You seem to have failed to read my previous posts carefully. I specifically mentioned that I had been assuming (erroneously) that the odds were set in such a way that a winning bet would recover all the previous losses plus win a profit equal to the losses accumulated in that sequence (not the original stake), since this is the way martingale is most often used (it makes no sense to win just the base bet)...
I guess you're referring to this:
You set your odds in such a way that each winning bet covers all the accumulated losses from the previous losing bets in a row plus gives you the same amount in profit (in the simplest case).
I thought by "the same amount" you mean "the same amount each sequence", ie. the base amount. But you meant "the same amount as the size of the last bet in the sequence".
That's not how martingale is most often used. It is probably most often used to bet on red or black on the roulette table where a winning bet doubles your money. On Just-Dice (where you can chose your own payout multiplier) martingale is by far most often used at 49.5% chance of winning, 2x payout. There are a few people who play with lower chances, higher payout multipliers, but they're in the minority.
This depends on what you mean by "the odds are in your favour". I offer you this bet:
5 times out of 6 you win. You're 5 times more likely to win than to lose. But when you win you only win $1, and when you lose you lose $100.
I would say that the odds are not in your favour.
Based upon a strict interpretation of my point, then yes, the odds are in my favor.
Again, it depends on what you mean by "odds in your favour".
If you mean "more likely to win than to lose" then yes.
If you mean "
you are likely to succeed because the conditions are good and you have an advantage" then no. Your expectation is negative - it's a bad bet for you. You're more likely to win than to lose, but the amount you win is so small compared to the amount you risk that it's not in your favour. You don't have an advantage even though you win 5 out of 6 times.
It's hard to find a decent definition. All I find is Hunger Games junk.
In that case the stake is life/death so it's hard to evaluate expected values.
My point is best demonstrated by imagining that a hypothetical secondary bet is placed on top of the original bet.
Using your example, let's say I had a 5:6 chance of winning $1 and a 1:6 of losing $100, and I guarantee a roll according to these odds.
Now imagine that you are a spectator who is asked to bet as to whether I will profit or if I will lose. Someone says, "Hey, I'll bet $50 that he (i.e. me) loses." You have a spare $50 in your pocket. Do you take the bet?
Of course you would, so the point holds. Though, as you point out, the odds of profiting alone might not be the only thing you want to take into account...
That 2nd bet is a good bet. I would take that one, because its odds ARE in my favour. You're paying even money for a 5-in-6 event. Just because the 2nd bet is a good one to take doesn't mean the 1st one is too.
This, exactly. Because each roll is an independent event you never know if you're in the middle of a 100 loss streak. However, some part of me thinks it also has to be true that rolling consecutive losses into infinity is also highly improbably and that longer and longer streaks of losses have to be more and more improbable. So I always have a hard time rectifiying these two facts: the independence of each roll and the increasing unlikelyhood of increasingly large streaks.
Well, look at it this way:
Streaks of length 20 are twice as common as streaks of length 21, which are twice as common as streaks of length 22, etc.
And streaks of length 20 are exactly as common as streaks of length 21 or more (assuming a 50/50 game).
To see that last point, suppose streaks of length exactly 20 occur with probability p. Streaks of length 21 will occur with half that probability (p/2), Length 22 with probability p/4, and so on. So the probability of a streak of length 21 or more is p/2 + p/4 + p/8 + ... = p(1/2 + 1/4 + 1/8 + ...) = p.
By pre-rolling until you hit 20 losses in a row, you've probably had to make a million or so rolls. And now you're wondering whether the streak will end at 20, or go on to be more than 20. Well as we've just seen, the probability of those two things is the same. probability p it will end at 20, and probability p*(1/2+1/4+1/8+...) = p that it goes to length 21 or more.
Back to the "does martingale works?" question - we had a guy playing on Just-Dice over the last day or so who has won huge amounts using something very like martingale betting.
Here's a chart of his profit over time:
and the site's profit over the last week:
So even though he's using a losing strategy, he's managed to get lucky and win.
