Hypothetical Gamble

myflipflops

I'm bored so:

Someone offers you 6/4 to correctly guess the result of a single toss of a coin. How much of your bankroll would you be willing to put on it?

Mellor

I'd bet 1/6 of the bankroll. And always 1/6, so the mean wager amount would increase as I moved up.
My reason for 1/6, Kelly Criterion. Its a probability theory that is used to find the optimum amount to bet. Its based on the odds offered and the chance of occuring. Its rare that these are both specificly know, but in the above they are and its a great example of KC.
Obviously betting the lot has highest potential earning, but the highest risk of ruin. Inversly 1% has very low risk of ruin, but low potential earnings.
Betting 1/6 has the highest mean progressive earnings.

myflipflops

A flawless answer Mellor. I was hoping to generate some discussion first though so boo to you for being first in. For anyone else the calculation is:

X = 1.5 (0.5) - 0.5
1.5


Where:
x = premium amount to risk
1.5 are the odds offerred (6/4)
and 0.5 represents the liklihood of winning (Even money)

It's an interesting formula to keep in mind when gambling on certain markets.

Mellor

lol, opps, there goes the thread.

Seriously though, would be good to keep the talk/discussion going.
People thoughts on the formula, has anyone ever applied it?

myflipflops

I thought it might develop some discussion regarding smart betting patterns. I've used it to work out value before. Obviously my example will never occur in actuality. A bookmaker would offer you 5/6 on the toss of a coin. It's real use is when you spot a similar 2 way market that you feel has been priced incorrectly. A market priced at 5/6 both sides where you feel one selection is a 1/2 shot would be one such scenario. The formula can be handy in these cases (but obviously far from fool proof as we are entering the area of opinion).

5starpool

There was something like this discussed in the poker forum a few months back I believe, but I obviously can't be arsed to go and look for it.

hotspur

Have you actually read the posts from the people in this forum? Most of them would probably just turn down the bet flat and lump on a 10 match accumulator on the Greek 2nd division instead.

myflipflops

I know, i was hoping to stimulate reasoned conversation and try and bring other profitable sports gamblers out of the woodwork. While there's absolutely nothing wrong with it from an entertainment point of view, i have no interest in discussing €4 football accers.

myflipflops

5starpool wrote: »

There was something like this discussed in the poker forum a few months back I believe, but I obviously can't be arsed to go and look for it.

I considered posting it on the poker forum too but i didn't for a few reasons. Firstly, the general topic will have been discussed in depth already over there. Secondly, i specifically wanted to generate a discussion on sports gambling. Most people on the poker forum wrongly believe sports betting to have a negative equity expectation. I believe this view to be false. Finally, the liklihood that a thread over there turns into a slagging match between 2 individuals means i rarley post there anymore.

I'm also hoping to drag a few more posters onto this forum and make a better, more informative place. I'm sick of the Betfair forum to be honest.

Mellor

5starpool wrote: »

There was something like this discussed in the poker forum a few months back I believe, but I obviously can't be arsed to go and look for it.

Yeah, it popped up before on the poker forum, but it was incorrrectky applied imo.
It was suggested that using the kelly citerion will result in the optimum amount to bet wit a hand. But this is misapplied.
It is used in terms of total roll, not table cash (or chips). And also you don't have a choice in how much to invest all the time. For example, it would suggest that the optimum amount to bet with AA AIPF is 60%, Assuming equal stacks, there is no way 60% of each is going in with out the rest.
Cash at the table will also be about 5% of the total, so get it all in as its nowhere near 60%.



Anyway, should stick to sports betting.
Sports betting is defo +EV, but most people fail to see how.
There was a post here when a player bet on the person who won the first set in tennis to win the match. Before the match players were even, after set 1 one player dropped to 1.3 (or similar), the other player obviously rose to 4 or so, where is the smart money? But where does it go in reality.

sports betting can be +EV, sports bettors generally are not.
Obviously, the same is true of poker players, generally.
Rather obvious from the fact that bookmakers and casino turn over

jameshayes

hotspur wrote: »

Have you actually read the posts from the people in this forum? Most of them would probably just turn down the bet flat and lump on a 10 match accumulator on the Greek 2nd division instead.

Most people on this forum bet as a hobby, so yes they/I would pop money down on a 3/4 fold accum.

Some people go shooting, some people play golf, others play X-Box live. All these things cost money and what do you get in return? A sore thumb from the x-box controller, a sore arm from shooting or a pain in the ass from golf? With gambling you have a chance to follow a hobby and you also have the possibility to make some money.

With flipping a coin, yes statistically, eventually you will make money by betting 1/6th but have you taken into account that the coin is heavier on one side? Does the flip start with the heads up or the heads down? What is the air density? Are you wearing you lucky jumper?

myflipflops

As i stated above, there's nothing wrong with recreational punters having a small accum to keep them interested in all the football on a Saturday afternonn or whatever. This is simply a different type of thread. I think there's plenty of room on the forum for them both.

paulizei

hotspur wrote: »

Have you actually read the posts from the people in this forum? Most of them would probably just turn down the bet flat and lump on a 10 match accumulator on the Greek 2nd division instead.

Fyi, betting on lower division football is where many pros make their money.

myflipflops

paulizei wrote: »

Fyi, betting on lower division football is where many pros make their money.

Lads, if ye want to have an arguement about the pros and cons of football accers then start a separate thread about it (actually, it would probably be quite interesting).

paulizei

pwhite587 wrote: »

Lads, if ye want to have an arguement about the pros and cons of football accurs then start a separate thread about it (actually, it would probably be quite interesting).

Apologies for derail, this was an interesting thread til yer man there decided to troll it.

Mellor

jameshayes wrote: »

With flipping a coin, yes statistically, eventually you will make money by betting 1/6th but have you taken into account that the coin is heavier on one side? Does the flip start with the heads up or the heads down? What is the air density? Are you wearing you lucky jumper?

Come on now, no need to be silly. But seeing as you are, I suppose i'll paly along.
Statisticlly you will make money no matter now much you bet. all bets are +EV. But 1/6 makes you the most money.

no it doesn't take into account that the coin is heavier on one side, why because it isn't heavier on one side. Any such physical device used in gambling must be fair, just like a die.

The coin may start either side, at random, likewise you guess may stay the same, alternate or be random.

Air density will remain constent and have no bearing.

And no lucky jumpers will not be allowed, due to the fact that they are an false economy, most likely produce in a sweat shop and will fail to work.
Depend on the rabbit's foot if you will, but remember it was no use for the rabbit

myflipflops

Bare with me here, i may be talking through my hole:

The toss of a coin is used in the example purely because it's proabably the best example of an even money chance going. In terms of sports betting, one market i think this approach would be applied to would be the 'Next man Out' market in a cricket match (bear with me if your not into cricket). Basically you bet on which batsman will be next out. In the event of a bookmaker judging it an even money shot, then they will price it up as 5/6 each man (an even money shot in theory but they take their margin).

What if you happen to be a cricket expert? You spot a next man out market at 5/6 but you're knowledge of the game tells you it should actually be 6/4 one side and 1/2 the other. Suddenly you have a bet, the gap from 1/2 to 5/6 is big. The question is, how much value is actually there? How much should you place on the market? The Kelly Criterion, i believe, can be used to help you define what your most profitable bet is. If you can accurately define a measurement scale of your opinion on the given market, it can be implemented into the equation to make it more accurate. Putting a specific monetary value on the premium amount to bet would (in theory) be an enormous boost to your potential profitability.

Obviously this whole concept depends on a) your opinion being correct and b) the scale you measure your opinion on being correct. These are obstacles to accuracy but certainly they can be worked put to a point where you are pretty confident of them. This is something i've just been thinking about for the craic. Any advantage i take over the bookies, even if it's in my head, is a good one!!

Robin1982

Kelly won't start much of a discussion because its just a formula. What's more interesting are people's perception's versus the realities of the underlying mathematics.

For instance, knowing how Kelly works, if 10000/1 was offered instead of 6/4 on the coin flip, is it obvious then how much to bet?

Or if in a coin flip example, you always bet heads. When heads comes up you win 50% of stake; tails you lose 50% of stake. Over a gazillion bets, you do expect to:

a) win some $
b) lose some $
c) break even

?

jameshayes

wikipedia wrote:

Using the Kelly system in practice does have drawbacks. While it guarantees that you will never lose all your bankroll, it does not guarantee that you will not lose money. When a series of serial bets are made the chance of dropping to 1/n of your bankroll is 1/n. Thus you have a 50% chance of at some point losing 50% of your bankroll, a 10% chance of dropping to 10%, and so on.

-

Mellor

That last bit from the wikipage is wrong.

You certainly don't have a 10% chance of dropping to 10% of bankroll. Although of course its possible,

In the original bet, to drop to 10% or less you would need to lose the opening 13 bets.
This is obvious not 10% chance, but rather 1 in 8192

Of course its not guaranteed to make money, its never claimed to be, it is just a way of calculating the the highest return.

Mellor

Robin1982 wrote: »

Kelly won't start much of a discussion because its just a formula. What's more interesting are people's perception's versus the realities of the underlying mathematics.

For instance, knowing how Kelly works, if 10000/1 was offered instead of 6/4 on the coin flip, is it obvious then how much to bet?

I believe it would suggest betting almost 50%, it would never suggest higher than 50% on a 50/50.

What exactly do you mean by peoples perceptions?
I have no false perceptions about the formula, its not some magic amount to bet that will always win, wont even always make money.
But if it is followed you will only bet on +EV situations, the will always bet the optimum. The optimum being the amount with the greatest geometric potential

Or if in a coin flip example, you always bet heads. When heads comes up you win 50% of stake; tails you lose 50% of stake. Over a gazillion bets, you do expect to:

a) win some $
b) lose some $
c) break even

?

I'm lost on this bit, you win half the stake, and lose half the stake.
Therefore, for all intents and purposes, the stake is actually the amount you win or lose.
Since you are getting evens (win and lose the same), on a 50/50 then in the long run you will break even.

Pj!

Robin1982 wrote: »

if 10000/1 was offered instead of 6/4 on the coin flip, is it obvious then how much to bet?

If I was getting 10,000/1 on the flip of a coin I'd bet closer to 50% of everything I had rather than 50% of my betting bank.

I'm another who finds it amusing the huge difference in gambling types here. Here we have a few who would follow the Kelly Criterion to the decimal and most threads here are about huge accumulators from the top of peoples heads and the infamous lotto value thread(which to be fair would be laughed off most gambling forums).
I don't want an argument and there is no reason both shouldnt be allowed here, but as I said, it is amusing.

Anyone want to offer me that 10,000/1???

Robin1982

Mellor wrote:

...I believe it would suggest betting almost 50%, it would never suggest higher than 50% on a 50/50...What exactly do you mean by peoples perceptions?...

Forky wrote:

...If I was getting 10,000/1 on the flip of a coin I'd bet closer to 50% of everything I had rather than 50% of my betting bank...

Right. I was being a bit dramatic by using 10000/1 but the point was that when betting in a situation which you know is +EV, your bet size is increases to the threshold, as you both know.

With the (fair) coin flip situation, fair odds are known in advance, and +EV can be identified quite easily. Sports betting situations (since the Coin Flipping markets haven't quite caught on) are more difficult as the fair odds cannot be calculated so accurately, perhaps if at all. If you wrongly identify a +EV situation, Kelly will hurt.

So its very important to identify "fairness" of odds in such situations. The way to do this is average results of a strategy over multiple bet plays. More bets equal more confidence in the accuracy of the results. I flipped a fair coin 5 times and only 1 head came up, most would believe that would be understandable. If I flipped it 500,000 times, for a fair coin, 100,000 or less 'heads' would be almost statistically impossible. ~50% would definitely be expected. As the number of bets approaches infinity, the results of the plays become asymptotic to the "fair odds". So....

Mellor wrote:

...I'm lost on this bit, you win half the stake, and lose half the stake. Therefore, for all intents and purposes, the stake is actually the amount you win or lose. Since you are getting evens (win and lose the same), on a 50/50 then in the long run you will break even...

'Fraid not. I know I said a gazillion, but let's use 500,000 again. Heads came up 250k times, tails 250k times. You won 50% when it came up heads, lost 50% otherwise. 500k is a lot, so let's look at it per event (coin flip):

[(1.5^250k) * (0.5^250k)]^(1/500k)

which is the same as [(1.5^.5) * (0.5^.5)], which equals ~0.87, a -EV bet.

A formula's just a formula. Knowing the theory behind it can sometimes be more useful. Perceptions can be deceiving.

hotspur

Forky wrote: »

I'm another who finds it amusing the huge difference in gambling types here. Here we have a few who would follow the Kelly Criterion to the decimal and most threads here are about huge accumulators from the top of peoples heads and the infamous lotto value thread(which to be fair would be laughed off most gambling forums).
I don't want an argument and there is no reason both shouldnt be allowed here, but as I said, it is amusing.

Yeah it's a shame that the forum became so bad so quickly. I suppose the truth of it is that there are very few people in the country who bet sports at the level of a pro sports bettor. This is partly because the main sport we are into -football- is not great as a betting sport unlike several American sports. Also it is very very difficult to do properly and takes huge time and effort.

There are a handful of people who contribute to this forum who at least understand the true nature of gambling. Mostly they gravitate to the poker forum where we have genuinely intelligent, skillful, and profitable gamblers.

As for the soccer accumulators Talk to *anyone* who works in a bookies about the amount of these bets they take in and the number they have to pay out on, and buy them a pint if they can tell you without cracking up laughing

Oh and that paulizei is just p*ssed at me for laughing at his recommendation to bet the under market of Villa-Spurs game, possibly the most guaranteed over in the history of professional football

Fremen

Kelly won't start much of a discussion because its just a formula. What's more interesting are people's perception's versus the realities of the underlying mathematics.

For instance, knowing how Kelly works, if 10000/1 was offered instead of 6/4 on the coin flip, is it obvious then how much to bet?

Or if in a coin flip example, you always bet heads. When heads comes up you win 50% of stake; tails you lose 50% of stake. Over a gazillion bets, you do expect to:

a) win some $
b) lose some $
c) break even

?

Starting with $100, suppose you win once and lose once. You'll have $75 left.
Same if you lose then win.
In an informal kind of way, this shows you stand to lose money, and pretty quickly.

A more interesting question would be:
If you get heads, you double up. If you get tails, your stake gets cut in half.
If you start with X dollars, what's your chance of going broke, assuming you can't bet less than one dollar?

(I really should know the answer to this, 90% of my current degree involves probability in some way)

paulizei

hotspur wrote: »

Oh and that paulizei is just p*ssed at me for laughing at his recommendation to bet the under market of Villa-Spurs game, possibly the most guaranteed over in the history of professional football

me wrote:

Fulham v Chelsea
I'm not touching Chelsea til they at least have Drogba back. Fulham are pants but at home with a new manager, they could cause a shock here. Might go for Fulham +2 @ 4/9.

Villa v Spurs
Looks like a low scoring game to me. Spurs don't score much away from WHL, their record at Villa is terrible, one win in 14 years, and the schedule must be taking its toll on fitness. The emphasis will be on defence and trying to keep a clean sheet I reckon. So, if I go for anything it'll be unders or 1-1 CS.

That's what I wrote. My info was correct, my prediction regarding team tactics was correct and I backed a 1-1 CS. Ramos and O'Neill are not idiots. After Defoe's equaliser, I backed the over at a very good price to ensure a handy profit no matter what happened subsequently. I was right about Fulham. You forgot to mention that somehow.

I look forward to reading some of your football tips if you ever post any.

paulizei

Forky wrote: »

I'm another who finds it amusing the huge difference in gambling types here. Here we have a few who would follow the Kelly Criterion to the decimal and most threads here are about huge accumulators from the top of peoples heads and the infamous lotto value thread(which to be fair would be laughed off most gambling forums).
I don't want an argument and there is no reason both shouldnt be allowed here, but as I said, it is amusing.

It is amusing that there are people here who post rubbish like 'Get on Man City @ 3.95' or whatever without giving any reasons, info or analysis, and then sneer at other people's bets.

Pj!

paulizei wrote: »

It is amusing that there are people here who post rubbish like 'Get on Man City @ 3.95' or whatever without giving any reasons, info or analysis, and then sneer at other people's bets.

Lol. Sorry. I thought the price was too big. Simple enough.
Football is wide open to everyone. Everyone can see whats going on. Its up to each individual to make up their mind about value. I could have rambled on about both teams last few games, the history, next games, managers favourite month... but I am not getting paid to and see no reason to.
If it was a horse selection you may have some argument.
Anything I post up in future wll be because I see it as value (what I believe everyone should be doing).

And I wasn't sneering at anybodys bets. I'm sneering at accumulator bets and lotto bets.
I'll admit to occasionally doing the lotto, sometimes picking 3 or 4 numbers (for my sins!). But I certainly wouldnt go posting my 3 numbers up here. Same way I wouldn't post an 800-1 football accumulator up here.

Mellor

Robin1982 wrote: »

'Fraid not. I know I said a gazillion, but let's use 500,000 again. Heads came up 250k times, tails 250k times. You won 50% when it came up heads, lost 50% otherwise. 500k is a lot, so let's look at it per event (coin flip):

[(1.5^250k) * (0.5^250k)]^(1/500k)

which is the same as [(1.5^.5) * (0.5^.5)], which equals ~0.87, a -EV bet.

A formula's just a formula. Knowing the theory behind it can sometimes be more useful. Perceptions can be deceiving.

You didn't read my post, you said lose half the stake, (I said there therefore the stake is actually half the amount)
But you never said that the stake was the entire roll, what you should of said was that the win/lose half your roll.
Of course this is a bad bet. I would of never of suggest that was good, increasing and decreasing the bet amount like that is clearly bad,
A win doesn't replace a lose, and lose outweights a win. Fremens prove of this is much better, no need to go to 500k flips, EV is the same for each, -25%EV per 2 flips.

Mellor wrote:

Therefore, for all intents and purposes, the stake is actually the amount you win or lose. Since you are getting evens (win and lose the same), on a 50/50 then in the long run you will break even...

As I said, you said stake, not roll in the original, this makes a huge difference, if the stake was unchanged, the bet would be neutral EV after 500k bets or so. This is what I said when said it is neutral, and I stand by that. I see now this is not what you meant, but you did say stake ans not roll. Two different things.

Bankroll management is very important, and any serious bettor (or poker player) would gamble with 50%, not even close.

A formula's just a formula. Knowing the theory behind it can sometimes be more useful. Perceptions can be deceiving

I think you should slow down for a second, I understand the theory behind the formula, most probably dont. Are you trying to suggest that your -ev coinflip example is in anyway related to Kellys formula???

with odds at 1000/1 Kellt suggests betting 50%
In the flip example with -87 EV, the kelly formula says not to bet.

I really have kind of lost your point. And fail to see how the example is relevant.

The downfalls you listed for Kellys formula do apply. But they were already mentioned, by me and others previously

twerg_85

Mellor wrote: »

That last bit from the wikipage is wrong.

You certainly don't have a 10% chance of dropping to 10% of bankroll. Although of course its possible,

In the original bet, to drop to 10% or less you would need to lose the opening 13 bets.
This is obvious not 10% chance, but rather 1 in 8192

Or you could win some, then go on a losing streak. Or you could lose 3 for every 1 you win over a long period etc. Doesn't have to be all losses at the start.

If you run some simulations you'll get a number pretty close to 10% chance of your roll falling to 10% or less (I got 9.8% chance). Same for 50% loss (I got 48% chance on my simulations).

p.s. The reason simulated odds are slightly lower is cos there's a cutoff on the number of bets you make in a row. Kelly criterion assumes you bet infinitely I guess.

jameshayes

jameshayes wrote: »

With flipping a coin, yes statistically, eventually you will make money by betting 1/6th

twerg_85 wrote: »

Kelly criterion assumes you bet infinitely I guess.

Some people dont have that long.