Roulette Wheel Game

ETcallhome · Feb 13, 2016

Pension_Admin said:
The calculation will differ depending on what you do with the removed winnings. If you bought real estates with it, and subsequently your account get wiped out, would you eventually sell the real estate and put the money back into your strategy? If that is the case, then the removed winning just act like a reserve. It would not make the strategy profitable. How money is managed will not turn a losing strategy into a winning strategy.

no kidding, when you are first starting out you may be (and must be) willing to accept 100% risk of ruin. If you survive that gauntlet, then ratholing is the main technique to reduce your risk of ruin. The risk of ruin is always out there, but it will only ruin a smaller and smaller amount of your total net worth.

Not saying you will make money, but when your account finally blows up you will be the one guy left with a fairly impressive collection of non leveraged investments. All the result of trading.

botpro · Feb 13, 2016

Here's the exact analysis of this game:

We can reduce it to n=50 and p=49/50, and analyse it as a Binomial Distribution (--> https://en.wikipedia.org/wiki/Binomial_distribution ):

Code:

n=50 k=49 p=0.9800 :
  k    p          pCum       pRest        win
  0   0.00000    0.00000    1.00000       0.00
  1   0.00000    0.00000    1.00000       3.00
  2   0.00000    0.00000    1.00000       6.00
  3   0.00000    0.00000    1.00000       9.00
  4   0.00000    0.00000    1.00000      12.00
  5   0.00000    0.00000    1.00000      15.00
  6   0.00000    0.00000    1.00000      18.00
  7   0.00000    0.00000    1.00000      21.00
  8   0.00000    0.00000    1.00000      24.00
  9   0.00000    0.00000    1.00000      27.00
10   0.00000    0.00000    1.00000      30.00
11   0.00000    0.00000    1.00000      33.00
12   0.00000    0.00000    1.00000      36.00
13   0.00000    0.00000    1.00000      39.00
14   0.00000    0.00000    1.00000      42.00
15   0.00000    0.00000    1.00000      45.00
16   0.00000    0.00000    1.00000      48.00
17   0.00000    0.00000    1.00000      51.00
18   0.00000    0.00000    1.00000      54.00
19   0.00000    0.00000    1.00000      57.00
20   0.00000    0.00000    1.00000      60.00
21   0.00000    0.00000    1.00000      63.00
22   0.00000    0.00000    1.00000      66.00
23   0.00000    0.00000    1.00000      69.00
24   0.00000    0.00000    1.00000      72.00
25   0.00000    0.00000    1.00000      75.00
26   0.00000    0.00000    1.00000      78.00
27   0.00000    0.00000    1.00000      81.00
28   0.00000    0.00000    1.00000      84.00
29   0.00000    0.00000    1.00000      87.00
30   0.00000    0.00000    1.00000      90.00
31   0.00000    0.00000    1.00000      93.00
32   0.00000    0.00000    1.00000      96.00
33   0.00000    0.00000    1.00000      99.00
34   0.00000    0.00000    1.00000     102.00
35   0.00000    0.00000    1.00000     105.00
36   0.00000    0.00000    1.00000     108.00
37   0.00000    0.00000    1.00000     111.00
38   0.00000    0.00000    1.00000     114.00
39   0.00000    0.00000    1.00000     117.00
40   0.00000    0.00000    1.00000     120.00
41   0.00000    0.00000    1.00000     123.00
42   0.00001    0.00001    0.99999     126.00
43   0.00005    0.00006    0.99994     129.00
44   0.00042    0.00048    0.99952     132.00
45   0.00273    0.00321    0.99679     135.00
46   0.01455    0.01776    0.98224     138.00
47   0.06067    0.07843    0.92157     141.00
48   0.18580    0.26423    0.73577     144.00
49   0.37160    0.63583    0.36417     147.00

This means that with at least 63.58% probability we will always be in the win-zone.
pRest means "p for higher than k consecutive wins", ie. p for 50 - k.
On average once in 50 cases we will be broke.

botpro · Feb 13, 2016

Here's a better table with account (starting with $100) and P/L:

Code:

n=50 k=49 p=0.9800 :
  k    p          pCum       pRest       acct     P/L%
  1   0.00000    0.00000    1.00000     103.00     3.00
  2   0.00000    0.00000    1.00000     106.09     6.09
  3   0.00000    0.00000    1.00000     109.27     9.27
  4   0.00000    0.00000    1.00000     112.55    12.55
  5   0.00000    0.00000    1.00000     115.93    15.93
  6   0.00000    0.00000    1.00000     119.41    19.41
  7   0.00000    0.00000    1.00000     122.99    22.99
  8   0.00000    0.00000    1.00000     126.68    26.68
  9   0.00000    0.00000    1.00000     130.48    30.48
10   0.00000    0.00000    1.00000     134.39    34.39
11   0.00000    0.00000    1.00000     138.42    38.42
12   0.00000    0.00000    1.00000     142.58    42.58
13   0.00000    0.00000    1.00000     146.85    46.85
14   0.00000    0.00000    1.00000     151.26    51.26
15   0.00000    0.00000    1.00000     155.80    55.80
16   0.00000    0.00000    1.00000     160.47    60.47
17   0.00000    0.00000    1.00000     165.28    65.28
18   0.00000    0.00000    1.00000     170.24    70.24
19   0.00000    0.00000    1.00000     175.35    75.35
20   0.00000    0.00000    1.00000     180.61    80.61
21   0.00000    0.00000    1.00000     186.03    86.03
22   0.00000    0.00000    1.00000     191.61    91.61
23   0.00000    0.00000    1.00000     197.36    97.36
24   0.00000    0.00000    1.00000     203.28   103.28
25   0.00000    0.00000    1.00000     209.38   109.38
26   0.00000    0.00000    1.00000     215.66   115.66
27   0.00000    0.00000    1.00000     222.13   122.13
28   0.00000    0.00000    1.00000     228.79   128.79
29   0.00000    0.00000    1.00000     235.66   135.66
30   0.00000    0.00000    1.00000     242.73   142.73
31   0.00000    0.00000    1.00000     250.01   150.01
32   0.00000    0.00000    1.00000     257.51   157.51
33   0.00000    0.00000    1.00000     265.23   165.23
34   0.00000    0.00000    1.00000     273.19   173.19
35   0.00000    0.00000    1.00000     281.39   181.39
36   0.00000    0.00000    1.00000     289.83   189.83
37   0.00000    0.00000    1.00000     298.52   198.52
38   0.00000    0.00000    1.00000     307.48   207.48
39   0.00000    0.00000    1.00000     316.70   216.70
40   0.00000    0.00000    1.00000     326.20   226.20
41   0.00000    0.00000    1.00000     335.99   235.99
42   0.00001    0.00001    0.99999     346.07   246.07
43   0.00005    0.00006    0.99994     356.45   256.45
44   0.00042    0.00048    0.99952     367.15   267.15
45   0.00273    0.00321    0.99679     378.16   278.16
46   0.01455    0.01776    0.98224     389.50   289.50
47   0.06067    0.07843    0.92157     401.19   301.19
48   0.18580    0.26423    0.73577     413.23   313.23
49   0.37160    0.63583    0.36417     425.62   325.62

I would say this is a very profitable game! ;-)
Where can I join the game? ;-)

kut2k2 · Feb 13, 2016

botpro said:

Here's a better table with account (starting with $100) and P/L:

Code:

n=50 k=49 p=0.9800 :
  k    p          pCum       pRest       acct     P/L%
  1   0.00000    0.00000    1.00000     103.00     3.00
  2   0.00000    0.00000    1.00000     106.09     6.09
  3   0.00000    0.00000    1.00000     109.27     9.27
  4   0.00000    0.00000    1.00000     112.55    12.55
  5   0.00000    0.00000    1.00000     115.93    15.93
  6   0.00000    0.00000    1.00000     119.41    19.41
  7   0.00000    0.00000    1.00000     122.99    22.99
  8   0.00000    0.00000    1.00000     126.68    26.68
  9   0.00000    0.00000    1.00000     130.48    30.48
10   0.00000    0.00000    1.00000     134.39    34.39
11   0.00000    0.00000    1.00000     138.42    38.42
12   0.00000    0.00000    1.00000     142.58    42.58
13   0.00000    0.00000    1.00000     146.85    46.85
14   0.00000    0.00000    1.00000     151.26    51.26
15   0.00000    0.00000    1.00000     155.80    55.80
16   0.00000    0.00000    1.00000     160.47    60.47
17   0.00000    0.00000    1.00000     165.28    65.28
18   0.00000    0.00000    1.00000     170.24    70.24
19   0.00000    0.00000    1.00000     175.35    75.35
20   0.00000    0.00000    1.00000     180.61    80.61
21   0.00000    0.00000    1.00000     186.03    86.03
22   0.00000    0.00000    1.00000     191.61    91.61
23   0.00000    0.00000    1.00000     197.36    97.36
24   0.00000    0.00000    1.00000     203.28   103.28
25   0.00000    0.00000    1.00000     209.38   109.38
26   0.00000    0.00000    1.00000     215.66   115.66
27   0.00000    0.00000    1.00000     222.13   122.13
28   0.00000    0.00000    1.00000     228.79   128.79
29   0.00000    0.00000    1.00000     235.66   135.66
30   0.00000    0.00000    1.00000     242.73   142.73
31   0.00000    0.00000    1.00000     250.01   150.01
32   0.00000    0.00000    1.00000     257.51   157.51
33   0.00000    0.00000    1.00000     265.23   165.23
34   0.00000    0.00000    1.00000     273.19   173.19
35   0.00000    0.00000    1.00000     281.39   181.39
36   0.00000    0.00000    1.00000     289.83   189.83
37   0.00000    0.00000    1.00000     298.52   198.52
38   0.00000    0.00000    1.00000     307.48   207.48
39   0.00000    0.00000    1.00000     316.70   216.70
40   0.00000    0.00000    1.00000     326.20   226.20
41   0.00000    0.00000    1.00000     335.99   235.99
42   0.00001    0.00001    0.99999     346.07   246.07
43   0.00005    0.00006    0.99994     356.45   256.45
44   0.00042    0.00048    0.99952     367.15   267.15
45   0.00273    0.00321    0.99679     378.16   278.16
46   0.01455    0.01776    0.98224     389.50   289.50
47   0.06067    0.07843    0.92157     401.19   301.19
48   0.18580    0.26423    0.73577     413.23   313.23
49   0.37160    0.63583    0.36417     425.62   325.62

I would say this is a very profitable game! ;-)
Where can I join the game? ;-)

Your p/l is wrong. The most you could win is

N*.03 - 1.03

where N is the number of the losing spin.

botpro · Feb 14, 2016

kut2k2 said:
Your p/l is wrong. The most you could win is

N*.03 - 1.03

where N is the number of the losing spin.

I don't think so, because the original rules of the game as defined by the OP are:

If there was a roulette wheel that has 100 numbers on it, and this includes the green 0 and 00.

The rules are simple, every day you get 1 spin:

1) If you land on 0 or 00, you lose your whole account. (2% chance)
2) If you land on the other 98 numbers besides 0 or 00, you make +3% of your account every spin. (98% chance)

Rule #1 says you risk 100% of your current account value (p for this to happen in each play is 2/100 = 1/50 = 2%).
Rule #2 says you make +3% of your current account value (p for this to happen in each play is 98/100 = 49/50 = 98%).
This is applied in the table in the "acct" column, and the P/L% column shows the cumulated compounded P/L.
In fact the P/L is just +3% each time, the rest is the magic of this compounding.

The table also shows that for winning in 41 consecutive plays the probability is practically 100% (column pRest)
(that's because the p for a win in a single play is so high: 98/100 = 49/50 = 0.98 = 98%).
As the table shows, for winning in more than 41 consecutive plays the probability starts to degrade... --> see column pRest.

kut2k2 · Feb 14, 2016

botpro said:
I don't think so, because the original rules of the game as defined by the OP are:

Rule #1 says you risk 100% of your current account value (p for this to happen in each play is 2/100 = 1/50 = 2%).
Rule #2 says you make +3% of your current account value (p for this to happen in each play is 98/100 = 49/50 = 98%).
This is applied in the table in the "acct" column, and the P/L% column shows the cumulated compounded P/L.
In fact the P/L is just +3% each time, the rest is the magic of this compounding.

The table also shows that for winning in 41 consecutive plays the probability is practically 100% (column pRest)
(that's because the p for a win in a single play is so high: 98/100 = 49/50 = 0.98 = 98%).
As the table shows, for winning in more than 41 consecutive plays the probability starts to degrade... --> see column pRest.

Sorry, I thought you were playing the second variation where winnings are taken out of the game.

Why would you play the original game? You could lose everything at any spin, including the very first spin. I see you've chosen a ceiling of 50 spins. Actually that's the expected number of spins but there's no guarantee you'll get there. The number of the losing spin can be any integer from one to infinity. Risk of ruin is assured, eventually.

With the second game, once you have won 34 spins, you're in profit thereafter.

JB3 · Feb 14, 2016

I said that the winnings is allowed to be taken out if you choose to. But you can definitely keep spinning the wheel with all of the winnings in it (including compounding). I'm just giving a theoretical framework, you tell me what you would do and how you would play this.

So far, I see certain individuals will flat out say, they will not play at all because they don't want to risk losing their whole account. Some say, they will play, but only if they can take their winnings off the table..and even suggest to flip those winnings into other stable investments. Others, want to play all the way because the statistics is actually in their favor, so they feel that they should play because the odds are good.

I see trading systems as basically game theory, application of statistics, money management and leverage.

botpro · Feb 14, 2016

JB3 said:
I said that the winnings is allowed to be taken out if you choose to. But you can definitely keep spinning the wheel with all of the winnings in it (including compounding). I'm just giving a theoretical framework, you tell me what you would do and how you would play this.

So far, I see certain individuals will flat out say, they will not play at all because they don't want to risk losing their whole account. Some say, they will play, but only if they can take their winnings off the table..and even suggest to flip those winnings into other stable investments. Others, want to play all the way because the statistics is actually in their favor, so they feel that they should play because the odds are good.

I see trading systems as basically game theory, application of statistics, money management and leverage.

+1
Game theory is indeed very important in many fields.
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." (--> https://en.wikipedia.org/wiki/Game_theory )

botpro · Feb 14, 2016

kut2k2 said:
Sorry, I thought you were playing the second variation where winnings are taken out of the game.

No, my example was using the original rules and continued playing, ie. applying compounding.
In real world practice I think I would play each time max. 25 consecutive plays, to be on the safe side.
I've not yet analyzed if that strategy is maybe too-cautious, because the probability table says I could on average safely play upto 41 consecutive plays...

Why would you play the original game? You could lose everything at any spin, including the very first spin. I see you've chosen a ceiling of 50 spins. Actually that's the expected number of spins but there's no guarantee you'll get there. The number of the losing spin can be any integer from one to infinity. Risk of ruin is assured, eventually.

I would play the original game, but decide myself how long I continue a series of the game,
then restarting anew with a new initial account value that is a portion of the hopefully made profit
of the last series....

With the second game, once you have won 34 spins, you're in profit thereafter.

That could indeed be true, though I must admit I've not analyzed yet that aspect myself, will re-read your postings.

botpro · Feb 14, 2016

Btw, I've posted the C++ source code for calculating the binomial distribution table I had posted here:
http://www.elitetrader.com/et/index.php?threads/binomial-distribution-source-code-in-c.297845/