In the hypothetical case that true "leverage" investing is offered, how would the dilution fee work?
Would someone investing 1 BTC at 2x kelly be charged the same dilution fee as someone investing 1 BTC at 1x kelly? Or would they be charged the same amount?
Would people be allowed to change their kelly setting at will, without incurring dilution fees? Or would it work much like the "offsite" feature does at the moment?
Allowing people to reduce their kelly multiplier for free re-enables 'whale dodging" behavior, which the dilution fee was designed to prevent.
I guess the most reasonable way to work it would be to charge dilution fees on ((onsite + offsite) * kelly), since that is the effective contribution to the bankroll.
Topic: bustabit – The original crash game - page 108. (Read 61394 times)
I like how dooglus explained what he learned from his reading, made it a lot clearer to me too how things are actually computed mathematically in terms of how much investors really can profit from each bet depending on the parameters of the casino investment and the house edge. Would say that I've always just trusted that my money will grow in casino bankrolls bu never knew the science of how things really worked.
Let's use Dooglus as the judge on the matter.
If I can convince Dooglus that you deceived investors, you agree to be red-tagged by everyone.
If I can convince Dooglus that any of you lied, you agree to be red-tagged by everyone.
If I can convince Dooglus that investors were not on the same playing level as RHavar, RHavar agrees to be red-tagged by everyone.
If I can convince Dooglus that your lies and deceit led to negative consequences for investors, you agree to publicly acknowledge this in a written statement.
Was not able to watch this thread, and checked it just know. I don't see your point why you commented this on my post. I only commended dooglus on how he explained how house edge and casino investments work, since I really never had the time to research how it truly ticks. But hey, you are entitled to your opinion, but I just don't see any point why you were so hostile to it.
I don't see any. I think it's a very good idea. I think "ideally" the site should probably have 4 bankrolls, one for 0.5x, 1x, 2x and 4x. (and then combine them into 1 "virtualized" bankroll). And allow people to invest into any leveraged bankroll they want. I think combined with offsite, it would be a pretty ideal system.
I'm definitely for being able to choose the max kelly risk. The only thing keeping me from investing into the site is the crazy amount of potential volatility when a whale/whales bets for max profit (as many have seen with that multi account mega whale). There are huge potential swings in the bankroll that can occur at 1.5x kelly and even at 1x kelly. I would personally like to invest at 0.5x kelly and I'm sure many investors probably feel the same.Also I think a per game max profit of 0.5x, 1x, and 1.5x kelly (current) should be sufficient.
With the current system that isn't necessary. If you have 10% of the bankroll before a bet, you still have 10% of the bankroll after the bet. The only time your percentage share changes is when people invest or divest.
Yes your % share of overall bankroll would change according to the kelly you set. The max profit would also be a variable % of overall bankroll (wouldn't really make a difference to players as they only see the max profit value). My maths are next:
Investor 1: 5 x1
Investor 2: 1 x2
Investor 3: 1 x3
Bankroll = 5*1+1*2+1*3 = 10
Bankroll's shares: investor 1 - 50%, investor 2 - 20%, investor 3 - 30%.
Casino'a wins/losses divides among investors according to their shares.
Investor 1: 5 x1
Investor 2: 1 x2
Investor 3: 1 x3
Bankroll = 5*1+1*2+1*3 = 10
Bankroll's shares: investor 1 - 50%, investor 2 - 20%, investor 3 - 30%.
Casino'a wins/losses divides among investors according to their shares.
Dividing the wins/losses among investors changes that 50/20/30 split. You have to recalculate the percentage after every bet.
With the current system that isn't necessary. If you have 10% of the bankroll before a bet, you still have 10% of the bankroll after the bet. The only time your percentage share changes is when people invest or divest.
I do not exactlly understand what is meant by a a lot of bankrolls and virtual bankroll.
Just terminology, you understand =)
I would do exactly what you say: Group all investors by their leverage amount, each of those would be a "bankroll". And then the "virtual bankroll" is the sum of all those bankrolls * the leverage. And then after each game, wins and loses are shared amongst the bankrolls according to their size relative to the "virtual bankroll"
RHavar, dooglus, is there any problems with such "real leverage" investments?
I don't see any. I think it's a very good idea. I think "ideally" the site should probably have 4 bankrolls, one for 0.5x, 1x, 2x and 4x. (and then combine them into 1 "virtualized" bankroll). And allow people to invest into any leveraged bankroll they want. I think combined with offsite, it would be a pretty ideal system.My maths are next:
Investor 1: 5 x1
Investor 2: 1 x2
Investor 3: 1 x3
Bankroll = 5*1+1*2+1*3 = 10
Bankroll's shares: investor 1 - 50%, investor 2 - 20%, investor 3 - 30%.
Casino'a wins/losses divides among investors according to their shares.
RHavar, dooglus, is there any problems with such "real leverage" investments?
I don't see any. I think it's a very good idea. I think "ideally" the site should probably have 4 bankrolls, one for 0.5x, 1x, 2x and 4x. (and then combine them into 1 "virtualized" bankroll). And allow people to invest into any leveraged bankroll they want. I think combined with offsite, it would be a pretty ideal system.
Although I think though there is a point where the bankroll gets big enough, that it's no longer a limiting factor for any whales -- and as such there's no real need to even be offering such leverage (and would be better off making sure everyone is on the lowest)
One more table.
How expected growth depends on investor's leverage and player's bet
As you can see, normal investor gain profit on whales. 4x-leverage investor do not gain profit on whales.
On other side, 4x-leverage investor gain up to 4 times more than normal investor on non-whales.
So, leverage is a mechanism for investors to focusing investments on a specific type of players. Looks very clear.
RHavar, dooglus, is there any problems with such "real leverage" investments?
How expected growth depends on investor's leverage and player's bet
As you can see, normal investor gain profit on whales. 4x-leverage investor do not gain profit on whales.
On other side, 4x-leverage investor gain up to 4 times more than normal investor on non-whales.
So, leverage is a mechanism for investors to focusing investments on a specific type of players. Looks very clear.
RHavar, dooglus, is there any problems with such "real leverage" investments?
This likely means that the "real leverage" player does worse than the fixed offsite investor in the much more common case where the player wins and loses more equally.
Shouldn't "real leverage" still do better in that scenario if the players lose slightly more than they win as expected due to house edge?
I kind of ran out of steam at that point. I can't imagine that "real leverage" is better than "offsite investing" in every case. Shouldn't there be a trade-off?
Back to the example:
A has 10 onsite and 90 offsite.
C has 10 onsite with 10x "real" leverage.
Suppose a whale plays for a long period with 50% chance of winning each bet. All bets are the maximum, aiming to win 1% of the bankroll. The payout when he wins is 1.98x (1% house edge), and he wins and loses the same amount of bets (as he is expected to do, long term). Let's call the effective bankroll "B".
50% of the time the player wins 1% of the bankroll: B/100. When this happens, A's effective bankroll is multiplied by 99/100, and C's is multiplied by 90/100.
The other 50% of the time the player loses his stake. He's aiming to profit by B/100, with a payout multiplier of 1.98x, so he's risking and losing B/98. When this happens, A's effective bankroll is multiplied by 99/98, and C's is multiplied by 108/98.
Since the whale wins and loses the same number of bets, we can pair these bets. Each pair consists of one win and one loss.
For each pair, A's effective bankroll is multiplied by 99/100 and 99/98, for a net growth factor of 99/100 * 99/98 = 9801/9800 ~= 1.0001x
And C's effective bankroll is multiplied by 90/100 and 108/98, for a net growth factor of 90/100 * 108/98 = 9720 / 9800 ~= 0.9918x
And so we see that my intuition was correct, and that "real" leverage is worse than this "offsite investment" thing. The "offsite investment" has a (small but) positive expected bankroll growth whereas the "real leverage" expects to lose almost 1% of the bankroll for every pair of (1 win + 1 lose) bets.
But leverage multiplier should be limited!
For max win = 1KK max leverage = 2x.
For max win = 0.5KK max leverage = 4x.
Investor with max leverage is EBG 0+ always.
When player is whale, regular investor's EBG+, max leverage investor's EBG-zero.
But when player is not whale, both EBG are positive. And regular investor's EBG is lower than max leverage investor's EBG. So, leverage works.
Therefore, "real leverage investment" properly works in all cases. But "offsite investement" not. Or am I wrong?
This likely means that the "real leverage" player does worse than the fixed offsite investor in the much more common case where the player wins and loses more equally.
Shouldn't "real leverage" still do better in that scenario if the players lose slightly more than they win as expected due to house edge?
I kind of ran out of steam at that point. I can't imagine that "real leverage" is better than "offsite investing" in every case. Shouldn't there be a trade-off?
Back to the example:
A has 10 onsite and 90 offsite.
C has 10 onsite with 10x "real" leverage.
Suppose a whale plays for a long period with 50% chance of winning each bet. All bets are the maximum, aiming to win 1% of the bankroll. The payout when he wins is 1.98x (1% house edge), and he wins and loses the same amount of bets (as he is expected to do, long term). Let's call the effective bankroll "B".
50% of the time the player wins 1% of the bankroll: B/100. When this happens, A's effective bankroll is multiplied by 99/100, and C's is multiplied by 90/100.
The other 50% of the time the player loses his stake. He's aiming to profit by B/100, with a payout multiplier of 1.98x, so he's risking and losing B/98. When this happens, A's effective bankroll is multiplied by 99/98, and C's is multiplied by 108/98.
Since the whale wins and loses the same number of bets, we can pair these bets. Each pair consists of one win and one loss.
For each pair, A's effective bankroll is multiplied by 99/100 and 99/98, for a net growth factor of 99/100 * 99/98 = 9801/9800 ~= 1.0001x
And C's effective bankroll is multiplied by 90/100 and 108/98, for a net growth factor of 90/100 * 108/98 = 9720 / 9800 ~= 0.9918x
And so we see that my intuition was correct, and that "real" leverage is worse than this "offsite investment" thing. The "offsite investment" has a (small but) positive expected bankroll growth whereas the "real leverage" expects to lose almost 1% of the bankroll for every pair of (1 win + 1 lose) bets.
But isn't "B" changing as well and affecting the investors differently, as well as the max bet? I'm really bad at this abstract math thing so I tried to fill out a spreadsheet:
Maybe I messed something up but I can figure out what exactly.
Edit: I did mess it up. My previous calculation didn't do the leverage correctly.
Edit2: Never mind. I think I get it now. Will pour myself a couple more and try to actually understand it.
It doesn't make sense to sum those growth multipliers.
Obviously, and that is indeed the reason why I'm not summing them. I said "in absolute numbers" multiple times now.
These "absolute numbers" you're talking about are the expected profits, not the expected growth factors. They are different things.
Expected profits are "absolute numbers" - you can add them. Expected growths are multipliers - you can multiply them.
So you have nothing but semantics and quibbling over the meaning of the word "growth"? Do you perhaps have something substantial to say about the argument I made?
Let's define this properly. Let B_0 be the initial bankroll and B_N the bankroll after a sequence of N bets. Then BG is a random variable which, when given said sequence of N bets, takes the value B_0 * log(B_N / B_0) / N. Likewise for PG.
I can't imagine that "real leverage" is better than "offsite investing" in every case. Shouldn't there be a trade-off?
Agree. I think they're largely orthogonal. Although "offsite investing" can be used to (poorly) emulate "real leverage" and vice versa, but I think they largely serve different goals. There's definitely no reason you couldn't combine both
It doesn't make sense to sum those growth multipliers.
Obviously, and that is indeed the reason why I'm not summing them. I said "in absolute numbers" multiple times now.
These "absolute numbers" you're talking about are the expected profits, not the expected growth factors. They are different things.
Expected profits are "absolute numbers" - you can add them. Expected growths are multipliers - you can multiply them.
This likely means that the "real leverage" player does worse than the fixed offsite investor in the much more common case where the player wins and loses more equally.
Shouldn't "real leverage" still do better in that scenario if the players lose slightly more than they win as expected due to house edge?
I kind of ran out of steam at that point. I can't imagine that "real leverage" is better than "offsite investing" in every case. Shouldn't there be a trade-off?
Back to the example:
A has 10 onsite and 90 offsite.
C has 10 onsite with 10x "real" leverage.
Suppose a whale plays for a long period with 50% chance of winning each bet. All bets are the maximum, aiming to win 1% of the bankroll. The payout when he wins is 1.98x (1% house edge), and he wins and loses the same amount of bets (as he is expected to do, long term). Let's call the effective bankroll "B".
50% of the time the player wins 1% of the bankroll: B/100. When this happens, A's effective bankroll is multiplied by 99/100, and C's is multiplied by 90/100.
The other 50% of the time the player loses his stake. He's aiming to profit by B/100, with a payout multiplier of 1.98x, so he's risking and losing B/98. When this happens, A's effective bankroll is multiplied by 99/98, and C's is multiplied by 108/98.
Since the whale wins and loses the same number of bets, we can pair these bets. Each pair consists of one win and one loss.
For each pair, A's effective bankroll is multiplied by 99/100 and 99/98, for a net growth factor of 99/100 * 99/98 = 9801/9800 ~= 1.0001x
And C's effective bankroll is multiplied by 90/100 and 108/98, for a net growth factor of 90/100 * 108/98 = 9720 / 9800 ~= 0.9918x
And so we see that my intuition was correct, and that "real" leverage is worse than this "offsite investment" thing. The "offsite investment" has a (small but) positive expected bankroll growth whereas the "real leverage" expects to lose almost 1% of the bankroll for every pair of (1 win + 1 lose) bets.
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)
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)
It doesn't make sense to sum those growth multipliers.
Obviously, and that is indeed the reason why I'm not summing them. I said "in absolute numbers" multiple times now. Anyway, I'm pretty sure my argument is correct, especially since the edge case trivially shows that it is indeed possible for a player to be -EV and +EBG.
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)
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)
When we talk about "growth", we're talking about multipliers, not deltas.
For example, if a player's bankroll grows from 10 to 11 while the house's bankroll shrinks from 10 to 9, the player's bankroll growth is 1.1x while the house's is 0.9x.
It doesn't make sense to sum those growth multipliers.
"Negative expected growth" means an expected multiplier of less than 1.
It's at least definitely possible for a player to be +EBG yet -EV, the edge case is simple. Suppose the casino bets 100% of its bankroll on each bet, then even though it may have +EV, at some point it's going to lose. So the player will have, with probability one, gained money and hence is at +EBG - though he may require a deep bankroll.
Yes, that's the angry whale with tons of money scenario with over aggressive kelly criterion applied. It was present in Bustabit for a big stretch there all while devans and RHavar profited in excess of a million dollars.
The thing is though that these models assume that there are no investments or divestments in between.
Because the whale is betting at a negative house edge, there should be opportunities for you, as an investor, to pull the rug and divest (not to be confused with deleveraging onsite/offsite) your earnings with profit. This then means that you're not investing anymore, but gambling at a positive house edge.
If, however, you keep your money locked in the investment forever, you make zero at 0EBG and lose it all at -EBG. This is one of the reasons that the predatory system which punishes investors for divesting is just plain wrong.
While taking commission, devans makes his highest profit when the bankroll is its highest; the higher the bankroll, the higher the max profit and amount of wagering can be. That's why it is dishonest and shameful to keep soliciting for a bigger bankroll and to try and pitch Bustabit as a stable investment (lie) with only positive expected bankroll growth (lie) at 1x kelly (lie).
By far, the easiest solution was to cap max profit per game/round at 1% (or 0.75% with commission) with no dilution. You'd think they'd figure it out by now. The excuse that it was to protect the players is absolute bullshit. It's a 1% house edge game strictly against the house with no bonuses at all.
It's at least definitely possible for a player to be +EBG yet -EV, the edge case is simple. Suppose the casino bets 100% of its bankroll on each bet, then even though it may have +EV, at some point it's going to lose. So the player will have, with probability one, gained money and hence is at +EBG - though he may require a deep bankroll.
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".
Do you know what a random variable is? Do you know what the expected value of a random variable is? I'm not talking about the expected value of the bet, I'm talking about the expected value of the bankroll growth.
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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