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