pije76 replies to: Hanover replies to PMs


I will reply here, so that I don’t further disrupt Torontoman’s thread, where the topic is trend trading rather than roulette.

I’m afraid I must respectfully disagree once again. What I’m saying is that no matter what strategy you use, i.e. regardless of whether you bet on the colour (red or black) that has recently come out more frequently (a ‘hot streak’), or the colour that has recently come out less frequently (a ‘cold streak’), or even if you just bet on red or black randomly, you will (on average) lose $2.70 for every $100 that you bet, over a large enough number of spins. A strategy of betting black after two blacks and red after two reds is no better or worse than doing the complete opposite, i.e. betting on red after two blacks and on black after two reds, or indeed any other of a zillion different strategies that anybody could ever think of. All of these strategies will on average lose $2.70 every $100 that you bet (that is because the house edge is around 1/37, due to the one green ‘0’ on the wheel, and 1/37 = 0.027 or 2.70%). There is no mathematical strategy that can beat roulette; either you get lucky over a small number of spins, or you don’t.

It also doesn’t matter whether you bet on rows, columns, corners, single numbers, two adjacent numbers, odds or evens, highs or lows, etc etc, or even cover different combinations of any of these with multiple bets on the same spin: the payoff structure is such that you will still on average lose $2.70 every $100 that you bet!

It also doesn’t matter how you vary your bet size, e.g. use progressions like martingale, reverse martingale, d’Alembert, Labouchere, Guetting, or any of a zillion possible progressions that anybody could ever devise, you will still on average lose $2.70 every $100 that you bet.

And it also doesn’t matter whether you quit while you’re ahead by a certain amount of money, because if you visit the casino often enough you’re slightly more likely to fall behind than get ahead, and indeed on a few (relatively rare) occasions get further and further behind so that you would have to stay in the casino for several lifetimes before you return to breakeven, in such a way that, once again, it all balances out that you would on average lose $2.70 of every $100 that you bet. Such is the beautiful symmetry of expectancy math!

If there was any kind of strategy that could actually beat the house edge in the long-term, then naturally everybody would use it, and casinos would immediately change the rules and/or the payoff rates, or even shut down their roulette tables altogether, to save themselves from descent into bankruptcy. But they have had no need to do this for decades, even centuries. The expectancy math that underlies roulette is totally bulletproof.

To test all of this using your spreadsheet, you would need to extend columns H through N downwards to accommodate a million ‘spins’. Start with $1,000,000 in column N and bet $1 per spin/row. At the end of the exercise, you should be left with approximately 1,000,000*(1-1/37) or $972,973 of your starting capital, after a million spins. (Of course this assumes that your version of Excel is big enough to this, that its RNG generates numbers that are close enough to being truly random, and that there are no errors in your formulae/calculations). Then press the recalculate button several times, both checking that the final balance averages out to around $972,973, and also that your bankroll falls far enough behind often enough to satisfy yourself that a strategy of quitting while you’re ahead doesn’t work.

Have fun!

[EDIT] Sorry, I think I misunderstood your strategy, which was to simply bet on the second most recently spun number. I’ve created (and attached) a spreadsheet of my own that works over 10,000 spins (a million was too harsh for Excel), using a strategy that bets on the second most recent spin, and after pressing the recalculate button hundreds of times, I’ve yet to see a single situation where the player is ahead (see the ending capital value in cell J10003) after 10,000 spins.

Column K keeps track of the highest value that the capital has achieved to date. This usually ends up higher than the starting value, but if you pick a value to quit on (e.g. when capital has reached 10,050, you’ve won $50), then every time you achieve this value or greater, you’ve limited your session gain to this value; while if you don’t ever achieve this value, then you must obviously accept whatever the full loss is after the 10,000 spins.

I’m afraid I must end this here, I have other things to get on with. Thanks for the discusion.

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