EV for a D'Alembert
Quote: ThatDonGuyQuote: JyBrd0403Quote: ThatDonGuyI just ran another simulation, but this time, the stop point was not when losses = wins, but when you started to make a profit (so losses could still exceed wins).
At one point, I got a run that consisted of the following before it eventually turned a profit:
621,937,312 bets
Max bet was 70,120x the initial bet
Lowest loss point was 2,147,438,594 initial bets
So if the minimum bet is $1, you had to have had a bankroll of at least $2.147 billion - otherwise you had to stop with an overall loss at some point.
Also, you had to be at a table that would allow a bet of 70,000x your initial bet (e.g. minimum bet $5; maximum bet $350,000). I haven't seen many of those around.
Finally, even if you are playing a game that has one resolution every 5 seconds (not many of those around, either, except maybe electronic ones), that would require playing 24 hours a day for 35,991 days, so even if you had a team playing that could cover 24 hours a day, you have to play nonstop for 98 consecutive years.
If you can meet all three of those conditions, then you have a legitimate claim that D'Alembert always wins. Otherwise, such claims are meaningless.
Legitimate claim that the D'Alembert always wins. Remember you said that.
I don't remember ever saying that it didn't.
Name one mathematician, much less "all of them," that ever said that D'Alembert doesn't always "eventually" win given infinite time and bankroll.
What I want to know is, how is the claim "D'Alembert always wins eventually" useful in any way, shape, or form in real life? Certainly not in gambling.
Go, through some of my old threads, if you want to see the mathematicians say the D'Alembert Breaks even. You yourself, just gave 3 conditions that had to be met in order to say the D'Alembert wins. But, to make the point clear, when I say it eventually wins, it means it goes into the Black and NEVER goes into the red at some point. Not at all like the Marty that goes up and down.
It's useful because it's the only system that I know of, that actually wins. It's useful because it does what every mathematician says is impossible, the betting system changes the EV, if not the HE. So, that's every mathematician on the planet you just proved WRONG. Congrats, again.
Quote: JyBrd0403Quote: ThatDonGuyName one mathematician, much less "all of them," that ever said that D'Alembert doesn't always "eventually" win given infinite time and bankroll.
Go, through some of my old threads, if you want to see the mathematicians say the D'Alembert Breaks even.
The only ones I saw that claim that it breaks even assume there's a real world stop condition. When there is a stop condition - either time or budget - then the EV is zero for a 50/50 game. However, your continual use of the word "eventually" means that these don't apply.
Quote: JyBrd0403But, to make the point clear, when I say it eventually wins, it means it goes into the Black and NEVER goes into the red at some point. Not at all like the Marty that goes up and down.
What does "goes into the black and never goes into the red at some point" mean? Martingale played under the same "play until you eventually reach the stated goal" condition as D'Alembert always ends with a return of +1, so when does it ever "go into the red"?
Quote: JyBrd0403Quote: ThatDonGuyWhat I want to know is, how is the claim "D'Alembert always wins eventually" useful in any way, shape, or form in real life? Certainly not in gambling.
It's useful because it's the only system that I know of, that actually wins.
Not under real life conditions, it doesn't - at least not every time. Prove otherwise. Remember, "real life conditions," including limits on betting amounts and how much money you have. Claims that I already proved this are false.
Quote: DeMangoCan we run a sim and get over this thread?
You don't think facts will change his opinion, do you ?
So, after 30 million trials, I can only ask myself, WTF have you guys been talking about?????
Remember, in the real world, some arbitrary point will stop you. So... 28 million trials? Where were you after EXACTLY 1 million... 2 million... 3... 4... 5... 6... 7...?
Quote: 24BingoWell? Let's see it. The full sequence.
Remember, in the real world, some arbitrary point will stop you. So... 28 million trials? Where were you after EXACTLY 1 million... 2 million... 3... 4... 5... 6... 7...?
This real world stuff is something you guys started. I simply said the D'alembert wins. Wins, meaning it goes into the Black and doesn't come back, just like a 51% game would do.
Actually, with these RNG's, I think the D'Alembert needs 10 to 20 million to get into the clear. I'm still running the simulation, but I can see that it's just going to go UP DOWN UP DOWN, as expected.
The bets will go up and go down I mean, 1000+ units back down to 150 units. Up Down Up Down.
Quote: JyBrd0403So, I sit down and start fiddling with this simulator. 28 million trials so far, profit of 14 million dollars so far. Some notes. The game has been in the Black for the last 20 million trials or so. At the +10 million mark, the bet was 1,668 units (the starting bet is 1 unit). What did surprise me a bit was the loss limit appears to be around 2 million dollars, of course, we're up 15 million now so that doesn't really matter. Most units bet so far was 3862. A quick observance and you can see that what happens is that the betting goes up to 1000+ units, and surprise surprise surprise it comes back down to 150 or so units, then it goes back up to 1000+ units and back down to 150 or so. UP DOWN, UP DOWN, UP DOWN, kinda what you'd expect from a 50/50 game.
So, after 30 million trials, I can only ask myself, WTF have you guys been talking about?????
Keep playing.
I ran some trials as well.
After 247 million trials, I was up 113 million.
After 299 million trials, I was down 29 million.
Of course, this works both ways:
After 345 million trials, I was down 135 million.
After 366 million trials, I was up 23 million.
Over 1 billion trials, the largest loss point was 256 million (between 844 million and 845 million - and by 860 million, the losses were wiped out and I was back on the plus side) and the largest bet was 36,847.
You will keep going back and forth. Your periods between losses will almost certainly get longer and longer, but "eventually" your total profit goes back down below zero - and "eventually" it goes back up above any point you were at in the past. However, you will never reach a point where you will always be ahead.
It's just that "eventually" is meaningless if you aren't immortal and you can't cover every possible overall loss level. You have to stop sometime. No bank is going to lend you billions of dollars if you tell them, "Don't worry; D'Alembert guarantees that you will get it back, with interest!"
Why don't you compare D'Alembert against, say, a modified Martingale, where your initial bet is 1, then, after each win, it resets to twice the previous starting point bet minus 1? For example, your initial bet is 1; after your first win, reset to 3 (then bet 6, 12, 24, etc. after losses until you win again); after your second win, reset to 5; after your third win, reset to 7, and so on. After your Nth win, your profit is N2.
Quote: JyBrd0403This real world stuff is something you guys started.
Damn that reality!
Quote: JyBrd0403I simply said the D'alembert wins. Wins, meaning it goes into the Black and doesn't come back, just like a 51% game would do.
You'd have to define that, but if we're going with the definition that there comes a point where your chance of never again falling behind converges to a non-zero value, nope. TheDonKing explains better than I could.
But also you asked for the EV. That has a specific definition, and under that definition, the expected values of multiple trials always add, so if the expected value of each trial is zero, it will be zero. When you introduce infinite parameters into the mix, things get a bit fuzzy, for the same reason limits that approach 0*∞ will sometimes converge to nonzero values, but you have to understand that the parameters do truly have to be infinite, not "very large."
Quote: JyBrd0403I'm still running the simulation, but I can see that it's just going to go UP DOWN UP DOWN, as expected.
The bets will go up and go down I mean, 1000+ units back down to 150 units. Up Down Up Down.
...what exactly do you think we were expecting? To this point, you'd been saying "up up up up."
If the probability of winning an even-money bet is p and we let q = 1 - P, then, if the system ends only after a loss of an N-unit bet, then the EV for the entire run is:
(p / (q-p))2 * (1 - (p/q)N) - N p / (q-p) + N (N+1) / 2
For example, with the pass line on craps, if the stop condition is 20, then the EV is -37.78765, and the average length is 349.365 bets.
Yes, I do realize that the OP had a different stop condition - "keep betting until the bet drops back down to 1 (i.e. you win a bet of 2)".
