Bitdice.me it is negative EV for investors?

[ztephen]

I hear that they take 10% of profits weekly. Too bad, I wish I could get a better answer than that because they don't tell you the terms for investing.

so assume that 10btc is wagered a week. the percentages show negative ev on all of the odds a player can choose.

(-10BTC)(0.495)+(9BTC)(0.505)= -0.405

(Investors Loss)(chance of losing)+(Investors Profit)(chance of winning) = (Expected Loss per 10BTC wagered)

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[yakuza699]

They have a positive house edge of 1%.So if someone would wager 10BTC it is expected to earn 0.1BTC you get 0.09 and they take their 10%.

[ztephen]

the house edge is expressed in chance of win and chance of loss from the investors perspective.

[Astargath]

the house edge is expressed in chance of win and chance of loss from the investors perspective.

But what is the problem of that? If investing into the site would be always +EV then everyone would invest and wait to win their money, eventually, that would just ruin the site, when a site allows investments is also because they can win from it as far as i understand it

[xKomatsu]

I hear that they take 10% of profits weekly. Too bad, I wish I could get a better answer than that because they don't tell you the terms for investing.

so assume that 10btc is wagered a week. the percentages show negative ev on all of the odds a player can choose.

(-10BTC)(0.495)+(9BTC)(0.505)= -0.405

(Investors Loss)(chance of losing)+(Investors Profit)(chance of winning) = (Expected Loss per 10BTC wagered)

Isnt the formula you used is wrong? I dont think invesyment is always -EV because of the 1% house edge

[michinzx]

investing doesn't guarantee profit, but it should, more or less, in the long run given a house edge. what probably happened in your case was someone won big, causing that shirt term investment to be -EV.

[RHavar]

I hear that they take 10% of profits weekly. Too bad, I wish I could get a better answer than that because they don't tell you the terms for investing.

so assume that 10btc is wagered a week. the percentages show negative ev on all of the odds a player can choose.

(-10BTC)(0.495)+(9BTC)(0.505)= -0.405

(Investors Loss)(chance of losing)+(Investors Profit)(chance of winning) = (Expected Loss per 10BTC wagered)

At a glance, that looks correct for a single wager (which is a real investor worst-case).

However, assuming that bitdice.me works like JD, investors are given commission free earnings on any investing loss since the last commission was taken (a high water mark). Which has an interesting effect with a small amount of wagers: every week you have >= 0 profit, investors are -EV. However, when investors are at a loss: they are now +EV (since there's no 10% haircut), which means over an infinite amount of weeks you are still +EV

There's certainly different ways to do it. For instance in MoneyPot we take a commission in such a way that every individual bet is still +EV for the investors: https://www.moneypot.com/faq#what-commissions-do-you-charge-

[NLNico]

edit: -snip-

I think OP's calculation is correct, however because BitDice only charges commission on net profits, it's still EV+.




BTW Alex, still would be nice if you could list "Commission amount" in "Invest" tab, noticed this isn't there anymore since V3

[RHavar]

You count it wrong.

When someone loses on site investors get 100% of it. Profits from investors, and ONLY net profits, are being deducted at the end of the week or when investor divests, which happens first.

Are you sure?


What is the EV for the investors (including commissions) if there is a single wager placed that week, 10 BTC @ 2x?

[RHavar]

AFAIK, the calculation should be:

Profit = (loss)*(chance of losing)+(win)*(change of winning)
Actual profit = profit * investor edge (house edge - commission)

So you don't calculate the commission on the win only, but on the overall profit. For example:

(-10)*(0.495)+(10)*(0.505) = 0.1 (is actually just: wagered * house edge = 10*0.01 = 0.1)
0.1*0.9 = 0.09 = actual profit.

Your maths shows paying 10% commission on the EV, not on the profit =) I believe the OP Maths is actually correct. For instance, the only wager the entire week is a gambler placing a single 10 BTC bet, and loses it. The investors profit is 10 BTC, and thus the weekly commission due is 1 BTC.


The real question here is, does bitdice.me have a commission high-water mark like JD? (In which case, everything is fine. There might be some weeks that it is -EV for investors, but all in all it's +EV)

[NLNico]

Yeh, realize it just now, whoops. Mm. So any site that has 10% commission on all profits of all bets are EV-? Cuz I am invested in a smaller site that does that, and I actually thought it was EV- but didn't take much time to figure it out.




"net profit" should be "commission high-water mark" (right?) so BitDice should be EV+ because of that. (I am currently down 2 coins on BD investing, yeahhhh EV+ FTW)

[webchris]

From my understanding, this is a similar model other dice sites used and investors at bitdice, JD, etc have done very well. You can check the site's profit, or the amount invested as evidence of that.

[RHavar]

"net profit" should be "commission high-water mark" (right?) so BitDice should be EV+ because of that.

I'm not sure, that's a question for Alex. It could mean one of two things: either resetting the profit after each week (in which case, it's theoretically possible for it to be -EV for investors) or keeping a high-water mark like JD (in which case, it's possible for an individual week to be -EV for investors, but long term +EV)

[RHavar]

Are you sure?


What is the EV for the investors (including commissions) if there is a single wager placed that week, 10 BTC @ 2x?

(-10BTC)(0.495)+(10BTC)(0.505)= 0.1*0.9 = +0.09 BTC

?!! That is taking a commissions on EV, not profit. But one second ago you wrote:

When someone loses on site investors get 100% of it. Profits from investors, and ONLY net profits, are being deducted at the end of the week or when investor divests, which happens first.

so which is it? 

[shanem]

Of course not, I believe they are giving away a percentage from their house advantage.
It just reduces their profit earned from the house advantage.

[RHavar]

Let's break the maths down a bit:

(-10BTC)(0.495)+(10BTC)(0.505)= 0.1*0.9 = +0.09 BTC

So let's first look at the left hand of the equation, which we both agree on:

Code:

(-10BTC)(0.495)+(10BTC)(0.505)

This says investors have 49.5% chance of losing 10 BTC, and 50.5% of making 10 BTC. And thus, they have a total EV of 0.1 BTC.


I'm not sure how your commissions work, so let's use JD's. In the 49.5% chance that the investors lose 10 BTC, they owe 0 commissions.  But there's a 50.5% chance that they just made 10 BTC. Since their net profit for that week was 10 BTC, they need to pay 10% of it in commissions.

So let's plug that back in the equation:

(-10BTC)(0.495)+((10BTC)(0.505) * 0.9)

which gives:

-0.405 BTC


The same number the OP gave. In effect, the investors have an expected loss of 0.405 BTC. JD makes up for this, by using a high-water mark on commissions, so that if you've taken an investing loss you get pure +EV until you're eventually back in the profit


I guess what's not clear is how bitdice.me works. If investors lose 1 BTC the first week, and then make it back the 2nd week, how much commissions do they owe?

[RHavar]

I've never said that I take commission on profits, I've said that I take comm on NET INVESTMENT PROFITS.

In the given case, the net investment profit is 10 BTC, not 1. Which means the commissions due is 1 BTC, not 0.1

[dooglus]

Let's break the maths down a bit:

[...]
So let's plug that back in the equation:

(-10BTC)(0.495)+((10BTC)(0.505) * 0.9)

which gives:

-0.405 BTC

The same number the OP gave. In effect, the investors have an expected loss of 0.405 BTC. JD makes up for this, by using a high-water mark on commissions, so that if you've taken an investing loss you get pure +EV until you're eventually back in the profit

I calculated the EV for the investor when there's a single bet of 10 BTC at 2x when you first asked, without reading on to see how you calculated it. I wrote:

player loses 50.5% of the time, investor wins 10 BTC, pays 1 BTC commission, net win +9  
player wins 49.5%% of the time, investor loses 10 BTC, net win -10

EV for investor: 0.505 * 9 - 0.495 * 10 = -0.405 = -4.05%

so we agree. If there's only a single 10@2x bet in the first week, the EV for the investor is -4.05% of the amount wagered.

However, I disagree that JD makes up for this by using the high-water mark. While the high-water mark helps a little, I think the most significant factor is that we only take commission on *net* profits, at the end of each week. There's never only a single bet, and as soon as there are more than 17 bets, the EV for the investor goes positive.

Here's the EV for the investor for various numbers of bets:

  1 -4.0500%
   2 -1.5502%
   4 -0.9254%
   6 -0.6130%
   8 -0.4177%
  10 -0.2811%
  12 -0.1786%
  14 -0.0981%
  16 -0.0327%
  17 -0.0327%
  18  0.0218%
  20  0.0681%
  30  0.2266%
  50  0.3872%
 100  0.5501%
 200  0.6654%
 500  0.7672%
1000  0.8176%

and the script I wrote to calculate that:

Code:

#!/usr/bin/env python

f = {}
def factorial(x):
    if f.has_key(x): return f[x]
    if x < 2: return 1
    f[x] = x * factorial(x - 1)
    return f[x]

def c(n, k): return factorial(n) / (factorial(k) * factorial(n - k))

p = 0.495
for trials in [1, 2, 4, 6, 8, 10, 12, 14, 16, 17, 18, 20, 30, 50, 100, 200, 500, 1000]:
    sum = 0
    for wins in range(trials + 1):
        profit = (trials - 2 * wins) * 10
        if profit > 0: profit = profit * 0.9
        v = 100 * c(trials, wins) * p**wins * (1-p)**(trials-wins)
        sum += v * profit
    print "%4d %7.4f%%" % (trials, sum / (trials * 10))

Edit: I would have run it for bigger numbers of bets, but the script fails shortly after 1000, with errors like:

    v = 100 * c(trials, wins) * p**wins * (1-p)**(trials-wins)
OverflowError: long int too large to convert to float

and:

RuntimeError: maximum recursion depth exceeded

I guess I need a better implementation of c().

[Astargath]

Let's break the maths down a bit:

[...]
So let's plug that back in the equation:

(-10BTC)(0.495)+((10BTC)(0.505) * 0.9)

which gives:

-0.405 BTC

The same number the OP gave. In effect, the investors have an expected loss of 0.405 BTC. JD makes up for this, by using a high-water mark on commissions, so that if you've taken an investing loss you get pure +EV until you're eventually back in the profit

I calculated the EV for the investor when there's a single bet of 10 BTC at 2x when you first asked, without reading on to see how you calculated it. I wrote:

player loses 50.5% of the time, investor wins 10 BTC, pays 1 BTC commission, net win +9  
player wins 49.5%% of the time, investor loses 10 BTC, net win -10

EV for investor: 0.505 * 9 - 0.495 * 10 = -0.405 = -4.05%

so we agree. If there's only a single 10@2x bet in the first week, the EV for the investor is -4.05% of the amount wagered.

However, I disagree that JD makes up for this by using the high-water mark. While the high-water mark helps a little, I think the most significant factor is that we only take commission on *net* profits, at the end of each week. There's never only a single bet, and as soon as there are more than 17 bets, the EV for the investor goes positive.

Here's the EV for the investor for various numbers of bets:

  1 -4.0500%
   2 -1.5502%
   4 -0.9254%
   6 -0.6130%
   8 -0.4177%
  10 -0.2811%
  12 -0.1786%
  14 -0.0981%
  16 -0.0327%
  17 -0.0327%
  18  0.0218%
  20  0.0681%
  30  0.2266%
  50  0.3872%
 100  0.5501%
 200  0.6654%
 500  0.7672%
1000  0.8176%

and the script I wrote to calculate that:

Code:

#!/usr/bin/env python

f = {}
def factorial(x):
    if f.has_key(x): return f[x]
    if x < 2: return 1
    f[x] = x * factorial(x - 1)
    return f[x]

def c(n, k): return factorial(n) / (factorial(k) * factorial(n - k))

p = 0.495
for trials in [1, 2, 4, 6, 8, 10, 12, 14, 16, 17, 18, 20, 30, 50, 100, 200, 500, 1000]:
    sum = 0
    for wins in range(trials + 1):
        profit = (trials - 2 * wins) * 10
        if profit > 0: profit = profit * 0.9
        v = 100 * c(trials, wins) * p**wins * (1-p)**(trials-wins)
        sum += v * profit
    print "%4d %7.4f%%" % (trials, sum / (trials * 10))

Edit: I would have run it for bigger numbers of bets, but the script fails shortly after 1000, with errors like:

    v = 100 * c(trials, wins) * p**wins * (1-p)**(trials-wins)
OverflowError: long int too large to convert to float

and:

RuntimeError: maximum recursion depth exceeded

I guess I need a better implementation of c().

So what that pretty much means is that the more bets the more chances you get to profit from the site? When that guy lost 7k btc at your casino how much money would an investor have won if he invested lets say 10 BTC?

[dooglus]

So what that pretty much means is that the more bets the more chances you get to profit from the site?

Yes. Except that after the first few thousand bets each month the EV for the investor doesn't increase much more. It will top out at 0.9% (the 1% house edge, minus the 10% of that taken as commission).

When that guy lost 7k btc at your casino how much money would an investor have won if he invested lets say 10 BTC?

That would depend on the total size of the bankroll at the time. I don't remember what it was, but let's guess it was 30k BTC. That won't be too far off.

If someone loses 7,000 when you own 10 out of 30,000 of the bankroll, you get 10 1/30,000ths of the loss, of 7000 * 10 / 30000 = 7/3 = 2.333 BTC

(Then at the end of the week the site takes 10% of your net profit. Note that the 7k loss came after he had won 5k, so that 2.333 isn't all profit. Most of it is recovering from the losses you took when he won the 5k, assuming you were invested for that too).

Personally I was invested for the first half of his betting (where he won ~3k) and not invested for the second half (where he won another 2k then lost 7k). So I did badly out of it. But then I took 10% of everyone else's profit, so it worked out.