[UTILITY] SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)
11-28-2016
, 09:37 PM
Maybe you could add an average bounty of 8.333% (25%/3) to each place of the prize pool distribution, as shown below. (Then save the settings so you can easily reload them for future use.) I can't say precisely how accurate that would be. An alternative would be to add the entire 25% bounty to 1st place. Perhaps bunching the prize pool like that would show closer to a worst-case scenario in terms of swings.
(Note that 4th place is awarded for the top tier in SNG Hero, but that is not represented in this simulation setup. I think the impact should be small).
01-31-2017
, 06:54 AM
Hi guys 
First of all, wanted to thank Max Cut for such a great work. I’m very grateful for this program, it’s very useful. Also wanted to thank coon74 for his posts, seems to be a very brilliant mathematical mind. Read some parts of this thread and understood a bit better the whole thing.
Wanted to talk about standard deviation (WARNING: BIG WALL, no summary). Afaik it seems that Max/**** made some crafted approximations, but it’s something still far to be calculated in an easy, fast and precise way. I’ve read you say we want to know standard deviation of luck-adjusted chips won / game. I would rather like to know standard deviation in buy-ins/game or buy-ins/100 games, since gives you an immediate idea of how big variance will be. Also because this is the way to compare it to std dev. in cash games.
I have seen too that there is a “standard deviation” box at Swong Sim visualizer, I guess you have to make a guess here¿? And I’ve also seen in some posts in this thread, that in an old version of the program it was calculated “mean deviation”. Mean deviation it’s ok, but it’s not so useful as standard deviation because it doesn’t get bigger when samples are more spread out, so std dev. would give us a better approximation of what should we expect.
We know that in cash games (let me know if you need some graphs for explanation of what I want to say), standard deviation responds to a gauss curve in a frequency/winrate graph, whose vertex is our EV. Moreover, we know 1 standard deviation is the maximum difference you will have with your EV during 68% of the time (that means 34% max to either negative/positive side). And 2 std dev is the maximum difference you will have with your EV 95% of the time.
What about spins? First consideration is that a graph frequency/winrate is not a gauss curve anymore. So first question would be: is regular std dev. useful for measure variance in this case? Maybe we should use a “standard spin deviation” stat. A graph would look as a sloping gauss curve on the left side of the vertex, and it will be a very flat gauss curve on the right side since you can get very big winnings but not very big losses (compared to winnings). Another important point here, is that the vertex of the curve is not our EV anymore, but something a little bit lower. That means our EV point would bet a little right from the vertex; and also that the “most frequent spot” is not getting our EV as it happens in cash, but getting what I would call “Real Spin EV” (RSEV). The bigger the prizes or its frequency are, the bigger the distance between RSEV and EV will be. Also the more games you play, distance gets lower in relative terms, and bigger in absolute terms.
Since the graph is not a symmetric curve anymore, I think regular std dev. is not specific enough (even that it’s going to be necessary to know it if we want to compare it with cash games). I consider it would be better to calculate 2 kind of std deviations: the “Negative Standard Spin Deviation” (will call it NSSD), and the “Positive Standard Spin Deviation” (will call it PSSD), being of course the last one much more bigger than the first one. Obviously these std dev. will have the RSEV point as a reference, not the EV point. A result example would be something like: “For 3.000 games you have a PSSD of 800 buyins and a NSSD of 260. You have a 30% of getting PSSD and a 38% of getting NSSD from your EV point, and you have a 34% each side from RSEV point. Your RSEV will be 40 buyins lower than your EV”. Ofc I’m inventing buy-ins numbers, but I guess it shows what I mean.
Also, although is not so specific, we could calculate usual Standard Deviation. Its formula is the result of calculating the square root of: sum of squares of each difference from the sample with the mean divided by the number of samples. Taking into account that the mean is RSEV, not EV. This would give us a good idea of how big variance is compared to cash or other games.
I think it shouldn’t be difficult to implement in Swong Sim these calculations with every sample and get some numbers.
Thank you for reading
First of all, wanted to thank Max Cut for such a great work. I’m very grateful for this program, it’s very useful. Also wanted to thank coon74 for his posts, seems to be a very brilliant mathematical mind. Read some parts of this thread and understood a bit better the whole thing. Wanted to talk about standard deviation (WARNING: BIG WALL, no summary). Afaik it seems that Max/**** made some crafted approximations, but it’s something still far to be calculated in an easy, fast and precise way. I’ve read you say we want to know standard deviation of luck-adjusted chips won / game. I would rather like to know standard deviation in buy-ins/game or buy-ins/100 games, since gives you an immediate idea of how big variance will be. Also because this is the way to compare it to std dev. in cash games.
I have seen too that there is a “standard deviation” box at Swong Sim visualizer, I guess you have to make a guess here¿? And I’ve also seen in some posts in this thread, that in an old version of the program it was calculated “mean deviation”. Mean deviation it’s ok, but it’s not so useful as standard deviation because it doesn’t get bigger when samples are more spread out, so std dev. would give us a better approximation of what should we expect.
We know that in cash games (let me know if you need some graphs for explanation of what I want to say), standard deviation responds to a gauss curve in a frequency/winrate graph, whose vertex is our EV. Moreover, we know 1 standard deviation is the maximum difference you will have with your EV during 68% of the time (that means 34% max to either negative/positive side). And 2 std dev is the maximum difference you will have with your EV 95% of the time.
What about spins? First consideration is that a graph frequency/winrate is not a gauss curve anymore. So first question would be: is regular std dev. useful for measure variance in this case? Maybe we should use a “standard spin deviation” stat. A graph would look as a sloping gauss curve on the left side of the vertex, and it will be a very flat gauss curve on the right side since you can get very big winnings but not very big losses (compared to winnings). Another important point here, is that the vertex of the curve is not our EV anymore, but something a little bit lower. That means our EV point would bet a little right from the vertex; and also that the “most frequent spot” is not getting our EV as it happens in cash, but getting what I would call “Real Spin EV” (RSEV). The bigger the prizes or its frequency are, the bigger the distance between RSEV and EV will be. Also the more games you play, distance gets lower in relative terms, and bigger in absolute terms.
Since the graph is not a symmetric curve anymore, I think regular std dev. is not specific enough (even that it’s going to be necessary to know it if we want to compare it with cash games). I consider it would be better to calculate 2 kind of std deviations: the “Negative Standard Spin Deviation” (will call it NSSD), and the “Positive Standard Spin Deviation” (will call it PSSD), being of course the last one much more bigger than the first one. Obviously these std dev. will have the RSEV point as a reference, not the EV point. A result example would be something like: “For 3.000 games you have a PSSD of 800 buyins and a NSSD of 260. You have a 30% of getting PSSD and a 38% of getting NSSD from your EV point, and you have a 34% each side from RSEV point. Your RSEV will be 40 buyins lower than your EV”. Ofc I’m inventing buy-ins numbers, but I guess it shows what I mean.
Also, although is not so specific, we could calculate usual Standard Deviation. Its formula is the result of calculating the square root of: sum of squares of each difference from the sample with the mean divided by the number of samples. Taking into account that the mean is RSEV, not EV. This would give us a good idea of how big variance is compared to cash or other games.
I think it shouldn’t be difficult to implement in Swong Sim these calculations with every sample and get some numbers.
Thank you for reading
02-02-2017
, 12:47 PM
Quote:
Hi guys First of all, wanted to thank Max Cut for such a great work. I’m very grateful for this program, it’s very useful. Also wanted to thank coon74 for his posts, seems to be a very brilliant mathematical mind. Read some parts of this thread and understood a bit better the whole thing.
Wanted to talk about standard deviation (WARNING: BIG WALL, no summary). Afaik it seems that Max/**** made some crafted approximations, but it’s something still far to be calculated in an easy, fast and precise way. I’ve read you say we want to know standard deviation of luck-adjusted chips won / game. I would rather like to know standard deviation in buy-ins/game or buy-ins/100 games, since gives you an immediate idea of how big variance will be. Also because this is the way to compare it to std dev. in cash games.
I have seen too that there is a “standard deviation” box at Swong Sim visualizer, I guess you have to make a guess here¿? And I’ve also seen in some posts in this thread, that in an old version of the program it was calculated “mean deviation”. Mean deviation it’s ok, but it’s not so useful as standard deviation because it doesn’t get bigger when samples are more spread out, so std dev. would give us a better approximation of what should we expect.
We know that in cash games (let me know if you need some graphs for explanation of what I want to say), standard deviation responds to a gauss curve in a frequency/winrate graph, whose vertex is our EV. Moreover, we know 1 standard deviation is the maximum difference you will have with your EV during 68% of the time (that means 34% max to either negative/positive side). And 2 std dev is the maximum difference you will have with your EV 95% of the time.
What about spins? First consideration is that a graph frequency/winrate is not a gauss curve anymore. So first question would be: is regular std dev. useful for measure variance in this case? Maybe we should use a “standard spin deviation” stat. A graph would look as a sloping gauss curve on the left side of the vertex, and it will be a very flat gauss curve on the right side since you can get very big winnings but not very big losses (compared to winnings). Another important point here, is that the vertex of the curve is not our EV anymore, but something a little bit lower. That means our EV point would bet a little right from the vertex; and also that the “most frequent spot” is not getting our EV as it happens in cash, but getting what I would call “Real Spin EV” (RSEV). The bigger the prizes or its frequency are, the bigger the distance between RSEV and EV will be. Also the more games you play, distance gets lower in relative terms, and bigger in absolute terms.
Since the graph is not a symmetric curve anymore, I think regular std dev. is not specific enough (even that it’s going to be necessary to know it if we want to compare it with cash games). I consider it would be better to calculate 2 kind of std deviations: the “Negative Standard Spin Deviation” (will call it NSSD), and the “Positive Standard Spin Deviation” (will call it PSSD), being of course the last one much more bigger than the first one. Obviously these std dev. will have the RSEV point as a reference, not the EV point. A result example would be something like: “For 3.000 games you have a PSSD of 800 buyins and a NSSD of 260. You have a 30% of getting PSSD and a 38% of getting NSSD from your EV point, and you have a 34% each side from RSEV point. Your RSEV will be 40 buyins lower than your EV”. Ofc I’m inventing buy-ins numbers, but I guess it shows what I mean.
Also, although is not so specific, we could calculate usual Standard Deviation. Its formula is the result of calculating the square root of: sum of squares of each difference from the sample with the mean divided by the number of samples. Taking into account that the mean is RSEV, not EV. This would give us a good idea of how big variance is compared to cash or other games.
I think it shouldn’t be difficult to implement in Swong Sim these calculations with every sample and get some numbers.
Thank you for reading
First of all, wanted to thank Max Cut for such a great work. I’m very grateful for this program, it’s very useful. Also wanted to thank coon74 for his posts, seems to be a very brilliant mathematical mind. Read some parts of this thread and understood a bit better the whole thing. Wanted to talk about standard deviation (WARNING: BIG WALL, no summary). Afaik it seems that Max/**** made some crafted approximations, but it’s something still far to be calculated in an easy, fast and precise way. I’ve read you say we want to know standard deviation of luck-adjusted chips won / game. I would rather like to know standard deviation in buy-ins/game or buy-ins/100 games, since gives you an immediate idea of how big variance will be. Also because this is the way to compare it to std dev. in cash games.
I have seen too that there is a “standard deviation” box at Swong Sim visualizer, I guess you have to make a guess here¿? And I’ve also seen in some posts in this thread, that in an old version of the program it was calculated “mean deviation”. Mean deviation it’s ok, but it’s not so useful as standard deviation because it doesn’t get bigger when samples are more spread out, so std dev. would give us a better approximation of what should we expect.
We know that in cash games (let me know if you need some graphs for explanation of what I want to say), standard deviation responds to a gauss curve in a frequency/winrate graph, whose vertex is our EV. Moreover, we know 1 standard deviation is the maximum difference you will have with your EV during 68% of the time (that means 34% max to either negative/positive side). And 2 std dev is the maximum difference you will have with your EV 95% of the time.
What about spins? First consideration is that a graph frequency/winrate is not a gauss curve anymore. So first question would be: is regular std dev. useful for measure variance in this case? Maybe we should use a “standard spin deviation” stat. A graph would look as a sloping gauss curve on the left side of the vertex, and it will be a very flat gauss curve on the right side since you can get very big winnings but not very big losses (compared to winnings). Another important point here, is that the vertex of the curve is not our EV anymore, but something a little bit lower. That means our EV point would bet a little right from the vertex; and also that the “most frequent spot” is not getting our EV as it happens in cash, but getting what I would call “Real Spin EV” (RSEV). The bigger the prizes or its frequency are, the bigger the distance between RSEV and EV will be. Also the more games you play, distance gets lower in relative terms, and bigger in absolute terms.
Since the graph is not a symmetric curve anymore, I think regular std dev. is not specific enough (even that it’s going to be necessary to know it if we want to compare it with cash games). I consider it would be better to calculate 2 kind of std deviations: the “Negative Standard Spin Deviation” (will call it NSSD), and the “Positive Standard Spin Deviation” (will call it PSSD), being of course the last one much more bigger than the first one. Obviously these std dev. will have the RSEV point as a reference, not the EV point. A result example would be something like: “For 3.000 games you have a PSSD of 800 buyins and a NSSD of 260. You have a 30% of getting PSSD and a 38% of getting NSSD from your EV point, and you have a 34% each side from RSEV point. Your RSEV will be 40 buyins lower than your EV”. Ofc I’m inventing buy-ins numbers, but I guess it shows what I mean.
Also, although is not so specific, we could calculate usual Standard Deviation. Its formula is the result of calculating the square root of: sum of squares of each difference from the sample with the mean divided by the number of samples. Taking into account that the mean is RSEV, not EV. This would give us a good idea of how big variance is compared to cash or other games.
I think it shouldn’t be difficult to implement in Swong Sim these calculations with every sample and get some numbers.
Thank you for reading
On the settings tab there is an option "Show Summary Stats" which will give you the following stats in the text output.
Mean
Sum square deviation
Mean square deviation (Sample variance)
Root mean square deviation
These are for buyins or $ (depending on which you choose).
As you describe, the distribution of the simulation results can be multimodal and skewed, so these stats must be interpreted with caution. This is why they are only offered as an option and the warning is displayed. I like the idea of developing stats to better capture the distributions, precisely because these standard summary stats offered do not describe them in good detail (and can even be misleading). The main purpose of the visualizer is to give some bit of intuition for this. For example, you can see clearly the effect you describe (for spins) where significantly more than 50% of simulated players can end up under EV after a fixed number of games.
Note that the standard deviation input on the Visualizer tab is for EV Chip Mode where the simulations attempt to represent swings in luck-adjusted winnings per game, rather than buyins/$.
Thanks a lot for the post. I appreciate you taking the time to write it out clearly.
Let me know what I missed!Cheers
--Max