Yeah, I am really going to just stop responding to him now.

Quote from: Archie on August 18, 2013, 04:11:12 PM
As to the order of bets, that was not the word I used.  And, I already clarified what was already clear in its context, the streaks of W/L.

Let's say we have a 0.52 win rate. We have 52 wins and 48 losses overall. With proportional betting this alone gives us the exact result.
The order of 52 wins and 48 losses don't matter. You can have 26W then (a long losing streak) 48L and then 26W again. It doesn't matter. It gives us the same result. Streaks don't matter. Win rate matters.
Am I not explaining this right?

Quote from: Bayes on August 18, 2013, 09:37:27 AM
By the way, the Kelly criterion says that you should bet a % equal to your edge in order to maximise growth rate. So in my simulation where the edge was 2%, 2% is the optimum percentage to stake each bet.

For this we can draw a function of average growth rate for 0.51 win rate: f(x)=(1-x)^0.49*(1+x)^0.51
[attachimg=1]
It shows why 2% is a good idea for this win rate. It also shows, that if we bet over 4% we should expect a decay, because the average growth rate goes below 1.

There is a typo in your starting point, it is supposed to be a multiplication instead of addition. Then the rest is correct. And looks simpler than what I did.


You can draw the function f(x) = 1 / (1 - log(1 + x) / log(1 - x)) with:http://rechneronline.de/function-graphs/
You can set it up to only show values between 0 and 1, and you can see the relation of the bet proportion and the corresponding win rate threshold.
It is just the threshold though, not the optimal bet proportion.

The more trials we have, the closer win rate gets to the probability of a single trial. Like a coin toss with 50% probability.
If we have 10 trials, the probability of winning 40%-60% (4 or 5 or 6 tosses) is about 66%.
If we have 100 trials, the probability of winning 40%-60% (40 to 60 tosses) is already more than 96%!!!
That is how win rate gets closer and closer to the probability of a single trial in the long run.

So if we have a 55% probability for a single trial, then if we repeat the same trial, we get closer and closer to 55% win rate. This is why actually the long run is our friend if we have +EV betting opportunity. (This is a very big if though... It is not easy to come by +EV bets)


With 5% proportional betting you have a threshold at roughly 0.513.

If we have the probability of a single trial above this threshold, we expect to make money.
If we have a win rate above this threshold, we actually made money.


If you have a win rate above this threshold it is impossible to arrange wins an losses in an order where you lose money. Because the order doesn't matter. You can arbitrarily arrange huge losing streak(s) in a result, if your win rate is above the threshold you can't possibly have a losing result.


If someone is interested in how we get the threshold:
The end result (final bankroll) is BR*0.95^nl*1.05^nw (where BR=initial bankroll, nl=number of losses, nw=number of wins)
To break even we need the multiplier at 1 (that makes our final bankroll=initial bankroll):
0.95^nl*1.05^nw=1
0.95^nl=(1/1.05)^nw    ---> because 1/1.05^nw=(1/1.05)^nw
nl=log_0.95((1/1.05)^nw)
nl=nw(log_0.95(1/1.05))

Win rate is nw/(nw+nl).
Replacing nl, that leaves us with a win rate of
nw/(nw+nw(log_0.95(1/1.05))) = 1/(1+(log_0.95(1/1.05))) which is a little less than 0.513

Quote from: Archie on August 16, 2013, 01:08:00 PMWhere did I write to the order of wins and losses?

You mentioned losing 15 in a row, that suggests the order of wins and losses.

Quote from: Archie on August 16, 2013, 01:08:00 PM
But doubling a stake is a lot harder than losing half of it.

Staying with the same 5% proportional scenario, doubling your BR takes 15 wins. That doesn't seem too hard comparing to the 15 losses it takes to lose half of it. It is a bit harder to double it, that is why you need 0.513 win rate and not just 0.5. But that still isn't "a lot" harder.

Quote from: Archie on August 16, 2013, 01:08:00 PM
I don't like your math.  (I could tell right off that you're not a professional mathematician, and certainly never a gambler.) I really don't like the way in which you're trying to suck gamblers in with it.

Calculations can be either correct or wrong. You are welcome to correct any of my calculations. Saying you don't like it is just the same thing when you picked at me writing decimal odds (2 for even money bet), while that is widely used in sports betting. These arguments are just invalid.

It doesn't matter how many times in a row you lose. Only the overall result matters.
At 5% even money bets a loss is BR*0.95 and a win is BR*1.05.
Your total result at even money bets is BR*0.95^nl*1.05^nw. Where nl is the number of losses, and nw is the number of wins. The order is irrelevant. Sure if it is 15 losses in a row it really does lose more than half of your current BR (which can be already much more than double your starting BR), but you have just as much or even more chance (at a +EV game with even money bets) to win 15 in a row.
If nl=nw then you lose, but with +EV and even money nw is expected to be greater than nl. With these numbers you break even around 0.513 win rate. Higher win rate gives you exponential growth. And again... the order of wins and losses is irrelevant.


PS. I might not answer to your further comments because I don't like your attitude. You might consider this to be my problem and not yours. It doesn't really matter.

Quote from: Priyanka on August 14, 2013, 02:51:10 PM
Would you advice decreasing the bet size to that 5% of BR when my BR decreases after a streak of losses?

Yes. Or be prepared to deposit again. The risk rises with the bet/bankroll ratio.

Quote from: Priyanka on August 14, 2013, 02:51:10 PM
Sure Dragoner, I think I get what you are saying. But again the EV is subjective isn't it. It is really hard to say the probability of Manchester united beating Swansea is 60% or 80%. What we can say is a range. Or is there any way we can make it more objective. Anything that has some subjectivity in it is susceptible to be inaccurate.

As long as we are only talking about sports betting, then yes, EV is subjective, because we can only calculate it with subjective probabilities.
Still, without knowing the game your estimated probability can be way off. While somebody who knows the game will have more accurate guesses.
If you have no information on the game, then your chances are better in roulette. And this should not be taken as a suggestion to play roulette instead. Rather a suggestion to not bet without information on the game.

I advise to any gambler who is actually looking to make some money to stay away from roulette. Or any other game that is played against the house.
At sports betting you actually have a chance to be profitable. So that is a good move to check out sports betting instead of roulette.


The bankroll size doesn't matter much. It is the ratio of the BR and bet size that matters. The 5% per bet seems to be fine. I would even suggest a larger bet size if the odds of your bets are around 2 (even money bets) and you are flat betting.
Progressions are different. I also don't recommend progressive betting. They don't change your long term results. The long term results are pretty much defined by your individual bets. How you combine them into progressive bet sessions doesn't matter in the long run. It just makes it harder to evaluate your real success rate. And it is harder to find the appropriate starting bet size as well.
The only progression that I advise is that when your bankroll increases you can increase your bet size as well.


About being safe... It is all relative. A smaller bet size is always safer, but the risk is never going to be 0. So there is no 100% safe.


Live/offline: I prefer offline. It is less stressful. You have more time to think. But that is just preference.


Knowledge of the game: If you make +EV bets and have the bankroll to keep yourself in the game, you should be a winner. The EV depends on the probabilities of the game outcomes. If you don't know the game, you don't know the EV, you can't really make a good bet. Either you need to know the game, or you need a good source for this kind of information about the games.

I don't know enough about sports.
"Your knowledge about EV is not going to be enough by itself. We need to know the EV of our bets, and for that we need EV knowledge and sports knowledge as well."

Archie,

I mention on my site that you shouldn't play roulette for profits:

"This is why players believe they can win in the long run. But the casino knows better. The longer you play the less luck matters.
If you consider roulette fun, go play it, and pay the price. There is nothing wrong about spending money to have fun. Only this site is not about that."

"Like I said earlier, there is no winning roulette system, because it is not possible to make positive EV bets, therefore you shouldn't play roulette for profits."

I think it should be obvious whose best interest is taken to heart. I actually advise against playing roulette for profits.

What does that tell you?


The other game on my site is sports betting.

Since this is a player vs. player game, there isn't much of a conflict between the interests of my readers and the "casino". You really can be successful in sports betting.


Why I chose Betfair:
Even if we subtract the commission, the available odds are still usually (with the occasional exceptions) better than any other bookie gives you.

Also as a Betfair affiliate I get paid when my referred customers win. As opposed to other bookies, where you get paid when your referred customers lose.

So if my referred customers are successful, I get paid more.

Hi klw,
It doesn't help us beat roulette. It helps us understand roulette, and how it can't be beaten. How a little house edge is enough for the casino for the guaranteed profits. This shows us how if we only make positive EV bets (in other games, where it is possible), we could make money just like the casino does.
As far as I know every bet in the no-zero roulette at Betfair has 0 EV. I just bet the same amount on every single number to verify this. With negative EV my bankroll should have decreased, but it stayed the same.

Hi Dane,


If you get back half of your bet in case 0 comes up, then we can calculate the EV as:
EV=18/37*1-18/37*1-1/37*0,5=-1/37*0,5=-1/74
(18 numbers win, 18 lose, and 1 loses half)
So yes, as you mentioned, you only lose half as much.


As for the Paroli progression probabilities:
We always have 37 numbers, and we can divide them up for all the possible outcomes. If you go with red and odd,
like you said 10 numbers win (red and odd)
10 number loses (black and even)
1 number loses half (zero)
For the rest of the 16 we break even, as 1 bet wins the other loses.
So the probabilities of 1 round:
Win:10/37
Lose: 10/37
Lose half: 1/37
No change in bankroll: 16/37
The probabilities are the same if you go with black and even.
If you go with black and odd or red and even, then 8 numbers win, 8 lose, 1 loses half and 20 break even.
Probabilities for that:
Win: 8/37
Lose: 8/37
Lose half: 1/37
No change in bankroll: 20/37


These probabilities can be then used to go into more levels.

Thanks everyone for the kind words.

Thank you esoito!


Just to be clear... Yes, I am indeed an affiliate for BF.
My site is not a charity site but I do provide free information on it to the best of my knowledge. Take roulette for example. If I were to just lure people to casinos, I could have written something like: "Mathematically proven roulette system", like most of the casino affiliates and system sellers out there. Instead I went with the honest route, which I think adds to the value of my website.