7/20/2014

EZ2 Lotto 95% Confidence Level And Margin Of Error


In statistics, what is probable in one period of time may not be the same in another period. Likewise, what is probable in one set or group of data, may not be the same in another group.

To address this variability, we establish a certain level of confidence together with a margin of error (MOE). The margin of error is a small percentage value that is added and subtracted to/from the statistic to establish a range of values with a level of certainty. MOE is expressed with plus-minus (±).

The confidence level of 95%, which is used entirely on this blog, is standard in statistical analyses; however, a confidence level of 90% can also be used for smaller studies like using a sample size of about 750.

95% Confidence Level and Margin Of Error

2004 - 2008 Data
From 2004 to 2008, the EZ2 lotto draws happened once daily. Based on this period, the winning numbers are summarized in the preceding table showing how many times each number has won, with the corresponding margin of error (MOE) at 95% confidence or certainty level. The sample data consists of 1497 actual EZ2 lotto results.
Lotto # Frequency Percent ±MOE
Sum 2994 100.0%
1 93 3.1 0.01
2 82 2.7 0.01
3 93 3.1 0.01
4 94 3.1 0.01
5 103 3.4 0.01
6 101 3.4 0.01
7 99 3.3 0.01
8 109 3.6 0.01
9 95 3.2 0.01
10 97 3.2 0.01
11 99 3.3 0.01
12 100 3.3 0.01
13 92 3.1 0.01
14 113 3.8 0.01
15 88 2.9 0.01
16 117 3.9 0.01
17 103 3.4 0.01
18 90 3.0 0.01
19 98 3.3 0.01
20 94 3.1 0.01
21 101 3.4 0.01
22 85 2.8 0.01
23 103 3.4 0.01
24 94 3.1 0.01
25 103 3.4 0.01
26 96 3.2 0.01
27 92 3.1 0.01
28 97 3.2 0.01
29 92 3.1 0.01
30 86 2.9 0.01
31 85 2.8 0.01

Based on the above data, notice that the percentage of winning of each number ranges from 2.74% to 3.77%, which is just around 3% for every number. This means that each number had a fair share of winning. Could the 3% probability be constant for every set of data? With MOE of ±1%, each number has the probability of winning at 2% - 4% (calculated as 3% ±1%). This can be true at 95% certainty or confidence level.

6/11/2014

EZ2 Lotto: Winning Frequency of Each Number

Scope of Data 

The following statistics covered EZ2 lotto drawings from 5 July 2004 to 10 June 2014. The lotto numbers are ranked 1 to 31 based on the number of times the numbers were drawn.

RankLotto # Times Drawn
1 14 530
2 04 520
3 08 504
4 16 502
5 10 500
5 25 500
7 22 494
8 06 491
9 23 490
10 05 489
11 21 484
11 28 484
13 15 479
14 31 474
15 01 473
16 12 471
16 26 471
18 19 468
19 02 467
20 07 466
20 30 466
22 13 465
23 03 463
24 29 461
25 11 459
26 27 457
27 24 449
28 18 444
28 20 444
30 17 440
31 09 429

Explanation

Based on the table above, the number 14, so far, is the most frequently drawn EZ2 number, dominating 3.6% of draw occurrences. In contrast, the number 09, so far, is lagging behind the rest of the numbers, covering 2.9% of all the draw occurrences. However, the difference between the two is just 0.7%; or 101 occurrences.

How To Use The Data

The question is: would you play for the number 09 considering it is not the most frequently drawn number? The answer is yes and no. Yes, because the difference between the winning frequency of 14 and 09 is just a small percentage (0.7%). This means that the number 09 is not exactly a "lazy" number.

No, because there are other numbers to choose from. If you have to narrow down your choices, then you can eliminate the numbers that ranked low.

In a game of chance, the winner is always the producer.

There are 961 possible combinations. It is not practical to play them all. If each ticket costs P10, you are risking P9610. The maximum amount that you can win is only P4000.

The same way, if you play your numbers in either order, you risk P4960 versus the amount that you are going to win, which is only P2000. Even if, you hit a double-number combination, say 14-14, you still lose P960. Therefore, to ensure that you do not lose by default, play at most 300 combinations. In case you win, you still earn P1000. But, that is, if you win.

Therefore, it is necessary to narrow down your choices of combinations. The table above gives you an idea which numbers you would rather eliminate.

Probability or Odds of Winning

There are 961 possible combinations that can be formed from 1 to 31. These combinations consider both possible order of combinations. For example, 12-21 is one combination; the reverse order, 21-12, is another. Your odds of winning, therefore, is 1 in 961 chances.

5/29/2014

EZ2: Would You Win Playing 100 Numbers Each Day?

What is your chance of winning if you are going to play 100 combinations each day for one month?

Gathered from EZ2 results beginning 1/2/2011, the following EZ2 numbers, 100 all in all, are the most frequently drawn combinations. Each combination had won 6 to 10 times as of 4/15/2014. (The last 17 combinations each won 6 times.)

01 - 04 07 - 07 15 - 02 21 - 10 30 - 24
01 - 30 08 - 01 15 - 05 21 - 18 30 - 29
02 - 24 08 - 14 15 - 10 21 - 30 31 - 24
03 - 06 09 - 14 15 - 20 22 - 08 02 - 14
03 - 10 09 - 24 15 - 23 22 - 17 02 - 20
03 - 13 10 - 01 16 - 03 22 - 28 04 - 29
03 - 30 10 - 06 16 - 11 23 - 12 07 - 27
04 - 04 10 - 09 16 - 16 25 - 01 08 - 24
04 - 22 10 - 22 16 - 17 25 - 05 12 - 08
05 - 01 10 - 27 17 - 03 25 - 17 13 - 05
05 - 03 10 - 28 17 - 10 25 - 25 14 - 23
05 - 11 11 - 09 17 - 24 26 - 01 15 - 08
05 - 13 11 - 20 18 - 08 26 - 02 15 - 14
05 - 16 12 - 06 18 - 10 26 - 19 18 - 02
05 - 23 12 - 28 19 - 28 27 - 18 19 - 20
06 - 02 13 - 01 20 - 04 28 - 22 20 - 18
06 - 09 14 - 04 20 - 05 28 - 28 24 - 10
06 - 11 14 - 07 20 - 06 29 - 01 27 - 08
06 - 13 14 - 16 21 - 02 29 - 04 29 - 30
06 - 15 14 - 28 21 - 03 29 - 06 30 - 15

If you are going to play the above top 100 most frequently winning EZ2 combinations every day for one month, from 4/21/2014 until 5/20/2014, how often could you have won?

You'd be surprised to know that you could have won only 4 times. Based on succeeding results from 4/21/2014 up to 5/20/2014 (there were no drawings from 4/16/2014 to 4/20/2014), only 4 of the EZ2 numbers above had won.

 Therefore,
  • Playing for the most frequently winning numbers does not guarantee a greater chance of winning;
  • Playing 100 numbers each day does not also guarantee a greater chance of winning.
In that case, where did the winning numbers come from?

Based on the results from 4/21/2014 to 5/20/2014, the following table shows which type of numbers were winning in that period. The label pf stands for performance factor. It indicates the winning frequency of a combination. Factor 1 denotes that certain combinations had won only once; while factor 7 denotes that certain combinations had won 7 times, and so forth and so on. Factor 0 means that certain combinations had not won even once. The pf is based on a one-month period. Instances (i) refers to the number of instances the factor occurred in a specific period. For this analysis, it covers a one-month period.


pfInstances
012
126
214
314
412
507
604
701

Explanation
pf = 1
This means that combinations that had won only once in the previous periods had 26 instances of winning in the next period.
pf = 2 or pf = 3
This means that combinations that had won only twice or thrice in the previous periods had 14 instances of winning in the next period.
pf = 0 or pf = 4
This means that combinations that had not won in previous periods; or had won 4 times in previous periods had 12 instances winning in the next period.
pf = 5, pf = 6, pf = 7
This means that combinations that had won most frequently in prior periods had only 1 to 7 instances of winning in the next period.
Therefore,


Let's test it.
 

As of 4/15/2014, there were only 65 EZ2 combinations that had won once (pf=1, i=26). If you played these numbers for one month every day, you could have won 12 times. This, of course, assumes that you played for every draw. The chances are greater, but unfortunately, it is not enough to break-even what you have spent. 

Would you like to try it? 

As of today, the following numbers had won only once since 12/9/2013. If theory serves us correct, any of these numbers might win again in the next 30 days. Let me know if you had won any.
 
20-0206-0129-0327-1324-01
10-1720-0322-0407-1213-24
06-2314-1523-1006-1708-16
30-1108-0516-0107-2314-24
18-0509-2024-2819-1725-14
17-2530-0316-0618-2129-28
29-2413-0928-2117-1522-14
05-2229-2527-2413-3028-23
11-1825-2806-1407-2808-29
19-0207-1012-2615-3124-07

Good Luck!

5/15/2014

Some Tips For Playing Poker More Wisely

It looks like I have saturated my mind studying numbers and statistics. While my analytic mind takes a respite, I thought I should write some off-topic articles, but still related to recreation. This is to keep my blog active. Among my blogs, LottoTips888 is the most widely visited with 66,000 pageviews as of today.

Poker is one game I have never played. In fact, I don't know how to play it. I'm not a gambler but it's okay with me to play cards for fun. I am thinking why some people are too engrossed in playing poker. What's in the poker that makes them glued to their seats?

To be a smarter player is to value your money for your family.
After some research, I now understand why poker is an exciting game. Though poker is a game of chance, it requires skill. Unlike the lottery, a poker player can increase his odds of winning by playing smart. To be smart means making wise decisions when to fold, see or call, and raise. To fold is to give up; to see or call is to stay in the game; and to raise is to increase your pot. This skill requires gut feel, keen observation, and bluffing.

To be a smarter player, of course, is to value your money for your family, more than for anyone else, such as your opponents.

Why the pros win more frequently

If professional poker players are winning more often than the average players, would they share their secrets, if ever they have one? Maybe not! Would you?

Remember this. The poker pros want your money. They are happy if you're a newbie player. They utilize their strengths, and capitalize on the weaknesses of others.

So, how do the biggest players win substantial amount of money? According to an article "Four Poker Tips The Pros Won't Tell You" by Paul Runyan, the "best players in the world aren’t doing anything really spectacular other than following basic poker tips."

What follows are some tips that I have gathered on the Net.
  1. Keep a "poker face". You must have heard this expression a hundred times not to mention, in Lady Gaga's song that you kept singing out of tune. In poker, it is necessary that your oponents do not see your facial expressions, your eye movements, gestures, and breathing. Otherwise, they, especially the pros, would have an idea if you're losing or winning.
  2. Observe your winning opponents. Study how they play the game. Then, copy how they play it. For a newbie, it's a trial and error. In time, you're going to learn how they actually play it. Your winning opponents observe you as well. They'll study your weaknesses. So make sure you have that poker face. Learn how to face your expressions and gestures.
  3. Bet wisely and budget your money. This is the wisest tip you can follow. Don't be a gambler; be a player. Have fun and enjoy the game but respect your money. Your loved ones deserve more your hard-earned money that your opponents. Set a limit on how much you are going to spend in the casino. Have the discipline to not exceed it. If you had a bad day at the tables, don't put yourself in debt. It's not worth it. Remember that there are other more fun things that money can buy.
  4. Don't bet high (aka high rollers). This can lead to drastic losses. Play moderately and just slightly increase your bets when you know you have a good hand. Avoid the extremes. Don’t bet too little because you might just lose money in the long run. Don’t bet too much because you might lose a lot of money on only one hand.
  5. Take your time. The pros think very fast because they are pros!
  6. Know when to fold (give up your cards), when to stay in, and when to raise your pot-money (nickel or token). Having two face cards is a good reason to stay in. Having two different low number cards may be a reason to fold. If you notice high bets from a player who does not bluff, you should probably fold. Know when to take risks and when to be cautious.
  7. Last but not least. Have fun! Instead of going to the casino, spend quality time with your family. Treat poker as a family activity. Instead of money, chip in to the pot a promise to do a household chore; or a treat to fastfood restaurant.

12/02/2013

EZ2 (Pick 2) Lotto All-Time Hot Numbers (Top Numbers)

Hot numbers are lotto numbers that frequently win within a short period like a month or shorter. Top numbers are referred to as all-time hot numbers that cover all the actual results. In some cases, covering all the actual results may not be necessary for the reason that the significance of the data remain the same or just slightly changes. In such case, the all-time hot numbers may cover only a few years.

Hot numbers that cover a longer period like a year or two slightly change from year to year. The ranking of the numbers may go up or down but rarely flank to the bottom or peak straight high. Once a number belonged to the top hottest numbers, it remained on top even if its ranking changes up or down. Likewise, a cold number remains in the bottom 10 from year to year even if its ranking slightly increases or decreases. What is transient are the numbers around the median. These numbers may be in the top 15 in the previous year but may be in the bottom 15 in the next year.

The following are the hottest EZ2 lotto numbers covering the drawings from 2011 to 2013.

Top Performers
Lotto#RankTimes Drawn
101235
042234
163221
014217
145216
255216
305216
068213
159212
2310211
2610211

Average Performers
Lotto#RankTimes Drawn
1312209
0513208
2213208
2115207
2815207
3115207
0818206
0219201
2920199

Bottom Performers
Lotto#RankTimes Drawn
2421198
0322197
2722197
1124196
1224196
1726195
2027192
0728190
0929188
1930185
1831178

How To Use These Data

The next question is: How do you combine the numbers? Must you combine top and top numbers only, or one top number and one bottom number?

Calculating the last 3183 results, the winning combinations are usually top numbers or a combination of 1 bottom number and 1 top number. Below is the summary.

Top & bottom numbers data
CombinationFreq%
Total results3183100%
Both #s are top104532.8%
Both #s are bottom58018.2%
Mix of a top & bottom #s155848.9%

Based on these data, if you're playing 10 combinations, 3 may contain both top numbers, 5 may contain a mix of top and bottom numbers, and only 2 may contain both bottom numbers.

Trending Today

Calculating the last 81 results, 34 combinations contain both top numbers; 39 combinations contain a mix of top and bottom numbers; and only 6 combinations contain both bottom numbers. To find out which numbers are top or bottom, refer to the tables above. Numbers that rank 1 to 15 are top numbers while numbers that rank 16 to 31 or bottom numbers.

For a larger scope of data, you can view the all-time hot numbers in this complete statistical report about the EZ2 lotto. It covers 6248 drawings dating back from 2004.

11/28/2013

The Coldest EZ2 Lotto Number Combinations In The Longest Hibernation Period

The EZ2 Lotto started in 5 July 2004 with the combination 17-06 winning the first draw. Since then, 17-06 has won 7 times, the last of which was on 10 Oct 2012.

There are, however, combinations that have won only once or twice since 2004. In particular, the combination 08 -29 (coldest and laziest combination) has won only once since the EZ2 lotto started. While other combinations have been frequently winning or currently active, some combinations have not been winning since 2009 or 2010.   These are combinations that have been hibernating for a very long period; or cold numbers that have become like frozen with time.

Cold Combinations In Either Order

These combinations in either order have remained cold since 2009 and 2010. The number of times these numbers have won were counted since the very first draw date. Are your favorite numbers listed here?

CombinationLast DrawnTimes Won
01 - 2410/01/092
24 - 0102/20/105
17 - 2704/12/102
27 - 1707/23/106
20 - 20 10/08/104

Cold Combinations In Their Exact Order (Since 2009)

These combinations in their exact order have not won since 2009. Since 2004, they have won only once to 4 times. Their reverse combinations, however, have been frequently winning; if not, have become active or currently hot today. If these are your numbers, it means you have not been winning.

CombinationLast DrawnTimes Won
08 - 2904/13/091
09 - 0105/05/093
27 - 1305/09/093
14 - 2011/29/093
24 - 1903/25/094
18 - 1109/25/094
16 - 0911/05/094




Cold Combinations In Their Exact Order (Since 2010)

The following EZ2 combinations in their exact order have not won since 2010. One combination has won only twice since 2004 which makes it not only cold but also lazy. On the contrary, one combination has won 11 times since 2010 but has turned cold after 2010. If these are your favorite numbers, try their reverse combinations. The two dates, Last Drawn and Drawn Again refer to the last 2 draws when the combination won. If it is empty, it means that the numbers have not won since. The last column After counts the number of days it took the numbers to win again. Take for example, 24 - 05. The last time it won was on 11/18/2010. Then it won again on 11/29/2013. The combination has been cold for 3 years and 11 days.

CombinationLast DrawnTimes WonDrawn AgainAfter
17 - 2902/24/102
08 - 0505/04/103
24 - 0708/20/103
28 - 0608/24/103
07 - 1611/16/103
06 - 1811/22/103
03 - 2704/18/104
19 - 2105/02/104
20 - 2605/13/104
15 - 1706/17/104
12 - 2609/02/104
09 - 0803/02/105
25 - 1108/22/105
16 - 1211/09/105
07 - 2811/04/106
22 - 0111/06/106
24 - 0511/18/10611/29/133 yrs 11 days
30 - 1411/27/106
09 - 1009/21/108
18 - 0112/30/108
14 - 1912/15/1011

Just a November 30 observation (Bonifacio Day). When I posted this on Nov 28, the numbers 11-30 won twice – on Nov 28 and Nov 29. The numbers 24 - 05 won again after 3 years and 11 days calculated as follows: 2013 - 2010 = 3; 11 - 11 = 0; 29 - 18 = 11. That's 3-0-11. Coincidence?

10/29/2013

Grand Lotto 6/55 All-Time Hot and Cold Numbers (as of Oct 2013)

The following are the all-time Grand Lotto 6/55 hot numbers as of the last draw (28 Oct 2013). This means that these are the most frequently winning numbers of all time, comprising draw results from 19 April 2010 (the very first draw) up to the latest draw.

Ranked according to each number's winning frequency, the top 28 hot numbers are shown in the left of the table that follows; while the bottom 27 are listed in the right. The top 28 numbers have won 60 to 83 times; while the bottom 27 numbers have won 46 to 59 times.

Top 28 (Hot)Bottom 27 (Cold)
RankLotto#RankLotto#
1 261437, 47
2 29158, 20
3 18, 55164, 5, 10, 41
4 7, 25, 401719, 50
5 24, 52182, 43
6 22, 28191, 33, 38
7 45, 542023, 27
8 6, 12, 31, 392149
9 9, 302211, 32, 46
10 362314, 15, 16, 44
11 17, 21243, 53
12 13, 34, 35
13 42, 48, 51

Top 28 Numbers Making It To The Jackpot

On the 21 Sep 2013 draw, the winning numbers 48-52-35-34-29-55 all belonged to the top 28 hot numbers. On 25 Sep 2013, five of the winning numbers 28-18-29-39-45-15 belonged to the top 28 hot numbers. On 2 Oct 2013, the winning numbers 22-7-9-13-18-21 all belonged to the top 28. On 23 Oct 2013, five of the winning numbers 26-6-37-34-28-40 belonged to the top 28.

In other draws from September to October 2013, six draws resulted to four top 28 numbers making it to the jackpot; while 8 draws resulted to three top 28 numbers winning. There were only 7 draws wherein 1 or 2 top 28 numbers made it to the jackpot.

10/28/2013

EZ2 Lotto Combinations In Hibernation (as of 10-28-13)

The following EZ2 lotto combinations are considered in hibernation. These combinations were last drawn some time between January 4, 2011 and December 17, 2011. So far, they have not won again as of this writing.

02 - 04  02 - 09 
03 - 14  03 - 31 
10 - 16  11 - 31 
12 - 23  13 - 14 
14 - 15  14 - 24 
18 - 19  20 - 21 
24 - 28  25 - 31

The following combinations have last won some time between June 29, 2012 and December 18, 2012. As of this writing, they have not won again.

02 - 03 09 - 26
13 - 31 14 - 29
18 - 23 21 - 24
24 - 27