Topic: Satoshi Dice -- Statistical Analysis - page 31. (Read 192914 times)

It looks fine, as long as you have the win/lose probabilities right.

You can also calculate the expected number of rolls before n losses in a row:


I've seen a few methods of proving this. The one I have to hand uses Markov chains and is a bit dense, and I can't find the other which is more inuitive to follow. If I find it I'll post it.

Hi,

I got the latest numbers from dooglus post and tried the theoretical formula for consecutive losses in a row and came up with this.

bets     p-win   q-lose  loss-row
604294   0.5     0.5     18.20489587
1118230  0.48828 0.51172 19.71766168
244037   0.36621 0.63379 24.99911792
243386   0.24414 0.75586 39.27274907
94075    0.18311 0.81689 48.22841691
182495   0.12207 0.87793 76.89902593

So, those playing the 50% game can expect to lose 18 or 19 times in a row if they played that game since the beginning. Those playing the other games can expect to lose much more.


Did I do this correctly?

Those colourful violin plots are very nice.   

Meanwhile, back to the regular ugly graphs...

ggplot doesn't do multiple axes. I read (I think) that the devs planned on support for multiple axes when the axes scale linearly to each other, but they don't plan on the sort of multiple axes you're thinking of. I ccould annotate the chart with the actual numbers, but that's not very pretty.

So, number of bets as well as volume of betting? I have a think about it. I hadn't considered that, although it's might be interesting data to have.

If the 2-3 month cycles are valid and hold, May-June ought to be the start of a very active period.

Amazing charts OoC, does GGplot let you do multiple axes? It would be good to overlay a line showing total number of bets per month, or perhaps median number per day as well as max/day and min/day for each month.

I played around and got some quite beautiful tile plots and contour plots, but they didn't really help show bet size of volume trends. Then I realised that all I had to do was use the proportional violin plots and use colour as a guide to the volume. I hope this works for you. Please don't tell me you're colour blind - I didn't use the colour blind palette.

The two below just use different colour schema.

I plotted your request below - normalising to the volume of bets under 50btc (as an arbitrary cut off). I also plotted all bets before December, to make those trends a bit more obvious, too. Tbh, I should have written "the size and volume of bets in December 2012, January 2013 and February 2013 have increased compared to the previous months". Even so, it's not obvious from the plots.

I'm working on something similar to the "percentile" plots I did that will hopefully show this sort of information in a more intuitive and cntinuous way than either the violin - er scary hypodermic needle - plots or the percentile plots. Hopefully I'll be able to post it tonight.

Hi, Sorry for adding to the stress. I guess you just pick one way of ordering it, and use that for consistency. Actually, a real world example of a 50% game had 26 losses in a row, in a casino.

If you're bored ... you can do this. When you got more bored, you can also do the different ways of ordering.

I don't know if it will tell us anything useful, but I think it will be interesting. And the minute you post your analysis, all the gamblers who are reading this thread will suddenly start betting a little bit more, thinking that they can attempt 21 consecutive attempts to martinegale from 0.01 to 500. (I just might do it, hehe.)

If you're being grouchy, let me know what I need to download and I will try to do this. (Or at least someone else will, so you have less stress.)

Unfortunately, I'm on a crappy OS machine (windows), so I don't know if it's even possible.

It seems to be as expected since the analysis is done by block - a chart of betting would've levelled off for ~6 hours or so, but payouts would follow the consistent climb. Transactions still had to be processed into the blockchain block by block.

I think my graph only shows payouts though.  It ignores bets until they have been paid out.

They didnt shut off betting, just payouts afaik.

I was expecting to see a dead flat spot due to yesterday's temporary hard fork.  Any idea why I don't?

Dabs it's just random probabilities. You can do it by your own.

Hi Dabs.

Sorry, I was stressed out with other business yesterday when you posted about this.

One problem with your request is that there's not really a definitive ordering on the bets.  Do we count the time the bet transaction was seen by some random host on the network?  Or the timestamp on the block it got into?  Or the depth of the block?  (Blocks aren't always in order of timestamp).  Or do we count the order that the bets were paid out?

There are lots of different ways of ordering the bets, which will change the longest sequence of losses.

Another problem, and what puts me off from looking into this, is "who cares".  Are you wanting the information to check whether the dice rolls are random?  ie. "we would expect to see a chain of 10 losses but the longest chain is 20 so SDICE is cheating"?  Because other than that I don't really see the point.  Runs of good and bad luck happen, due to the random nature of the dice rolls.  Suppose I go through the blockchain and find that once there were 21 losses on the 50% game in a row, given some arbitrary ordering of the bets.  Then what?

I guess I'll do this when I'm bored, but I don't expect it to tell us anything very useful or interesting.  Maybe I'm just being grouchy though.  That happens too. 

Thanks for the tip organofcorti - that's very kind of you. 

Hi, I understand the theoretical part (on consecutive wins or losses). What I'm looking for is actual historical data, and I think you guys already have it. (or the block chain has it.) It just needs to be sorted out. I mean, Mr. Dooglus is already posting statistics of wins vs lose. Like, for the under 48000 I can see that there have been 336630 bets of which 246989 have won and 89013 have lost. I am just curious as to how many of those losses were consecutive and what is the longest chain.

Then you can plot the theoretical formula beside the actual results to compare the "should be" and the "what actually happened already", similar to the comparison of the odds and how each 1dice has actually performed.

The first of the pair of charts actually does that - sorry if I didn't make that clear.

Got some ideas, will get something up tomorrow. I could be wrong - I might have been letting the percentile charts guide me a bit.

That's really kind from you. Respect!

What about my request? Do you think it would be more revelant to normalize with the higest month volume? It would be easier to spot the trends month to month, I think.

Thanks! Much appreciated.

It's dooglus' data and he does much more work than I do so I've passed half onto him.