RHavar
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March 02, 2018, 05:08:48 PM 

Whereas the expected bankroll growth is more to do with the factor by which the bankroll grows with each bet. [snip]
Yup, great explanation btw. I think your summary is a lot clearer than the original. So now that we have a way of calculating the expected bankroll growth, we can introduce another term "the kelly". If you plot the expected bankroll growth (EBG) against how much you are risking  you will see the chart is sort of parabolic. And the point in which EBG is maximized is known as the kelly. Now a casino isn't really able to make every bet "a kelly" because that would require telling players how to bet, but what it can do is limit bets that get too risky. I'm not really sure there's a good robust way to do this, at it totally depends on the context. For instance it's my unconfirmed belief that physical casinos employ very strict limits on the general tables because they know if someone wins "big" they will just walk, instead of turning over the money. (i.e. last casino I was in, had a $50 limit on a number in roulette, unless you were a high roller in which case they were happy taking over x10 that). Bustabit also has some pretty unique constraints, as the limits can everyone. So it really needs to balance the idea of having a "hard cap" risk amount it accepts per game, while also being able to accept as much from a single player as possible. The system it uses of having a 1x kelly perplayer and a hardcap of a 2x kelly (or currently 1.5x) pergame seems pretty reasonable. The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0EBG (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)

Check out gamblingsitefinder.com for a decent list/rankings of crypto casinos. Note: I have no affiliation or interest in it, and don't even agree with all the rankings ... but it's the only uncorrupted review site I'm aware of.




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quickmaffs
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March 02, 2018, 05:16:05 PM 

Whereas the expected bankroll growth is more to do with the factor by which the bankroll grows with each bet. [snip]
Yup, great explanation btw. I think your summary is a lot clearer than the original. So now that we have a way of calculating the expected bankroll growth, we can introduce another term "the kelly". If you plot the expected bankroll growth (EBG) against how much you are risking  you will see the chart is sort of parabolic. And the point in which EBG is maximized is known as the kelly. Now a casino isn't really able to make every bet "a kelly" because that would require telling players how to bet, but what it can do is limit bets that get too risky. I'm not really sure there's a good robust way to do this, at it totally depends on the context. For instance it's my unconfirmed belief that physical casinos employ very strict limits on the general tables because they know if someone wins "big" they will just walk, instead of turning over the money. (i.e. last casino I was in, had a $50 limit on a number in roulette, unless you were a high roller in which case they were happy taking over x10 that). Bustabit also has some pretty unique constraints, as the limits can everyone. So it really needs to balance the idea of having a "hard cap" risk amount it accepts per game, while also being able to accept as much from a single player as possible. The system it uses of having a 1x kelly perplayer and a hardcap of a 2x kelly (or currently 1.5x) pergame seems pretty reasonable. The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0EBG (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) You would think with millions of dollars at stake, you would take it more serious and actually make sure you have all the facts stated clearly and run the proper models so that what you claim is true. You did not do this. There were much simpler solutions to keep investors protected, but you both refused to admit to mistakes and greedily kept accepting higher bets while soliciting for a larger bankroll. You two are dishonest and shameful human beings.




Luxo42
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March 02, 2018, 07:09:57 PM Last edit: March 06, 2018, 09:28:51 AM by Luxo42 Merited by RHavar (6), malevolent (4), DarkStar_ (4) 

The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0EBG (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 0ebg for any binary (twooption) bet. It's only for 50% bet. ADDED later: and one of multipliers is 0.For bets with low probability 0EBG point is very slightly less than 2x kelly. Wolfram alphaSomething like up to 1.9933 Kelly For bets with high probability 0EBG point is more than 2x kelly. Wolfram alpha




JackpotRacer
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March 02, 2018, 07:58:35 PM 

The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0EBG (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 0ebg for any binary (twooption) bet. It's only for 50% bet. For bets with low probability 0EBG point is very slightly less than 2x kelly. Wolfram alphaSomething like up to 1.9933 Kelly For bets with high probability 0EBG point is more than 2x kelly. Wolfram alpha
please dont forget the HE of a casino or the edge a player could have in case he uses KC




Luxo42
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March 02, 2018, 08:06:31 PM 

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)




quickmaffs
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March 02, 2018, 09:29:02 PM 

The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0EBG (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 0ebg for any binary (twooption) bet. It's only for 50% bet. For bets with low probability 0EBG point is very slightly less than 2x kelly. Wolfram alphaSomething like up to 1.9933 Kelly For bets with high probability 0EBG point is more than 2x kelly. Wolfram alpha https://i.imgur.com/8t8k8IP.png "In general, all investors have only been exposed to +EV and positive expected bankroll growth."RHavar




RHavar
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March 03, 2018, 03:28:46 PM 

The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0EBG (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 0ebg for any binary (twooption) bet. It's only for 50% bet. For bets with low probability 0EBG point is very slightly less than 2x kelly. Wolfram alphaSomething like up to 1.9933 Kelly For bets with high probability 0EBG point is more than 2x kelly. Wolfram alpha
Oh wow, brilliant work. I always thought 2x kelly = 0 EBG on a binary bet, but your formula looks correct and it shows that 2x kelly = 0EBG only for the specific case of 2x bet. This actually seems like it's rather good news for investors. So currently bustabit restricts the pergame limit to 1.5x kelly, but let's assume it used 2x  the worst behavior could be triggered by a whale maxbetting on 200 accounts which would set the forcedpoint 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 lotterystyle bets), a 2x kelly still leads to very healthy +EBG. 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 manualcashout, which would totally suck. Probably the best thing for bustabit would to never go above 1.99x at the most extreme. That should guarantee that all games are +EBG. Although honestly, I'm not entirely sure that's the best idea. As EBG is only one of the many things that bustabit needs to control for, another thing for instance is controlling variance. Because investing isn't provably fair, if a whale came and won 80% of the bankroll it would look pretty bad even though the site is doing everything correctly.

Check out gamblingsitefinder.com for a decent list/rankings of crypto casinos. Note: I have no affiliation or interest in it, and don't even agree with all the rankings ... but it's the only uncorrupted review site I'm aware of.



JackpotRacer
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March 03, 2018, 03:35:16 PM 

Because investing isn't provably fair, if a whale came and won 80% of the bankroll it would look pretty bad even though the site is doing everything correctly.
who will finally bring the Provably Fair option for investors?




devans


March 03, 2018, 03:39:23 PM 

who will finally bring the Provably Fair option for investors?
For dice games, bustadice goes pretty far. I've seen some interesting ideas to make it entirely provably fair for investors, but unfortunately none of them were really feasible.

bustabit – The original crash game bustadice – Fastpaced bustabitlike dice with no wager limit



Luxo42
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March 03, 2018, 04:25:32 PM 

So currently bustabit restricts the pergame limit to 1.5x kelly, but let's assume it used 2x  the worst behavior could be triggered by a whale maxbetting on 200 accounts which would set the forcedpoint 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 lotterystyle bets), a 2x kelly still leads to very healthy +EBG.
Vice versa. The worst case for casino is lowvaluebetting on high multipliers, until forced cashout. According to my calculations, maxprofit = bankroll * house_edge * (2houseedge) would be EBG 0+ for any cases.




RHavar
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March 03, 2018, 05:49:23 PM 

Vice versa. The worst case for casino is lowvaluebetting on high multipliers, until forced cashout. According to my calculations, maxprofit = bankroll * house_edge * (2houseedge) would be EBG 0+ for any cases.
You sure about that? It looks to me that the worst case is for the casino is lowvalue 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)

Check out gamblingsitefinder.com for a decent list/rankings of crypto casinos. Note: I have no affiliation or interest in it, and don't even agree with all the rankings ... but it's the only uncorrupted review site I'm aware of.



RGBKey


March 03, 2018, 05:53:09 PM 

who will finally bring the Provably Fair option for investors?
For dice games, bustadice goes pretty far. I've seen some interesting ideas to make it entirely provably fair for investors, but unfortunately none of them were really feasible. I'm happy with the solution that bustadice uses, but I'm still in search for the pot of gold at the end of the rainbow that would be a fully trustless zeroknowledge ondemand RNG. Something where nobody has to trust any number of people and could be used to make games fair for both players and investors.




Luxo42
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Vice versa. The worst case for casino is lowvaluebetting on high multipliers, until forced cashout. According to my calculations, maxprofit = bankroll * house_edge * (2houseedge) would be EBG 0+ for any cases.
You sure about that? It looks to me that the worst case is for the casino is lowvalue 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: lowvalue highmultiplier lowwinprobability Casino: highvalue lowmultiplier highwinprobability 0EBG 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.




RHavar
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March 03, 2018, 09:48:53 PM 

Rechecked again. Sure.
Touché, I checked again and you do indeed seem right. I'm both pretty embarrassed about my math and impressed by yours. Well done

Check out gamblingsitefinder.com for a decent list/rankings of crypto casinos. Note: I have no affiliation or interest in it, and don't even agree with all the rankings ... but it's the only uncorrupted review site I'm aware of.



Luxo42
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March 03, 2018, 09:56:32 PM 

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.




Luxo42
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March 03, 2018, 10:11:11 PM 

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 manualcashout, which would totally suck. I think you shouldn't pay attention to this. 0EBG point moves from 2xKelly very slow and only in extreme cases. max profit = 1xKelly or 2xKelly minus HE looks good solution for me.




devans


March 04, 2018, 01:42:43 AM 

Now that investors are comfortably back in profit at approximately 324 BTC, I have reinstated the wager commission of 0.25 %.
Consequently, the bet limit and the maximum profit per player have been lowered to 0.75 % of the bankroll again and the maximum profit per game has been lowered to 1.125 % of the bankroll.

bustabit – The original crash game bustadice – Fastpaced bustabitlike dice with no wager limit



dooglus
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March 04, 2018, 03:51:30 AM 

the maximum profit per game has been lowered to 1.125 % of the bankroll
inb4 "dishonest and shameful"...

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01010100b
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March 04, 2018, 05:18:02 AM 

That is only the case for an individual investor that (ab)uses the offsite investment system to risk more than he actually has.
The offsite system is meant to allow investors to lower their counterparty risk and free up liquidity by not depositing their entire investment. I strongly recommend to only use it for that purpose. If you use the offsite system properly or don't use it at all, you never have an expectation of negative growth.
This statement is false, just think about it. Suppose there are two investors, A and B, and each have 50 btc onsite and 50 btc offsite. A is lying about it but B isn't. Why would A have EBG but B have +EBG? Whether they are lying about it is only "revealed" when their onsite gets to 0, so why would A's onsite go to 0 whereas B's onsite doesn't  even before it is known whether they are lying or not? Surely the site can not predict the future of whether A or B will turn out to have been lying, and then set A to EBG and B to +EBG based on predicting the future. Whether they are at +EBG or EBG depends solely on their onsite and offsite, obviously...




DarkStar_
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March 04, 2018, 05:30:27 AM 

That is only the case for an individual investor that (ab)uses the offsite investment system to risk more than he actually has.
The offsite system is meant to allow investors to lower their counterparty risk and free up liquidity by not depositing their entire investment. I strongly recommend to only use it for that purpose. If you use the offsite system properly or don't use it at all, you never have an expectation of negative growth.
This statement is false, just think about it. Suppose there are two investors, A and B, and each have 50 btc onsite and 50 btc offsite. A is lying about it but B isn't. Why would A have EBG but B have +EBG? Whether they are lying about it is only "revealed" when their onsite gets to 0, so why would A's onsite go to 0 whereas B's onsite doesn't  even before it is known whether they are lying or not? Surely the site can not predict the future of whether A or B will turn out to have been lying, and then set A to EBG and B to +EBG based on predicting the future. Whether they are at +EBG or EBG depends solely on their onsite and offsite, obviously... When you leverage, the expectation is that you are willing to move those offsite coins on site as you lose, so that you do not get margin called. You are at a 2x Kelly maximum (current bustabit rules), which allows for +EBG. That person can expect their bankroll to increase. A 50 BTC + 50 BTC fake offsite gives a 4x Kelly, assuming no offsite is 2x Kelly. Once your investment loses 50 BTC, you are left with nothing. It doesn't matter what the site thinks about your investment. By treating 1 coin as 2 coins, you are increasing your exposure. If everything invested with 2x leverage on bustabit, the max win would technically be 2.5% of the actual investment.




