawings, so we multiply these probabilities together (logical AND), and this is the dth power:

Let’s run the same values from the example above: N=1,000; d=5; t=5

If we place one ticket in each of the five bowls, the odds of winning at least one prize is:

1-(1000/(5+1000))5 = 1-(1000/1005)5 ≈ 2.463%

This is a slightly higher chance than putting all the tickets in one drawing at 2.439% (plus there is also the chance of winning more than one prize!)

In the ten ticket example, if you place two tickets in each of the drawings: N=1,000; d=5; t=10

1-(1000/(10+1000))5 = 1-(1000/1010)5 ≈ 4.853% (cf. 4.762%)

The math is clear – Spread out your tickets*

*Assuming that the other tickets are fairly evenly distributed.

With a ‘spread the love’ strategy, not only are your chances of winning anything better, you also stand a chance of winning more than one prize.

Here is the data in graph format. Below are two curves showing the percentage chance of winning based on the two strategies. For both, the number of other tickets is kept constant at 1,000 and the number of parallel raffles is also kept at five. You can see that the orange line (spreading the love) is always higher than the blue line (putting all tickets in one drawing). Also, remember that by spreading your tickets out there is a chance that you may win more than one prize!

Pick Your Battles

Obviously, a bucket filled to the brim with tickets is going to provide little opportunity for success. If the tickets sold strongly outweigh the cost of the basket, then the raffle was a success for those hosting it, making it a lost cause for you. It’s just like playing the lottery. You’re more likely to spend the total jackpot before you win it, so the practicality in playing is greatly diminished. On the other hand, the cause might make buying a ticket worth it, or maybe just the thrill of gambling. If you want to be a good person or have a good time with it, just try dispersing.

Don’t Leave!

I’ve been around for many raffles in which someone just isn’t there to claim the prize. Don’t expect the drawing to occur before you go. In reality, those tickets aren’t being drawn until the very last minute in most cases. If you’re going to put out the money, at least give yourself a chance to win the raffle.

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Why Your Credit Score Is So Important

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Nowadays, our credit score is referenced for almost everything. Numerous banks now print credit scores on your month to month financial record. Americans progressively see how their score is ascertained and how to enhance it. Notwithstanding, only on the grounds that you have a decent FICO rating doesn’t mean you will be sanctioned for credit. Banks chooses who they will support and who they will dismiss. Regardless of what the scoring specialists like to infer, just knowing your score is insufficient to knowing your chances of getting a loan. Here are six reasons why you can have a fantastic score, yet at the same time get rejected.

1. What Credit Score Are They Using, Anyway?

You regularly hear individuals discuss their “credit score,” as though they just had one score. There are several scores in the business sector. On the other hand, there are different forms of the nonexclusive FICO score (the most generally utilized is Version 8). There are likewise FICO scores particularly for autos and bankcards. The score relies on the information from the credit agency. Also, there are three credit departments.

The VantageScore, a different option for FICO, has become progressively famous. Most sites that give a free financial assessment are really giving the VantageScore.

Anyway, it deteriorates. Most banks don’t settle on their choice utilizing one of these nonexclusive scores. Rather, they have a group of statisticians that help them assemble custom application scores. Frequently, every item and securing channel has its own particular score. Case in point, there could be a credit score for “applications from the web for money back Mastercards.” Risk administrators at banks would dependably need to demonstrate that their custom scorecards were superior to the nonexclusive adaptations.

Banks have a score cutoff. On the off chance that you are one point underneath that cutoff, you will be dismisses. Only on the grounds that you have a decent score from one of the free destinations does not mean you will have a decent score on the bank’s custom score. That is the reason your free score ought to be viewed as an aide only. It will help you comprehend in the event that you for the most part have great credit, yet it is no certification you’ll be sanction.

2. Least Income And A Job

When you seek credit, you will be finishing an application. The greater part of that application information is utilized as a part of the credit score. It can be a variable in the custom score. Then again, it can be utilized for a lethal cutoff, which implies an explanation behind programmed dismissal.

An ordinary deadly cutoff identifies with pay and livelihood. Numerous loan specialists will dismiss you in the event that you are unemployed. Furthermore, they may dismiss you if your salary is underneath the base situated by the loan specialist. Regardless of the fact that you are just $1 shy of the base, you could be dismisses, paying little respect to your score.

3. Obligation Burden

Banks and Mastercard organizations need to know whether you can stand to set aside a few minutes. A commonplace instrument used by banks is an obligation load. All in all, banks will take a gander at the aggregate regularly scheduled installments on your credit report. That would incorporate your home loan installment, auto installment, charge card installments and some other regularly scheduled installments. You would then divide that regularly scheduled installment by your gross compensation. As a rule, if that figure is over half, you will no doubt be dismisses. In the event that it is underneath 40%, you have a decent risk of approbation.

Be that as it may, each bank sets their own principle. They can choose what obligation to incorporate in the installment. They can likewise choose if unused charge cards ought to be incorporated or barred. A few banks have both front-end (barring home loan) and back-end (counting home loan) proportions.

Also, banks can change this proportion over the long run, contingent on the execution of their portfolios.

4. Major Derogatory Items

Most negative data vanishes from your credit report in 7 years. Also, the more established the item, the less effect it has on your score. Be that as it may, a few loan specialists have particular principles. Case in point, a moneylender may choose to reject anybody with an earlier liquidation, regardless of the possibility that it was six years prior. Different loan specialists may dismiss anybody with a gathering thing, or a missed installment in the most recent 12 months.

Along these lines, despite the fact that your score may have recuperated, a few banks may in any case need to dodge you. At the end of the day, they accept that this negative data is more critical than the nonexclusive score does.

5. Fast Acceleration Of Debt

Moneylenders need to stay away from clients who are heading towards insolvency. Attempting to assemble a model that distinguishes potential insolvencies ahead of time is an enormous piece of the logical work finished by danger chiefs. The most well-known pointer of somebody attempting to tackle more obligation is a credit request, which is incorporated in FICO and VantageScores. In any case, a bank or charge card organization may need to have significantly harder principles. Case in point, they could dismiss you in the event that you sought credit more than five times in the most recent six months, paying little respect to your score.

Likewise, they could attempt to gauge how rapidly your aggregate obligation has expanded. In the event that they see quick quickening in the red, you could be dismisses.

6. You Just Have Too Much Debt

A few banks get anxious at specific levels of obligation. Regardless of the fact that you have a superb FICO rating and a magnificent obligation load, they would prefer not to add to the unsecured obligation offset. This approach is regularly called the Maximum Unsecured Exposure guideline, and it puts a top on the aggregate sum the banks are willing to loan.

All in all, What Should I Do Now?

FICO ratings used to live in a black box. Presently we have a considerable measure more data. Simply recollect that the financial assessment reach is considerably more essential than the real number. On the off chance that you are over 750 on either FICO or your VantageScore, you are profoundly prone to do well on any custom score. On the off chance that your score is beneath 600, you are exceptionally liable to be turned away. Nonetheless, fixating on ten focuses is not beneficial.