"A random walk" help

[RS]

Based on EV and SD, how would I go about simming something like 10k rounds (in blackjack)? I'm not talking about graphing the EV, +/- SD, or any of that. I'm interested in making a graph (several graphs), and looking at it to see the path along the way, NOT: "EV is $28,581, 66% of the time you'll be between +$2,580 and +$54,582".


Is there a general formula for this?



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For example, if I were doing this in VP, I would look up the hand distribution (royal flush, straight flush, four of a kind....two pair, high pair), use an RNG that'll be mapped to a specific hand, then the BR and W/L would change by that hand's payout amount. Do that for some X number of hands. Then graph the results.

[Norm]

I could be wrong, but it seems to me that due to the fact the count has persistence, there must exist skewness. Since the count is periodically reset, there may also exist kurtosis. If so, unlike VP, SD and EV alone would not provide a completely accurate set of charts. Consider charting using a Martingale. The chart wouldn't look anything like a counter or flat-bettor. Don would have a better feel if I'm just being silly. The charts created by CVData use simulation instead of calculation.

There is a thread here on a hidden forum where this process was discussed by Auston, Cacarulo, Don, Grosjean, and myself. But, I don't think I can make it visible as it includes code and was used to improve proprietary software.

Sorry this isn't helpful.

[DSchles]

Get John Auston's genial "Random Walk" that I used for Chapter 12 of BJA3.

Don

[DSchles]

I might add: one of the least discussed chapters in BJA3, and one of my favorites. Never got the attention it should have. The Random Walk feature of John's software is addictive. And, to my knowledge, there's nothing like it anywhere.

Don

[RS]

Norm - that makes sense, re: Martingale vs flat-bettor vs counter, as well as the count having persistence / state. But for the case where you're looking at a chunk of a session (say 100 or 200 rounds), would that persistence still have an impact? I understand absolutely - round to round, it'll have an impact....but over a period of a hundred or so rounds?

Don - Thanks. Searched for that thinking it was a book - got nothing. But I did find the BJRM (BlackJack Risk Manager) software. Is this what you're talking about?


Although I'm not great at all this math stuff, especially with blackjack (because it's a funky game, not something simple like VP)....to me it seems like you should be able to do something like get a random number to represent some number of SDs, then add/subtract that # of SD's from the 100-round EV, and plot it on a graph. Then you come up with a graph that is the sum/combination of a bunch of 100-round sessions.



To add: I think this is a very important aspect when looking at a game to see if it's "worth it" / being able to stomach the volatility. I frequently do this kind of stuff for VP (mail / promotions), and it really brings to light what kind of results can be expected. Yes, you can look at numbers like $250/hour EV and $1400/hour SD...or a game with an edge of 3.5% with a variance of 25....or whatever it may be -- you can get some sort of an idea how good/bad you can run, but it's in no way comparable to looking at a graph and seeing exactly what those numbers translate to.

[Norm]

The CVData Results Log shows charts of the ups and downs during the first few hundred thousand hands of a sim. You can move through blocks of rounds, and/or group rounds while viewing charts.


And yes, Don was talking about BJRM.