variance in chinese poker

[FieryJustice]

So I have been playing $200/pt chinese high only with bonuses at rio for the last few days and I am down a happy 150 points...and that makes me super super sad, as I have spent a ton of time studying the program and getting pretty close to perfect at it. So...just how much is a "normal" downswing in the game? I assumed it was something like 100 points but being down 30k is just annoying. Any advice on this would be great.

[MarkGritter]

Time for some math abuse!

Attempt #1:

A random hand of CP has a mean value of 0. If we play without royalties, the actual score (heads-up) is usually -4, -2, +2, or +4. This gives us a (very crude) estimate of the variance as 10 points^2, or a standard deviation of about 3 points.

For 100 hands the standard deviation is 3 * sqrt(100) = 30 points
For 1000 hands the standard deviation is 3 * sqrt(1000) = about 95 points.

That means that 95% of the time you should expect to see a total between -190 and +190 points over 1000 hands (played heads-up.)

Attempt #2:

The number above seems a bit high. The reason is that not all four outcomes are equally likely. Scooping or being scooped is less common than +/- 2. (There are other problems with the estimate above--- it seems likely that the hand values are not evenly distributed around the mean--- but those are probably second-order effects.)

I don't know how often scoops occur relative to +/- 2, but we can look at some possibilities:

40% scoops: std deviation 2.97 points, 95% interval at 1000 hands = +/- 188
20% scoops: std deviation 2.53 points, 95% interval at 1000 hands = +/- 160
10% scoops: std deviation 2.28 points, 95% interval at 1000 hands = +/- 144

Attempt #3:

I don't have any CP high numbers, but I can calculate the mean value for samples of CP2-7 hands.

I took five 1000 hand samples:

+2
-146
-6
-47
+57
-106
-4

The sample standard deviation is about 70, so the 95% interval is +/- 140 points.

(The mix appears to be about 8-10% scoops, 90% +/-2 or other values. So there is a pretty good match between the thoretical and observed values.)

A couple notes:

If the mean value is not zero then the variance should be a little less (you will have more +'s than -'s, or vice versa).

With royalties the variance should be a bit more. I don't know how to go about estimating that.

I don't know what playing 4-handed instead of 2-handed does to the variance. I think it probably doesn't count as just playing 3x as many hands (i.e, there is probably some correlation) but I don't know how to take that into account either.

[FieryJustice]

Cool...thanks for this. I guess I will just play more and try to run better. [img]/images/graemlins/smile.gif[/img]

[monroe]

Just an FYI: I've played 822 hands of heads-up high CP with a friend. I've swept 99 of those hands, which is 12%. I should note that of those 822 hands, 116 of them were played with only 12 cards (a two-card front instead of a three-card front).

I wouldn't be surprised if 10% is the standard sweep% against an average player.