Forum
Virtual Table Boundaries
|
skrumgaer wrote
at 9:25 PM, Sunday May 4, 2008 EDT
Have you ever wondered what score is the best at which to start playing at a higher level table? For example, if by playing at the 100 level tables, you have advanced to a score over 500. Should you start playing at the 500 level tables immediately, or should you build a "cushion" over 500 before changing?
My answer is, according to calculations which I give below, is to change over immediately. The scoring of kdice is technically zero-sum, but since negative scores are reset to zero, the average score of players of zero skill should go as the square root of the number of games played (see random walk theory at Wikipedia). This is if there is only one level of table. But what if there are two levels of table, and the magnitude of score changes at the higher level table is b times the magnitude at the lower level table? If scores are distributed according to a normal distribution of mean mu and variance mu for players at the lower level table, the score at which the probabibility of having that score is the same for the lower level and the higher level table is the solution of the equation exp((x-mu)/mu)^2 = exp((x-bmu)/bmu)^2 the solution of which is x = 2mu/((b/(b+1)). Let us take the 500 level table, the middle level of the five levels, as our representative table. For the 2500 level table, where the value of b is 5 times that of the 500 level (I think. Nobody has been playing at 2.5k tables lately for me to check.), then the score at which you should switch to the 2500 level table would be exactly 2500. That is under the assumption that the mean score for the 500 level table is the midpoint of 2500 and 500 which is 1500. But if there were only two levels of table, 0 and 2500, then the lower table would have a mean closer to 1250 than 1500, which means that the score to switch at would be 2083. But you can't switch at 2083 because you have to have a minimum of 2500 to switch. Similar calculations can be made for the other levels of table. For each, the conclusion is that the lower limits (except for the zero limit table, of course) are set too high. There is too much tail of the probability distribution to your left when you reach the higher level table and you are too likely to be sent back to the lower level. Here are some rough calculations (estimates) based on means of the midpoint of each range of table and what its switchover point should be. 0 level table. Mean = 50 Switchover possible = 100 Better switchover point = 68 100 level table Mean = 300 Switchover possible = 500 Better switchover point = 428. 500 level table Mean = 1500 Switchover possible = 2500 Best switchover point = 2500 2500 level table Mean = 6250 Switchover possible = 10000 Better switchover point = 9680 Enjoy. |
Replies 1 - 9 of 9
|
lovekdicetodeath wrote
at 10:59 PM, Sunday May 4, 2008 EDT oh my....nice math.....but you are giving me a headache......
just play and have fun.....who cares about the score..... |
|
Pat Whalen wrote
at 2:21 AM, Monday May 5, 2008 EDT THANK YOU, i've been trying to tell people this sense i started playing, although i never explained it so precisely/confusingly. If you take out all the confusing math and put it simply it comes down to this: assuming you are going to loose when you move up to the next table, what is the difference between playing the 500s to build a cushion and then going up or switching over immediately and losing the first game and THEN playing the same games you would have played to build the cushion, to get back to the 2500s. The answer is nothing. So now if you add in the good chance that you will actually make points at the higher table, it becomes clear that you are taking no unnecessary risk in order to have a higher reward.
|
|
Shevar wrote
at 3:54 AM, Monday May 5, 2008 EDT i just tried it.
after playing a few 100s my score was at 502 finally.(took me damn long to reach 500 points) i sat down at a 500 and BAM, my score almost doubled. i played another and won again. now my score reads 1478. hence, math is truth. ps: we need a formula editor implemented in the forums |
|
phoneguy wrote
at 1:04 PM, Monday May 5, 2008 EDT you could have taken a shower instead of doing that complicated math. By the way Kdice is no longer a zero sum game. Don't know where you got that information.
|
|
|
skrumgaer wrote
at 2:02 PM, Monday May 5, 2008 EDT You are correct on that last, phoneguy. I have checked games at the zero, 100, and 500 level tables and they all net out to 36 points for place and 36 points for dom. So the average score would likely go as the number of games played instead of the square root of the number of games played. I will have to do the problem over.
|
|
|
skrumgaer wrote
at 7:48 PM, Monday May 5, 2008 EDT I have had my fingers debugged and did some re-counting on them and came up with some better figures and more observations.
If we consider the mean of the middle level table to be "true" = 1500, here are some better estimates of means and switchover points. 0 level table Mean = 30 Switchover possible = 100 Better switchover point = 93 100 level table Mean = 365 Switchover possible = 500 Better switchover point = 365 500 level table Mean = 1500 Switchover possible = 2500 Better switchover point = 2180 The net gain per table is 36 for place and 36 for dom at the 0, 100, 500, and 2500 level tables. When things average out, if you have no skill, it doesn't matter what level of table you play at, and your average gain per game would be 10.29. If you are better than average, like bomb, your gain per game will be better than 10.29. Bomb had an average gain of 58 points per game, which means he captured about 80% of the social surplus in all the games he was in. At the higher levels of table, the significance of dom decreases compared to place of finish. Thus, different players will do better at different levels of table. If you like farming, play at the lower level tables. If you are more into diplomacy, where the giving or taking of one land is important for change in place, play at the higher level tables. |
|
|
skrumgaer wrote
at 7:50 PM, Monday May 5, 2008 EDT For 100 level tables, make that
Mean = 139. |
|
wishbone wrote
at 10:02 AM, Tuesday May 6, 2008 EDT Good post skrum,
|
|
JDizzle787 wrote
at 9:28 PM, Tuesday May 6, 2008 EDT Skrum, You're crazy, in a good way. As far as opinion goes, even though this has almost no mathematical value, a cushion is relatively a good thing:
A) Take in account for worst-case scenario. You will lose a greater amount of points for 7th, even though you're not sure whether or not you will be subject to 7th place until you actually play. From patterns noticeable in gameplay, constant "bad luck" streaks (whether mathematically possible or not)do occur, and from a psychological stand point, you don't want to start a bad kdice day with a 5th- 7th place finish at a 500 table if you've got a score of 562. Does anyone else think there is a point where you should exclusively go to a specific table level at a certain point value? like 200 pts over 100, and stay there? I know several players don't care, but anyone have a set level? |
