I just don't see the point of implementing the simple fractional kelly system when you can get the same thing from just investing less.
You don't get the same thing by investing less. There was an example earlier: A: invest 500 at 1% or B: 125 at 0.25%. You'd think they were the same, but they're not. After a few thousand losses, A has lost nearly 500 coins and B has lost nearly 125 coins. That's not the same at all... I don't see anyone screaming for 1% kelly anymore. Just leave it at 0.5%, the variance is plenty. I just don't get how after bidding for 12 hrs straight 1.6M bitcoins between 3 whales (mostly coming from 1), we end yet another session down significantly. It seems the edge is too small to overcome the variance at such high bids. I cannot explain it, but the results continue to confound logic and be 3+ SDs off from the expected results no one is screaming because we thought doog was implementing variable max bet. No need to argue over what is "correct" - let people choose on their own. |
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Question regarding just-dice house edge
I'm trying to get a better understanding of the results of different investment strategies in j-d. Being the lazy person that I am, I chose to simulate first, before I try to solve anything analytically. But first, let me know if I understood the house edge on j-d correctly:
It is not an edge on the probabilities of the "dice throw" itself (like, say, in Roulette), but it is a reduced payout in case the player wins, right?
Example:
Say there is exactly one investor, who put in 100 btc, at 1% maxbet. A player places a maximum size bet of 1 btc.
In case the players loses, the investor's new balance is:
old_balance * (1 + 0.01) = 101 btc
In case the player wins, the investors new balance is:
old_balance * (1 - (0.01 * 0.99)) = 99.01,
where the factor 0.99 represents the house edge of 1%.
Yes? No?
There's no max bet. It's max profit. Right. But let's say we take the usual 50% bet, then max bet = max profit (ignoring for a moment house edge) In that case, did I get calculation of house edge right? No. If an investors has 100 BTC in an account and we're at full kelly (1%), a single 2x payout bet would yield +/- 1 BTC. The reason why is that a 2x bet is the range > 50.5 or < 49.5. The odds are different in the roll (see the log I posted above for an example). |
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it is an edge on the probabilities of the dice throw.
Eg: gambler wins 2x if RNG picks a number > 50.5 or < 49.5 (roll hi or roll low). So if gamblers hits roll high, house wins from 0-50.5, player wins from 50.5-100
Where do you get this from? The j-d FAQ seems to imply otherwise. user: berathea (161188) date: 2013-09-29 18:39:30 betid: 144345199 lucky: 91.4117 target: >50.4999 bet: 170.79869440 payout: 2x profit: +170.79869439 Two ways of looking at it: 1) 2x payout means you roll > 50.5 2) rolling > 50 means 1.98x payout both are true, FAQ points out (2), but the bet log has lots of (1), as shown above. |
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Question regarding just-dice house edge
I'm trying to get a better understanding of the results of different investment strategies in j-d. Being the lazy person that I am, I chose to simulate first, before I try to solve anything analytically. But first, let me know if I understood the house edge on j-d correctly:
It is not an edge on the probabilities of the "dice throw" itself (like, say, in Roulette), but it is a reduced payout in case the player wins, right?
Example:
Say there is exactly one investor, who put in 100 btc, at 1% maxbet. A player places a maximum size bet of 1 btc.
In case the players loses, the investor's new balance is:
old_balance * (1 + 0.01) = 101 btc
In case the player wins, the investors new balance is:
old_balance * (1 - (0.01 * 0.99)) = 99.01,
where the factor 0.99 represents the house edge of 1%.
Yes? No?
it is an edge on the probabilities of the dice throw. Eg: gambler wins 2x if RNG picks a number > 50.5 or < 49.5 (roll hi or roll low). So if gamblers hits roll high, house wins from 0-50.5, player wins from 50.5-100 |
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So, I have this awesome idea.
Someone should turn just-dice into a stock. So people can trade it on bitfunder or something. Now you ask why wouldn't you just do a regular stock? That's because now people can buy options on the stock. That would be cool.
A stock would be based off revenue from commissions and ads - that is a much better deal than being an investor. No it would be a third party who invested in just-dice. Doog doesn't need capital, so he doesn't need to sell stocks. You're proposing a pass through. Go ahead and set one up, offer an IPO, invest it all in JD, and distribute dividends above some bankroll if it is available a given week. Seems kind of silly to me since you could just directly invest in JD - but you're right, you want to setup a JD derivative and that needs some underlying security. With almost 3.5M wagered and the site at a loss, I think he looking for a way to short J-D there's an easy way to do that, gamble instead of invest  |
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So, I have this awesome idea.
Someone should turn just-dice into a stock. So people can trade it on bitfunder or something. Now you ask why wouldn't you just do a regular stock? That's because now people can buy options on the stock. That would be cool.
A stock would be based off revenue from commissions and ads - that is a much better deal than being an investor. No it would be a third party who invested in just-dice. Doog doesn't need capital, so he doesn't need to sell stocks. You're proposing a pass through. Go ahead and set one up, offer an IPO, invest it all in JD, and distribute dividends above some bankroll if it is available a given week. Seems kind of silly to me since you could just directly invest in JD - but you're right, you want to setup a JD derivative and that needs some underlying security. |
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Wow people retracted 10K bitcoins from their investments in a few hours.
em, we went from +5k to -6k, thats a 11k wipe in equity. it appears people are staying in.. I don't think the profit affects the equity? profit effects bankroll, directly and linearly |
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3 player currently making 100btc+ bets, holy hell...
Don;t you wish the max profit was 1% so we could have even higher variance? Mechs, you amaze me. You do realize that the more players we have doing near max profit bets the lesser variance we have, right? And YES, I'd like to have full Kelly again, as 99% of investors who understand how math works. No way, broseph. We won when we were at 1/4 Kelly and lost since we've been at 1/2 Kelly so LDO 1e-12 Kelly max bet will produce unlimited profits LOL :-P The smaller the max bet, the more reliable the profits will converge on predicted value due to less variance - with the assumption that the total amount wagered remains unchanged. Of course, the total amount wagered would likely be less with a lower max profit so that assumption is likely false It a matter of variance tolerance and how much vaiance the bankroll and investors can support. We are seeing a lot of divestments now with big bids in. Is that fair to investors who stay invested, especially those who invest & forget and not happen to be online when whales come on? Yes, it is fair because the rules didn't change mid game. Investors know what variance and expected value is, and they should only be investing what they are comfortable with or take action when site action moves in a direction they are not comfortable with. I guess we have different definitions of "fair" - to me it means I get exactly what I agreed to. |
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Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)
to some people, it is mathematical rational to not operate at full kelly. People are optimizing their utility, not their profit. To some investors, variance decreases their overall utility - therefore it is rational for them to want to exchange decrease in profit for decrease in volatility. It's sub-optimal for profit, but optimal for maximizing their own utility. It is irritation only if they declare their strategy to be maximum growth then ask for non-optimal max bets. Excuse me, but I need to ask: so why these people invested in a casino that has a 1% house edge, plus an optimal kelly (1%) max profit? Complaining about variance knowing those parameters is like complaining because at 3AM is dark. It's possible that JD is the closest thing to the risk/reward they want and are asking for it to be changed closer to how they'd like it. My stance: Doog made and is running an awesome site. Investors disagree over the risk profile they'd like the site to take, and it is rational to have that discussion. User level max bet implementation will allow for everyone to play with the risk/reward tolerance they are comfortable with. |
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Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)
to some people, it is mathematical rational to not operate at full kelly. People are optimizing their utility, not their profit. To some investors, variance decreases their overall utility - therefore it is rational for them to want to exchange decrease in profit for decrease in volatility. It's sub-optimal for profit, but optimal for maximizing their own utility. It is irritation only if they declare their strategy to be maximum growth then ask for non-optimal max bets. |
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why are people so obsessed with tiers? why can't it be continuous?
I think if you walked through the algorithm I proposed, you could see very clearly why having a substantial amount of tiers would add significantly to the computations. Every step down in the tier requires a new reiteration across the users in every tier above it. that's my point: don't use any tiers, don't use reiteration since it increases complexity, use a simpler algorithm... right now % of total bankroll is computed for each player. Winnings are assigned proportional to % of bankroll. Do the same exact thing, but with variable max bets... Example: Right now A invests 100 BTC, B invests 50 BTC. 1) Site keeps track of total invested (100=A, 50=B) 2) Site calculates total bankroll = 150 (sum of deposits) 3) Site keeps track that A gets 2/3 of winnings/loss (invest/bankroll), B gets 1/3 (invest/bankroll) Proposed: A invests 100 BTC at 0.96% max bet, B invests 50 BTC at 0.77% max bet 1) Site keeps track of total "invested" (A=100*.0096=0.96, B=0.385) 2) site calculates maximum bet = 1.345 (sum of "invested") 3) Site keeps track that A gets 71% of winnings/loss ("invested"/maximum bet), B gets 29% ("invested"/maximum bet) no tiers, and it uses the same calculations and computations as currently being done - but "invested" (in quotes) is now what is available for maximum bet. |
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This is how you do a sliding scale:
1.) Max return is whatever the highest investor(s) is willing to lose. Doesn't matter if it's percentage or a literal number.
2.) If a gambler loses the bet, divide the sum by the number of "tiers" that intersect it.
Example:
100 btc max return, and 100 btc lost by the gambler.
1% tier = 50btc.
.5% tier = 25btc.
.25% tier = 25btc.
Note: Tiers do not necessarily need to be percentages.
...
why are people so obsessed with tiers? why can't it be continuous? The counter argument was that not using tiers would be computationally intensive. I believe it is as difficult as the current implimentation and introducing tiers is computationally intensive (and confusing to investors/players). Right now JD keeps track of a player's fraction of the bankroll and distributes accordingly. Instead, with "set your own max bet percentage," JD needs to keep track of the player's fraction of the max bet and distribute accordingly. No need to introduce any other changes, no need for delays nor fractional reserve... everything stays the same as it is, no additional complicated rules. Players get to tune their variance and return to maximize their own utility, gamblers have a high maximum bet in a very similar fashion as before with the same edge. |
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To use a very simple example:
Investor A has 10 BTC, sets risk at 0.25%
Investor B has 10 BTC, sets risk at 1%
Investor C has 10 BTC, sets risk at 2%
House roll:
30 <= 0.25%
20 >0.25% and <= 1%
10 >1% <= 2%
House roll for all bets <0.25% is 30, making the max bet 0.075
For bets between 0.25% and 1%, the house roll is 30 for the first 0.075, and then 20 for the rest: so the max bet is 0.225.
For bets > 1%, the roll is 30 for the first 0.25%, 20 for the next 0.75%, and 10 for the final 1%: total of 0.325
So a better comes in and loses a 0.075 bet:
Investor A gets 0.025
Investor B gets 0.025
Investor C gets 0.025
On the other hand, a better comes in and loses a 0.325 bet:
Investor A gets 0.025
Investor B gets 0.1
Investor C gets 0.2
Edit - added 0.25% bet case.
this can be done without tiers, the only change to the ui is a "max % loss per single bet" field. the example you presented fits this model: https://bitcointalk.org/index.php?topic=242962.msg3234742#msg3234742 |
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This was said before, but it'd actually be easy to build this max bet system mathematically, and only a little more difficult UI-wise, but not significantly more difficult than the current UI. The biggest UI challenge would be the expression of the size of the house bankroll, as it would have to be tiered, which would be ugly.
If we move to this model, I would eventually like to see a two basket approach like Betterment, where you can invest a proportion of your investment at a lower level and a smaller proportion of your investment at a (much) higher level. More coding, but still not much more work. The site already has two "baskets;" a gambling wallet and an investment. This would be just breaking the investment number up one more time.
why does it have to be tiered? the proposal I laid out (and the one I thought we were discussing) works exactly the way the current site works with no change to UI (except a field for investors to input their maximum risk per bet) and is not tiered - you can choose whatever risk level you want and it just works. |
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Doog proposed a solution: make max bet a market. You choose what your tolerance is and the site will adjust. Mech could have set his to 0.25%, I would have kept it at 1%, every investor votes with their wallet. From there you get the max bet and the proportion to be paid out to each investor.
No controversy, no arbitrarily choosing numbers. House edge can remain fixed so that from the player's point of view, nothing changes or is unfair.
The more I think about this, the more I like it. This is doable. It would be cool. Big work for Doog however. Only way for the house to limit min/max spreads is to put each user in a "time out" in whatever min/max bracket they're in. But then they'd just open a 2nd account and both each bracket with a different bot. min/max spreads is the reason physical casinos don't get hammered like this. It's also because they can keep track of physical humans.  I think you're over thinking it: every users sets their percentage on a scale from 0-100% (someone may want to go crazy and make it 100%, literally gambling). Maximum bet is continuously calculated, like it currently is, but change the cacluation to: sum of each user (user bankroll * user risk percentage) each win/loss is attributed to each user, exactly like it is now, but with different calculation: percentage of gain/loss = (user bankroll * user risk percentage) / site max bet really easy to implement, fits right in to the existing calculations and infrastructure |
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I want to have a no-limit casino to invest , like you can bet all the investment , which was like 30k or something , be able to bet 30k than. Thats more fun , casinos should take some courage to run , even if its not your money to run , even better if its like that.
Could not agree more. The fearful investors are messing this up for everyone. If there's no/little chance for the house to lose, then there's little/no chance for the players to win, and the whole thing loses its luster. For more on Mechs and his discussions (pleading with Doog) on im yesterday. Doog should release this chat as he has done with Naks in the past. Doog proposed a solution: make max bet a market. You choose what your tolerance is and the site will adjust. Mech could have set his to 0.25%, I would have kept it at 1%, every investor votes with their wallet. From there you get the max bet and the proportion to be paid out to each investor. No controversy, no arbitrarily choosing numbers. House edge can remain fixed so that from the player's point of view, nothing changes or is unfair. Either way, I think doog made a brilliant site and I'm happy to participate in the experiment. |
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Also increasing house edge for big bet is completely laughable, even Las-Vegas would not think of doing such a thing. Why punish a high-roller for giving more action and volume? In Las-Vegas they would actually lower their edge to get those players.
Does any Vegas casino allow a player to win 1% of the casino's bankroll on a single hand? Land casinos actually have insurance companies insure their jackpots, so it is possible to win a small percentage of the bankroll on a single roll, but the casino doesn't pay out. (is there some way you could do this? Probably best to reduce variance with lower kelly since your minimum bet size changes with kelly). |
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My initial plan was to allow each investor to choose their own house edge and risk level and have them form a market like on an exchange, so the player gets matched by whichever investor(s) are offering the lowest house edge(s). This would result in competition between investors to get gambler action and cause the edge to be the lowest available anywhere. I wonder how such an idea would go down. It would probably result in a few crazy investors offering very low edges, and leave the sensible investors getting matched by none but the biggest bets. (Like how when you ask for more than the current market rate on MtGox when selling coins, you only get matched by the big buy orders).
that would be cool, I love the idea of a market for house edge... You could also do a market for variance: Have a slider for people to choose what their own personal "maximum bet" is (in percentage of bankroll). All of that gets pooled together to be the site's max bet, and returns are proportional to that. Someone that wants low variance can choose 0.1%, someone more aggressive can choose 1% (and someone that wants to really gamble can go > house edge%). This is a way to have investors have a decentralized vote on what the minimum bet should be. Investors would be basically running their own dice site! Investors set their personal edge AND the variance! |
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Think doog has to maximize the bets, 10-20 BTC, or sg else. If he won't do that, the site will be destroyed in a week by Nakowa....
We should coin the term "investors fallacy." The mathematical correct thing to do to push profit in your favor is to pump the house edge. Variance will flicker around a quicker growing profit line. Minimum bet can be raised to full Kelly, or kept at fractional Kelly. |
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So what do I do? Continue to let the investors take these horrific losses?
Barring cheating, it is what it is. JD is a high-risk gambling site. Variance increases when someone comes by with a bigger bankroll than JD. I'm down 20%, but I know what I'm getting myself into and that this could happen. Keep on running the business, improve features - try to attract more whales. I'll take my shots. |
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