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Now, if you change the "Kelly" bet strategy, and use 8% of the max Bankroll instead of 8% of the current Bankroll, and compare with a fixed $80 bet, the stats change as follow: $80 fixed-bet: better in 35.4% of the 10-spin runs 8% of max Bankroll: better in 28.7% of the 10-spin runs Tie...

You didn't prove anything, you did not even try. I can't blame you, proving the Kelly fraction is the best bet for a single spin is impossible task. But I am going to show you that even on 10-spins, it is not the optimum bet, at least from a statistical point of view. I run a 10-spins MC...

The law of large numbers does NOT apply to small sample-sets.

Please, prove it. Red-16 1-spin scenario has the odds stacked against it, 89.2% chances of losing your bet. You have to believe in Santa to make that *one* bet. But if you do, then just bet whatever you are comfortable losing. This not a matter of long-term profit maximization. One last...

Anyway, thank you for posting that interesting problem :)

Now for Red betting: 24%-bankroll Red : ending bankroll 50th percentile +1213, stdev 1342 $93-fixed bet: ending bankroll 50th percentile +1186, stdev 286 Both betting strategies have the same minimum guaranteed ending bankroll of $66, assuming 10 losses in a row. Do you still think...

My bad, all of the MC results I posted were using 36-1 for a single number win, instead of 35-1 as mentioned in post #1. Here are the corrected results: 8%-bankroll Red-16 : ending bankroll 50th percentile +1786, stdev 26483 4%-bankroll Red-16 : ending bankroll 50th percentile +1656...

I used "guarantee minimum ending bankroll" as I computed it assuming 10 losses in a row. It is your true guaranteed minimum ending bankroll using those betting strategies.

On a single-spin opportunity, I would not even bother looking at Red16 as the odds clearly favor a net negative P&L, in case you didn't notice. The law of large numbers requires really large sample-set to apply. Back on betting strategy for Red16, betting fixed $50 until the 10th spin or a...

Here are some MC results: 8%-bankroll Red-16 : ending bankroll 50th percentile +1823, stdev 68626 4%-bankroll Red-16 : ending bankroll 50th percentile +1682, stdev 7463 $50 fixed bet Red-16: ending bankroll 50th percentile +2350, stdev 1821 Those 3 strategies guarantee a minimum ending...

When was the last time the law of large number was applicable to small sample-sets, 10 or even 1 as you suggest? I welcome the proof here that the Kelly fraction is the way to bet on a 1-spin limit. I will certainly learn something and have no shame about it.

I am most certain Kelly fraction & such doesn't apply because of the 10-spin limit Betting 1 on red every spin, the average ending P&L on 10 spins is +2.43 with a stdev of ~3.05 Betting 1 on red-16 at every spin, the average ending P&L on 10 spins is +28.92 with a stdev of ~35.4 (stdev...

Because of the limit of 10 spins, the outcome of any betting strategy is still mainly governed by luck. But betting red has the greatest chances of a positive P&L on 10 spins, followed far-behind by Red-16. The "optimal" betting strategy varies depending on the player's goal ... I chose to...

Not at all. When I go to a casino (never in actual facts), I expect to loose my bankroll, so my betting strategy here is to maximize the win potential, not the ending bankroll. Of course, if I wanted to maximize the ending bankroll, I would play red, and keep the bet the same ($100) to make...

I play $100 on Red-16 until I win (at which point I stop playing) or the 10 spins are over.

Results for the week ending March, 28th, 2014: - 3 wins ; 0 losses ; net +2405 The end of last week (Thursday 20th) & the beginning of this week (Monday/Tuesday had some unusual spiky / yo-yo price-action in Crude-Oil. To the contrary, Wednesday was unusually lame, with a tight 65-ticks...

Poor trading is either: - not having a trading plan with a "real" edge - not executing that trading plan What gets you into either of these conditions doesn't matter, what matters is: 1. doing the homework to get to a trading plan with a "real" edge 2. doing what it takes to execute the...

This is where those stats from the underlying market model become really useful in assessing the validity of the patterns found through statistical analysis. A basic MC simulation gives the standard deviation for a set of N coin-flips, with the coined biased 33% then 62%. This is used to...

I am now getting to the two most important statistics generated by this market model: the % of trends that need to be traded "with-trend" (TR), and the % of trends that need to be traded "counter-trend" (CT). These 2 figures don't add-up to 100%, because any trend which UsefulSize is between...

The key datapoint in the stat analysis is what I call the trend UsefulSize, which is the number of points from a trend-change to the next trend-change, always measured so that a positive value indicates a winning trade if taken "with-trend", and a negative value if that same trade would have...