This is one of those lottery questions that can make your head spin. Should I play the same lottery numbers or change them? It can turn your brain inside out if you overthink it…
If my numbers haven’t come up yet, surely they are more likely to in future?
This is comments page 2. Read the full post here:-
Should I Play The Same Lottery Numbers In Every Draw?
L.G., Patiently waiting for your Lottery Strategy Invite. Bob L.
Surely sticking to the same numbers makes it more probable to come up next time?
Consider this:
If I flip a coin and predict heads, tails shows up first time, now we know there is a 1/2 chance for each side to come up and since we got tails first time, even common sense tells you it will probably be heads next time since it didn’t show up the first time! Meaning I should stick with my initial prediction which failed me the first time and is likely to show up the next time.
Hi Colin
This is one of those occasions where human intuition fails us miserably 🙂
(To think of it a slightly different way. What happens if you get tails the first time, but then change to using a different coin..?)
As you say, there is a 1/2 chance for each side to come up. But that is always the case, and doesn’t change based on what result you just got (or the ones before that). It can’t, because there are still 2 sides, and nothing about either of them has physically changed to make them more or less likely.
So no matter what result you just got – it’s still 1/2 for both heads and tails the next time.
And that same principle also applies to lottery games. What happened in the last draw has no impact on the next draw.
Hi LG, Surely Colin has a point, and on closer reading he has used the word “probability”. (I have noticed that you rarely refer to probability or statistics in your blog, whereas, in my opinion, looking at past results may influence a person’s decision on what they think is likely to happen next). I agree that in a lottery “the balls have no memory” and every draw is an independent event. But when looking back over past results you CAN see how an event may have become more likely as time passed by, e.g. a number that has not come up for a very long time must come up eventually, that much is certain, and someone may think that is worth a bet. Returning to the coins example, say you have flipped a coin nine times and got nine tails in a row (incredible!), surely it becomes more and more likely that a head must come up next, because probability says so!
Well no, not really 🙂
It wouldn’t matter if you got a thousand tails in a row. For that very next coin toss there are still two sides to the coin. And each side still has the same 1-in-2 chance of being next. Time or repetition don’t change this.
When you’re looking into the future and calculating probability of a sequence of results, it doesn’t matter if that sequence is all Heads, all Tails or a combination of them – the probability of ANY sequence is actually the same – because each of the two results are equally likely. It’s therefore just as likely you will get HHHHH as it is you’ll get HTHTH, or THHTH or anything else.
Hi Lottery Guy
Just wanted to express MY take on this.
It’s bothered me for years how statisticians imply that probability and intuition are incomparable and/or incongruous. Supposedly a completely RANDOM event such as a lottery draw could REPEAT at any time, yet nobody with an ounce of “reality” ever really expects it to happen… so WHY is this?
Any lottery machine which repeated a draw of 6 numbers two weeks in a row would be SUSPECT from the moment it happened… EVEN though it is eaqually likely as any other set of six numbers. Even experts in probability would “probably” (lol) think it a little surprising.
But what would people think if that same lottery machine were to pick those SAME 6 BALLS for an EQUALLY-LIKELY 3rd draw in a row? Very few people in the whole world would believe that there was NOT something “dodgy” going on!
Still think this is “equally likely”?
What if it happened a fourth, or a fifth, or a sixth consecutive draw???
Nobody in there RIGHT MIND would believe that the draw was RANDOM… YET IT COULD BE!
The point is, even when we toss coins, we know that in REAL LIFE situations what COULD or SHOULD happen (logically and/or statistically) often DOESN’T.
If you toss a coin 1,000 times and EVERY time it lands HEADS up… what do you do?
Do you choose TAILS because it’s been seen for so long? Or do you choose HEADS believing the coin is either “loaded” that way or it’s having a fantastic HOT run of heads which you suspect will continue?
Like you said, if it’s truly random… “anything can happen” (but experience tells us more than statistics alone)
For example: I have 5 sets of numbers which I have bought every draw for several years, but not from the very start.
But… I have just checked some of the statistics of each set since the UK lottery started on Saturday 19th November 2004.
First set has won just £492 (£10 on 28 occasions – plus £73 / £67 / and £72 for 4 No’s on just 3 occasions)
Second set has won just £570 (£10 on 29 occasions – plus £128 / £83 / and £69 for 4 No’s on just 3 occasions)
Third set has won just £498 (£10 on 30 occasions – plus £54 / £62 / and £82 for 4 No’s on just 3 occasions)
Fourth set has won just £678 (£10 on 42 occasions – plus £105 / £91 / £62 for 4 No’s on just 3 occasions)
Fifth set has won just £333 (£10 on 24 occasions – plus £93 for 4 No’s on just 1 occasion)
Of course, I understand it makes NO DIFFERENCE how I number or name my sets, but that’s the order which I wrote them on the original ticket and they were allocated letters A, B,C, D and E.
What got me thinking about the numbers I’d chosen is: there “seems” to be a difference with the last set I chose, because FOUR numbers have matched only ONCE wheras each of the other four sets have matched FOUR numbers THREE times EACH.
I know it’s a rather small group for analysis, but when the first four sets you check have quite similar outcomes (3 x 4 No’s matched) but the last one has only one… it makes you wonder just a little.
The other thing I noticed is the set that made me MOST MONEY (set 4) has only two different colours of balls… whereas the other four sets EACH have FOUR DIFFERENT COLOURS of balls.
(makes you wonder, doesn’t it?) lol.
Hey Charlie
Thanks for your comment.
“…what COULD or SHOULD happen (logically and/or statistically) often DOESN’T.”
The thing is though, what could happen is often simply highly improbable. Such as getting the same results twice in a row.
But only as highly improbable as any other two specific results following each other (it’s like winning the jackpot twice in a row). Rolling a dice and getting a 1 then 2, has the same probability as rolling a 1 then another 1.
It’s just our perception and the significance we attach that make things seem unusual.
Thanks for your response LG
Anyway: To make my point simple, I shall use the COIN TOSS scenario. I realise that the “real world” tends not to exist in the calculation of probability, because there is always a very small chance that a REAL coin may not land with either heads OR tails facing up! Sometimes it may land on the edge and this doesn’t ALWAYS mean it’s going to roll away and settle “flat” on another surface.
A bird, such as a Jackdaw (known to collect shiny objects) might just swoop in and pluck the coin from the air mid-toss.
Leaving those presumably rare scenarios aside, along with many other possibilities I guess… we have only TWO choices (Heads or Tails) for each toss.
Theoretically, although the randomness of each toss is ultimately UNpredictable, after MANY millions of coin tosses (billions or even trillions if you like) it is understood that the results will be closer and closer to DEAD EVEN since as the number of tosses increase, the hundreds or even thousands of times one or the other is ahead (or behind if you like) is growing LESS and LESS significant… when measured by the ENORMITY of the results which came before.
During those (let’s say TRILLIONS) of tosses, I would say that it is EXTREMELY PROBABLE that the number of Heads and the number of Tails would have been exactly equal many, MANY times over as each side had a “good run” along the way and overtook the other option in their number of outcomes.
Therefore: Although each event is basically unique, we know that probability will have the effect of EVENING THE SCORE over and over again in a long cycle of events.
Therefore, even though with 49 balls in the UK national lottery makes possible outcomes much more complicated to calculate (irrespective of their identifying numbers) any individual ball should be drawn AS frequently as any other over an undefined, yet expectedly LONG period… if the system is truly random.
So when we haven’t “seen” a number drawn for many consecutive draws, we surely must KNOW that it WILL eventually appear to balance out the odds. (or suspect a faulty system, or foul play)
We will never know WHEN of course… but looking forward more than a few minutes or so (if we are lucky) we also never know WHEN we are going to DIE… yet everyone believes it MUST happen eventually as “life” is essentially RANDOM!
Finally: There is a reasonably well-known sequence of 163 sets of ticket numbers which you can purchse for the UK Lottery which will “guarantee” you win at least £10 on each draw.
But, although an investment of £163 to win just £10 seems rather FLAWED… it doesn’t mean you still can’t win the JACKPOT with them as well.
Most people of course, can’t afford to spend that much money on each draw knowing that there is a good chance they would be losing £153 each time they played.
Hope this might be of use to someone out there. ;o)
“we know that probability will have the effect of EVENING THE SCORE over and over again in a long cycle of events”
But it’s just as possible in your 1 trillion example that we get 1/2 trillion heads in a row followed by 1/2 trillion tails – and it never balanced at any stage 🙂
It’s just our perception that sees that alternating string of heads and tails as ‘more random’, and therefore somehow normal.
When it comes to the next coin toss it’s still just a 50/50 heads or tails every time. No matter what happened before.
So if you stick with heads, or change each time, you’re still just as likely to be right.
I do a lot of research regarding the Ga. Fantasy 5 (a 39 number game.) This is what I’ve found from Jan 2013 – May 2013:
3 Odd/2 Even drawn numbers came in 8 to 9 times EACH month and 3 even/2 Odd came in 10 to 11 times each month.
My point being that patterns exist from month to month such as 5 Odd/0 Even which has happened In Jan, April & May 2013 & 5 Even/0 Odd in Feb 2013.
I even break down 30s, 20s, 10s and 1-9’s each month & they also are consistent in their pattern.
But these ‘patterns’ are just phantoms. Balls do not know if they are odd or even. They don’t know if they are 20’s or 30’s. So why would they arrange themselves to come out in some nice ordered way that you can predict? It just doesn’t make any sense. Remember, it’s balls that come out of the machine, not numbers.
You can see patterns if you stare at clouds or grains of sand on the beach too, but they don’t help you predict what pattern comes next any more than analysing lottery balls does. That’s just the way it is I’m afraid.
Keep doing what you’re doing if you enjoy it though – it is about entertainment after all.
Every week your chances reset to whatever it was at the first lottery draw (1 to 150 million or so).
The probability of repeating the cominations three times in a row is no less of that of not repeating.
And the probability of your numbers to come up twice in a row is no less than other combinations to come up.
Basic mathematics 🙂
Yup 🙂
(Although some games have significantly better odds, e.g. 6/49 games are 1 in 13 million)
I shrink all our lotto numbers down to nine, e.g. 1 10 19 28 37 etc becomes 1 same with the rest, 2 11 20 29, 3 12, 4 13 etc etc. Then I choose a starting number, lets say three. OK, so I start high, our daily millions has 39 numbers, so I pick 39 now four lets say 13 now five 32 six 33 seven 7 this time lets jump eight and put in a one, how about a ten yep 10 now what have we got? We have 7 10 13 32 33 39. The idea is not to have two matching, two would be ok, you would see it but no more because it is rare e.g. 1 and 19. I hope this will help all you lotto fans.
Hi Arthur,
I’m not 100% clear, but it sounds like you’re using root sums? (i.e. adding up the digits of the numbers until you reduce them down to a single digit, i.e. 39 = 3+9 = 12, then 12 = 1+2 = 3, so 39 gives you a 3).
It’s another pattern based way of picking numbers. The theory behind it being that you’re somehow more likely to match the pattern of numbers drawn. But the reality is it doesn’t actually make any difference to your chances of winning at all I’m afraid.
But if you find it fun it can’t hurt too much, although a quick pick would be a lot less work 😉
If you think about it, it is better to play the same set of numbers. You have a set combination compared to different numbers every time. With the same numbers there’s a constant. With different numbers always changing as well as the jackpot numbes i believe my odds are better with the same numbers.
It’s tempting to think so — but you’d be wrong :-).
Because draws are independent events, your chances are exactly the same if you keep the same numbers or change them every single draw.
Think of a coin toss. It’s a 50/50 chance. If you chose heads last toss and were wrong, that doesn’t make heads more likely this time. So it’s still only 50/50 if you choose heads again.
LG, I was having this argument about using the same numbers each week with someone in my office and found this site while checking into it. Here’s why I’m confused:
Using the coin-toss analogy, the odds of heads coming up is 50/50 for each coin toss, regardless of the outcome of the previous toss (or million tosses). However, the odds of one heads coming up at least once in, say, 10 tosses is 1023/1024 (1 minus 1/2^10 for the math geeks) which is 99.9%. So if I continue to bet on heads over many coin flips, I have a very, very good chance of winning eventually, even though my chances on any given flip remain 50/50.
I know the math would be more complex, but why wouldn’t the same logic apply to calculating the odds of a lottery, with each drawing being considered another coin flip in a long series of coin flips?
I guess I’m looking at the odds of hitting your numbers for a drawing cumulatively over many drawings, while you’re looking at each drawing independently. Of course, the odds of winning are still miniscule! Better odds investing money in a typewriter ribbon company.
You’re absolutely right about the odds of getting at least one head in 10 coin tosses [note: for those scratching their heads right now… Rich used a nifty shortcut. Because getting tails 10 times in a row is the only possible sequence of results that doesn’t include a heads, the probability of at least one heads is ‘everything else’. Hence, ‘1 – probability of 10 tails’]
The key though is if you changed your selection each toss, and worked out the odds of ‘being correct at least once’, you’d still end up with that same answer :-). So it doesn’t really matter what the ‘value’ of your selection is (heads or tails) each toss, as you’re really just picking a probability (0.5 or 0.5).
Thankfully that same logic does indeed apply to the lottery. It just means you’re working out the chances of winnning over time (cumulatively, as you said), where I was referring to each single draw.
For anyone still confused. No it still doesn’t make any difference if you change your numbers or not. And ‘typewriter ribbons’ were not adornments to make your writing machine look nicer, they carried the ink that was transferred to the paper via using a metal hammer for each letter… there’s probably an app for it now 😉
Well let me tell you most of you are right that wining the lottery is purely on luck which is correct. However this is where one must play lotteries with lowest odds. Why play lotteries with odds that are stacked against you, there are lotteries out there that have low odds hence better chance of winning.
Well all lottery odds are stacked against you – it wouldn’t be a lottery otherwise 🙂
But don’t just pick the lowest odds. You need to balance the odds with the jackpot prize, and your own personal idea of what is ‘big enough’. More on that in my free lottery tips.
Isn’t it true though that it increases your chances by playing the same number each time? I mean if I were to flip a coin 10 times and guess head on all 10 times, isn’t there a higher probability of getting heads at least once. I know it’s 50/50 each time but if you flip a coin 10 times you are bound to get heads at least once. I don’t know the amount of years it would take, but if 100 years went by for a lottery number and it never got picked isn’t it likely to get picked sometime or another using my example. Please respond??
Hi Chan,
In short, no 🙂
The increase in your chances comes from guessing 10 times NOT from guessing the same thing 10 times. Your chances of being right are exactly the same if you guess heads 10 times in a row, or if you change it every single time.
Heads is likely to appear in 10 flips – but it’s likely because there are only 2 possible results. Repeatedly choosing it doesn’t make it more likely to appear :-). Mathematically speaking, each flip is an ‘independent event’ so what happened before has no bearing on the next flip – so if you were wrong last time, your chances of being wrong are still exactly the same next time.
Yes, I agree… but there is more of a likely hood of getting heads at least once within that 10 times. It would be :
Probability(at least one head in 10 flips)
Probability(not all tails in 10 flips)
1-Probability(10 tails in a row)
1- 1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2
1-(1/1024) = 1024/1024 – 1/1024 = 1623/1024 = 99.9% chance of heads at least once.
With that being said isn’t it likely out of 1 million lottery draws or so ( whatever the number may need to be to get that high of a probability)… to at least get your one combination of numbers at least once. So yeah, you may be wrong and wrong as you guess heads on each time as each time is independent but your likeliness of being correct with your lottery numbers at least once increases as you play many times with the same number in WHOLE.
But the calculation doesn’t change if you guess 10 heads in a row, 10 tails in a row, heads/tails alternately or any other combination of guesses.
So it’s not guessing the same result that gives you a high chance of being right – it’s purely down to guessing more times.
If you were to do a Billion lottery drawings for example. What are the odds that your combo of numbers get chosen at LEAST once. It’s got to be a great likeliness of happening. So wouldn’t it be safe to assume that your odds of getting it right out of many drawings would increase throughout the drawings of that game? What if I play the same numbers through out my life time and for 20 generations after my death. Do you think the likeliness of the numbers is likely to get drawn at some point or another collectively.
I was stunned to see that someone on here had the same exact question and used the same example as I did with the 10 flips and one heads. I see, the likeliness of getting a winning number picked throughout however many times (drawings) is the same regardless of if you guess the same numbers each time mathematically. It’s amazing as to how the brain can try and convince you based on intuition alone.
But the point is, you’re EXACTLY as likely if you play the same numbers or keep changing them 🙂
The same applies if it’s 10 draws or a billion.