Yes, the expected value of the bankroll growth in absolute numbers. BG and PG are random variables.
"Expected value of the bankroll growth in absolute numbers" - crazy confusing wording. There are "expected value" and "expected growth". |
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According to my calculations, minimum house edge = 2%, and maximum house edge = 10%. How did you calculate 1%?
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However I think he made the same mistake I struggled with too, which was thinking that if the bankroll is -EBG that would allow a player to be +EBG. Fortunately (for investors) this isn't the case, so there's no real abuse avenue.
Can you check where I'm going wrong with this? Here's how I looked at it: Let BG and PG be two random variables, BG is the house's bankroll growth and PG is the player's bankroll growth (in absolute numbers). Then: BG + PG = 0 (money only moves back and forth between the house and the player, so a loss for one is a gain for the other and vice versa) E[BG + PG] = E[0] (taking the expected value of both sides) E[BG + PG] = 0 (expected value of a constant is that constant) E[BG] + E[PG] = 0 (by linearity of expected value) E[BG] = -E[PG] Which leads to the player's EBG being the opposite of the house's EBG, so if the house is at -EBG then the player is at +EBG and vice versa. Perhaps by EBG is meant the median bankroll growth and not the mean bankroll growth? In which case the linearity condition above wouldn't apply. No. That is for expected value only. EVcasino + EVplayer = 0. Try EBG * EPG = 1 For example, EBG = 1.05 (+5%) So, EPG = 1/1.05 = 0.952 (-4.76%) But i'm not sure it would work. |
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Investment with fixed offsite bankrolls looks very bad unlike with fixed multiplier / leverage
It is not clear for me how such investment system will behave in some cases. I would like to see the source code or investment math of BaB and JD (if that's possible and appropriate for dooglus and devans)
And here is a case.
Two investors - A is onsite and B is offsite. 1xKK.
Very bad day for casino. Investor B is in pre-margin-call position.
Investor A: 8 onsite, 0 offsite
Investor B: 1 onsite, 991 offsite
Bankroll: 1000, max profit: 10. Player bet and win.
And thas is disaster. Max profit more than onsite bankroll. It's more than casino's "cash"! Casino can not pay to player. What EBG are you talking about?
Of course, this is rare case. But math should works always everywhere. if it is not, then the whole investement system is working incorrectly.
Looks like there is no such problems at leverage investment system.
Maybe, would be better to create separate topic?
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Net profit: -4 bits NOOOOOOOOOOOOOOOOOOOOOOoooooooooooooooooooooooooooooooooo................ |
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So you think this is the same operator as the one who created that game from over a year ago  Do you have substantial proof of this with support emails from them as something to go by maybe? It is hard to pursue a scam accusation against a casino operator without some sort of proof to back your claims.  Half a year ago. Of course i have no any proofs. But "style" is a same totally. For example, fake online users. There are a lot of such signs. But there is no reason to share them. |
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Just a fact. Same shit from you every month or so. What other gambling projects are you referring to? Every month there should be a trail of their past projects if they failed. You must be a backend programmer for them to know this since it is the only project they have had hence the name of this user correlating to their site. for example girlbtc.com bitkong-like game a few weeks ago there are a lot of them |
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are we scammed you ?
Yeap  About a year ago. |
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Just a fact. Same shit from you every month or so. |
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What would be a really cool solution, is that that you dynamically adjusted the limits based on the persons bet multiple. However, I can't really see how to do that cleanly in bustabit without removing the manual-cashout, which would totally suck. I think you shouldn't pay attention to this. 0-EBG point moves from 2xKelly very slow and only in extreme cases. max profit = 1xKelly or 2xKelly minus HE looks good solution for me. |
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In fact, it does not matter whether the maximum profit, kelly criterion, fees and others things was set correctly or not.
What if some lucky player won a lot at casino? Investors lost money.
Investor can not prove that a lucky player is a casino. And that is not just luck, but scam.
Casino can not prove that a lucky player is not casino. And that is not scam.
So such investment is entirely based on trust to the owner.
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Vice versa. The worst case for casino is low-value-betting on high multipliers, until forced cashout. According to my calculations, max-profit = bankroll * house_edge * (2-house-edge) would be EBG 0+ for any cases.
You sure about that? It looks to me that the worst case is for the casino is low-value betting on high multipliers from the casinos perspective, but this is generated by a player betting a large amount on a low multiplier. (i.e. if a player is betting 1 BTC to try win 10 BTC, from the casinos perspective this is a 10 BTC bet trying to win 1 BTC) Rechecked again. Sure. Player: low-value high-multiplier low-win-probability Casino: high-value low-multiplier high-win-probability 0-EBG at <2 Kelly Maybe, it's really counterintuitive. But, for example, casino (HE=1%) may lose 5% of bankroll per bet with high probability (slightly less than 99%). But player's bet is much higher than the whole bankroll. And that's is EBG+ for casino. |
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So currently bustabit restricts the per-game limit to 1.5x kelly, but let's assume it used 2x -- the worst behavior could be triggered by a whale max-betting on 200 accounts which would set the forced-point to 1.01x (and stop the game server accepting any new bets). In this kind of insane case, it would only be very slightly negative EBG. But in a more common case of people aiming at higher multiples (especially lottery-style bets), a 2x kelly still leads to very healthy +EBG.
Vice versa. The worst case for casino is low-value-betting on high multipliers, until forced cashout. According to my calculations, max-profit = bankroll * house_edge * (2-house-edge) would be EBG 0+ for any cases. |
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please dont forget the HE of a casino or the edge a player could have in case he uses KC
HE=1% (look at ev - it's 0.99) |
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If the script does not yield 20% ROI 18 times out of 20, I will admit that I "lied", and will leave the forum. I will also send a few bits to people who warned against me.
If the script yields 20% ROI 18 times out of 20 (or more)... well, then I guess my point has been proven.
18 times of 20 is 90%. ROI - 20%. Expected value is 1.08. There's a chance of 92.5% to reach so easy target without using any scripts. So, you would not prove anything. You are totally right. My bad. |
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The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0-EBG (but positive +EV). But actually bustabit (from the houses perspective) isn't a binary bet, it can lose some and win some. So assuming I calculated everything right (which very well might not be the case, as I can't come up with an analytical solution) it's actually quite common for a 2x kelly to be positive expected bankroll growth! (and the worst case is a 2x kelly is 0 EBG)
2x kelly is not 0-ebg for any binary (two-option) bet. It's only for 50% bet. ADDED later: and one of multipliers is 0.For bets with low probability 0-EBG point is very slightly less than 2x kelly. Wolfram alphaSomething like up to 1.9933 Kelly For bets with high probability 0-EBG point is more than 2x kelly. Wolfram alpha
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If the script does not yield 20% ROI 18 times out of 20, I will admit that I "lied", and will leave the forum. I will also send a few bits to people who warned against me.
If the script yields 20% ROI 18 times out of 20 (or more)... well, then I guess my point has been proven.
18 times of 20 is 90%. ROI - 20%. Expected value is 1.08. There's a chance of 92.5% to reach so easy target without using any scripts. So, you would not prove anything. |
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I think the worst-case risk growthed from 1.5x Kelly to 2x Kelly after comissions' suspend, but not dropped?
No, it was 2x Kelly with the commission and is now 1.5x Kelly without it. Without the commission, investors' EV for each bet is 1 % (the house edge) and the risk per round is 1.5 % of the bankroll. ok, i understand. i meant zero-growth bankroll point for investors was at 1.5% of bankroll, and now it's at 2% of bankroll. |
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