Why do increased stakes lower your chance to win?

[Gaze73]

Bet 1 unit on 100 coin flips, and you'll break even at +100 (at a magical no-juice book)

Bet 2 or 3 units on 30 of those 100 coin flips, and you're guaranteed to lose.

[agendaman]

study some basic game thory.

[Chi_archie]

wait.... what?

[jjgold]

This is a strange thread

[Gaze73]

I guess it's just me then. Whenever I bet big, suddenly statistics don't matter and I'm much more likely to lose.

[pavyracer]

What? If your level of confidence is big you bet big. Believe in the players you are backing to win your bets.

[Enkhbat]

I guess it's just me then. Whenever I bet big, suddenly statistics don't matter and I'm much more likely to lose.

That seems irrational. The statistics matter regardless of your bet size.

[eddycash]

cmon bro its simple

[Otters27]

We can't win. Your future is predetermined

[klemopixx]

I always run into the same problem. The bets that I think are a no-brainer usually are bad bets. Especially in the NFL. It always seems like I'm missing an angle that gets revealed on game day. Injuries and bad weather play into it a lot.

[semibluff]

Bet 1 unit on 100 coin flips, and you'll break even at +100 (at a magical no-juice book)

Bet 2 or 3 units on 30 of those 100 coin flips, and you're guaranteed to lose.

If you believe this you should stop betting and do something else with your life.

[texhooper]

If you believe this you should stop betting and do something else with your life.

You’re taking him way too literally bro. He’s just saying why when he increases his bets does he seem to lose, or at least why does it feel to him like that’s what happens. And I think we’ve all been there before and this isn’t some difficult concept to grasp like everyone’s making it out to be. He’s basically venting

[lonegambler23]

I guess it's just me then. Whenever I bet big, suddenly statistics don't matter and I'm much more likely to lose.

youre maybe just betting big to feel something

[dante1]

I guess it's just me then. Whenever I bet big, suddenly statistics don't matter and I'm much more likely to lose.

all in your head my friend. numbers can't change. at least not in the universe we reside in. you have to be careful today with the way science is advancing. some things we once thought were absolute truths are no longer. I am not a science/math guy but I believe that statement is true...at least for now.

[dante1]

I always run into the same problem. The bets that I think are a no-brainer usually are bad bets. Especially in the NFL. It always seems like I'm missing an angle that gets revealed on game day. Injuries and bad weather play into it a lot.

if this is true or you believe it is true here is an idea. when you think you have a no-brainer well then fade yourself.

[semibluff]

You’re taking him way too literally bro. He’s just saying why when he increases his bets does he seem to lose, or at least why does it feel to him like that’s what happens. And I think we’ve all been there before and this isn’t some difficult concept to grasp like everyone’s making it out to be. He’s basically venting

I have to take him literally. That's all there is on the page. There's no /sarcasm indicated, different colour font, emoji, video with voice inflection, etc. Additionally this poster has a history of making some unsubstantiated math-based claims in Think Tank that he absolutely believes and argues over for days. If someone else had made the post I would have read it as a rant. With him - who knows? I don't want to pick a fight with him. He's a knowledgeable poster who has posted some good stuff, but he also goes off the deep end occasionally and posts some bad advice.

The thread is misleading to any new poster coming to TT and looking for math-based, common-sense, facts or information. Players Talk is for sh!ts and giggles. If the thread was only in PT I wouldn't have responded. He may have vented in PT only for a mod to later link the vent to TT. I don't have a problem with people ranting or venting, but neither shouldn't grant you immunity from other people responding, just as i'm not immune from a negative response to my responses. I wish the op well. Hopefully he'll brush this off and come back with something better.

[klemopixx]

I think it has to do with overconfidence due to something outside the usual factors that you take into consideration while capping a game. You see it every week in the NFL. A really good team will be home against a struggling team and yet the line will be -6.5, leading you to believe that they can easily beat this team by a touchdown but not considering factors like injuries, division/rivalry game, weather, national tv, etc. A friend I know who was 'connected' used to go over with me my first reaction to next week's lines and which ones seemed like obvious picks. After a few weeks it occurred to me that most of my picks were losers and I looked back as to what were the reasons and there were many, mostly due to not digging deep enough when capping. If a line looks off, there's a reason. There's always a reason. I still struggle to this day with bigger bets though it's gotten much better.

[J. v. Neumann]

Bet 1 unit on 100 coin flips, and you'll break even at +100 (at a magical no-juice book)
Bet 2 or 3 units on 30 of those 100 coin flips, and you're guaranteed to lose.

If playing both at +100 there's no difference in the expected value at both which is .5 * 2 = 1,0 (for every dollar invested a dollar will be returned, in the long term of course).

The reason why you should rather go for the 1st staking strategy than for the 2nd lies in the higher variance for the lower number of bets (which makes it even worse with higher stakes). The mean of a fair coin (or random bit) tends to a normal distribution for large n (the number of bits or coin flips) with a mean of 1/2, whereas the standard deviation sigma can easily be calculated by 1/2 * sqrt(n). The mean is easy to understand, e.g. in a random bit sequence "1001001100...011" of 1000 bits we might have 498 ones and 502 zeros, so the mean in that example is .498 (i.e. you will win half of your bets on coin flips in the long term).

The standard deviation is maybe more difficult to understand for the random bettor. From theory we know, that with a normal distribution 95.5 % of the trials (of flipping a coin n times) will end up within the mean +/- 2 * sigma and even 99.7 % of the trials will end up within the mean +/- 3 * sigma, which is illustrated here (probability density function of the normal distr.):



Take 1000 coin flips, we know most often it won't end up exactly 500 times head and tail each (even if it is the expected value since 1/2 * 1000 = 500), but what is the range where we can expect the number of heads/tails to end up most often? The standard deviation is 1/2 * sqrt(1000) = 15.8 which means that in 99.7 % of experiments we can expect to find head between 500 +/- 3 * 15.8 = 453 and 547 times. Or see it that way: give 1000 studs a coin and tell them to flip it 1000 times, only 3 of those 1000 studs will record a head count of less than 453 or more than 547.

If you play that with an edge, let's say odds at 2.1 (american +110), your expected value is 1/2 * 2.1 = 1.05 (for every dollar at stake a dollar and 5 cents will be returned in the long term). We can now say in 99.7 % of the cases (of 1000 such bets) it is "unrealistic" to expect more bad luck than 453 * 2.1 = 951.30, i.e. you will not lose more than 49 dollars or ~5 % (from overall 1000 if a dollar at stake for each coin flip). Or, if we say everything within 3 sigma is realistic, we can expect not to lose more than 5 % after 1000 bets at constant stakes (many calculate with 2 sigma or 95 %, not so important here now). From our 1000 studs above, if they put 1 $ on each coin flip, only 3 of the studs will lose more than 49 $ after 1000 flips.

For 10000 flips it becomes even better: 5000 - 3 * sqrt(10000) = 4850, that multiplied by 2.1 gives 10185, which means that betting 10000 times at a 50/50 chance with an edge (at +110) in 99.7 % of the cases you will win at least 185 dollars, loosing money here becomes very unlikely.

Now the same for 100 coin flips (your first example): 50 - 3 * sqrt(100) = 35. Autsch... Flipping a coin 100 times in 99.7 % of the experiments gives head even between 35 and 65 times - this can be surprising since flipping a coin 1000 times will end up in a misbalance of 350-650 never ever (now btw you know what you can think of bettors telling you that their "strategy works" after 100 bets). 35 * 2.1 is 73.5, which means that now there is a much more realistic possibility of loosing nearly 30 % of the money after 100 bets even when doing everything right, i.e. betting positive expected value.

And now take your 2nd example, 30 bets: 15 - 3 * sqrt (30) = 6.8, that being multiplied with 2.1 (still having the same edge) gives 14.3 which tells us that after 30 bets only, loosing even half of the money becomes a realistic possibility (if taking 2 sigma instead, here still loosing 30 % can be considered as realistic).

Lesson 1: We go for 100 bets, not for 30 (we go for as much as possible).


Since the deviation is 1/2 * sqrt(1000), another painful lesson is that our safety from bad luck is not linear in the number of bets. If we want to decrease the deviation by the factor of at least 3, we even need 10 times more bets, i.e. we need to go from 100 to 1000 bets. To make this more concrete on an example, with a 50/50 chance at +110 with 100 bets we need to win at least 48 not to lose money - with 1000 bets we need to win at least 477. While the former leaves us with a nearly 1/3 probability to still lose money, in the latter that probability decreases to 7.3 % by a factor of roughly 4 only, even if we took 10 times more bets (such probabilities can be calculated by integrals over the normal distribution e.g. here).


Regarding your 2nd problem, taking higher stakes... let's say we play 10 bets in parallel (common in european football saturdays). Again we have a 50/50 chance (at +110, otherwise we don't play) - how many bets of those 10 can we expect to win? That can be answered simply by the binomial distribution (just type "binopdf([0:10],10,.5)" in Octave, a free math scripting language) the result (if plotted) is as follows (prob. density funct. of the bin. distr.):



So even if the chances are 50/50 at each of the 10 single bets, we can expect to win half of the 10 bets not even in 1 of 4 cases. Or, since 4 * 2.1 = 8.4 only (from 10 $ at stake), we will lose money in 37.7 % of the cases (the sum of the first 5 bars) even though betting positive expected value. Even worse, in 1 out of 18 such days where we place 10 bets in parallel, we will lose more than 7, i.e. at least 8 bets out of the 10. If we placed 5 % of the bankroll on each of the bets, we will lose 40 % of our bankroll at such a single bad day, and that day will come for sure this year. But since this happens not only once within 18 days exactly, but will also happen twice within 10 such betting days, we might end up loosing half of our bankroll in a short period of time if we put 3-4 % of the bankroll at stake each bet.

Lesson 2: We only place 1, max. 2 % of the bankroll at stake at each bet.

[KVB]

This isn't a math or binomial distribution question.

It's a question of psychology and reality.

Since the psychology isn't being addressed, and I'm not going to address it in this thread, let's get this garbage out of the Think Tank.

Seriously.

[KVB]

Bet 1 unit on 100 coin flips, and you'll break even at +100 (at a magical no-juice book)

Bet 2 or 3 units on 30 of those 100 coin flips, and you're guaranteed to lose.

Clearly you're not tracking your bets and why you made them.

Get back to basics Gaze.

[J. v. Neumann]

This isn't a math or binomial distribution question.

It's a question of psychology and reality.

Psychological traps in betting often have their roots in math and human's bad intuition for probability. First of all it's a wrong question since increased stakes do not lower the chance to win as claimed in the question. But if someone has the bad idea to decrease the number of bets and therefore increase the stakes, it can easily happen that higher losses will be recorded, so I didn't treat the question as "garbage" even if stated wrong.

I was just about to prepare a thread understanding variance or luck when I read this one, so I thought my contribution fits here and better to post it in an existing thread than open a new one - especially since this thread was tolerated for 2 days now.

[Optional]

Sometimes silly or flippant questions can inspire interesting discussion when approached seriously. Hence the thread being linked to the TT to start with.

I would like to see a few more high level Think Tank threads myself too though.

[MiDNiTe]

Well better to go big when you're hot instead of going huge when you're cold as fuk,

[JohnGalt2341]

Psychological traps in betting often have their roots in math and human's bad intuition for probability. First of all it's a wrong question since increased stakes do not lower the chance to win as claimed in the question. But if someone has the bad idea to decrease the number of bets and therefore increase the stakes, it can easily happen that higher losses will be recorded, so I didn't treat the question as "garbage" even if stated wrong.

I was just about to prepare a thread understanding variance or luck when I read this one, so I thought my contribution fits here and better to post it in an existing thread than open a new one - especially since this thread was tolerated for 2 days now.

I like this guy already. His only flaw in post #18 that I can tell was how he spelled "lose". I'm just busting your chops.

Let me know if you ever want to learn how to play Hexversi. It's a variation of the game Othello. You would likely be a natural at it. Check out my Hexversi threads in the Saloon if you are interested.

If this guy sticks around for a while I will be fairly surprised.

[J. v. Neumann]

I like this guy already. His only flaw in post #18 that I can tell was how he spelled "lose". I'm just busting your chops.

Oh damn... am not a native speaker... corrected it, 5 times "loose" in a single post was too painful for the eyes, thx.

[KVB]

Sometimes silly or flippant questions can inspire interesting discussion when approached seriously. Hence the thread being linked to the TT to start with.

I would like to see a few more high level Think Tank threads myself too though.

I get that, but read then original post again.

It can only inspire a psychological analysis, but it’s a weak one. Not even sure my input will help people lose less lol.

Even Neuman is trying, but let’s face it there’s not much to work with on this topic...lol.

This is not think tank material and twisting it into TT material is going to work very well here.

Hope all is well Opti, planning to finally reach out tonight Opti, should be calling this evening, at some point.

[Accrued Interest]

This actually is a good analytical question because it gets to the core of gambling which is EDGE.

When you are betting larger, you believe you have a larger edge. Therefore, you will increase your bet size. If you increase your bet size beyond your edge, you will go broke. So you have two fundamental problems: 1) You lack edge and 2) you lack the ability to size your bet appropriately.

This is actually an excellent way for a person that is slightly sharp to bet because you can maximize the edge that you do have and that can sometimes be significant. However, if you do not know your edge which a slightly sharp gambler almost assuredly cannot accurately estimate, you are doomed to failure.

The bottom line is that you are not good at gambling.

[swordsandtequila]

[QUOTE=Accrued Interest;30901184

The bottom line is that you are not good at gambling. [/QUOTE]

[stevenash]

This is a strange thread

[d2bets]

This actually is a good analytical question because it gets to the core of gambling which is EDGE.

When you are betting larger, you believe you have a larger edge. Therefore, you will increase your bet size. If you increase your bet size beyond your edge, you will go broke. So you have two fundamental problems: 1) You lack edge and 2) you lack the ability to size your bet appropriately.

This is actually an excellent way for a person that is slightly sharp to bet because you can maximize the edge that you do have and that can sometimes be significant. However, if you do not know your edge which a slightly sharp gambler almost assuredly cannot accurately estimate, you are doomed to failure.

The bottom line is that you are not good at gambling.

Nice in theory. In reality, for the best bettors the bet size is determined more by limits than by edge.

[Accrued Interest]

Nice in theory. In reality, for the best bettors the bet size is determined more by limits than by edge.

That would be because you do not have one. Limits don't really have anything to do with it. That is purely bankroll.

[PharaohUB]

For a lot of people bigger bets are made when chasing losses. Winning a bet that gets you back to what your balance was at beginning of day isn’t going to be as memorable as a loss that wipes your balance out. So it probably just seems that way. Depends on your betting pattern.

[Optional]

This actually is a good analytical question because it gets to the core of gambling which is EDGE.

When you are betting larger, you believe you have a larger edge. Therefore, you will increase your bet size. If you increase your bet size beyond your edge, you will go broke. So you have two fundamental problems: 1) You lack edge and 2) you lack the ability to size your bet appropriately.

This is actually an excellent way for a person that is slightly sharp to bet because you can maximize the edge that you do have and that can sometimes be significant. However, if you do not know your edge which a slightly sharp gambler almost assuredly cannot accurately estimate, you are doomed to failure.

The bottom line is that you are not good at gambling.

One funny thing about edge % is that sometimes it appears that those who's models are closest to reality are less likely to claim/feel like they know their true edge for sure. Whilst people in their first year or two and just getting on top of it will be thinking they are one of the few who can accurately estimate it.

[Optional]

That would be because you do not have one. Limits don't really have anything to do with it. That is purely bankroll.

You think he has no edge? Or has no limits?

You might have over stepped here...

[Accrued Interest]

One funny thing about edge % is that sometimes it appears that those who's models are closest to reality are less likely to claim/feel like they know their true edge for sure. Whilst people in their first year or two and just getting on top of it will be thinking they are one of the few who can accurately estimate it.

Yes, this is really a debate between two different strategies with one not understanding the other. So an edge percentage would apply to someone that would not really pursue this type of strategy as much. When a gambler is outsizing their bets, they believe they have a substantial edge that goes beyond quantifying which is where the danger lies. If you believe you have great bets, these bets should be winning at a high percentage and the games should be going as you expect. If they aren't, it is due to lack of edge.