Question about D'Alembert Betting Strategy

Ok I'm back again with some noob questions.

Strategy is Start $1, Lose bet $2, Lose bet $3, win bet $2, Lose bet $3, Lose bet $4, win bet $3. (+1 on loss, -1 on win)

Strategy is structured to cover highest loss plus 1 unit, so when you have wins=losses, you will be +1 from each win.

I want to know the optimal stop loss at any given time, assuming a base unit of 1% bankroll. Base unit will not change for the duration of the session.

This is not easy for me to determine, and I’ll explain why. I will use a difference of + 10 losses over wins as an example.

Start -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 = -55

10 wins 20 losses = +$10 from wins (10 losses covered) -$55 = -$45
100 wins 110 losses = +$100 from wins (100 losses covered) - $55= $45
1000 wins 1010 losses = +$1000 from wins (1000 losses covered) - $55= $945

As you can see if I set a standard stop loss of +10 losses over wins it will not be equally ideal at a random given point of the session.

Assume a game of true 50/50. (Yes, I am aware casinos do not offer these odds.)

If the session runs indefinitely I'm aware the optimal stop loss is never because eventually wins = losses, hoping someone can think about this a different way and maybe compare a few scenarios where you might be hoping to achieve a static outcome.

The goal of the optimal stoploss is to prevent a deficit such as -50 losses over wins during an extended session, which would be difficult to sustain if the base unit is 1% of bankroll.

No casino game is 50-50

Quote: billryan

No casino game is 50-50

I have a means of betting 50/50, and it is not in a casino.

Quote: billryan

No casino game is 50-50

War is, if it is still offered. The side bets had casino advantage but War was even money pay with no house advantage.

Quote: billryan

No casino game is 50-50

Pai Gow Poker is. That's why they charge a commission.

Quote: rsactuary

Pai Gow Poker is. That's why they charge a commission.

I don’t think it is 50-50. I think it actually favors the bank, hence the commission. If it was 50-50 they’d charge a commission on both sides.

Quote: es330td

War is, if it is still offered. The side bets had casino advantage but War was even money pay with no house advantage.

Where is that at? As far as I know it's even money until you have to go to war with the dealer(a tied hand) at that point you have to forfeit half your bet or put up double your bet to continue. If you win the war your original but will only push but they hey you on the extra bet. There may be different versions I suppose. If there's there's truly a version where you don't have to play a side bet but get a true 50/50 please let me know where because hopefully they would rate your play.

The last time I saw it at casino was over 15 years ago at a casino I have not been back to in 15 years. I don’t even know if they still offer it but at the time it was truly even money. The pit boss told me they were offering it as a “less intimidating way“ to get the slot machine player to try something else.

Quote: protosapien

If the session runs indefinitely I'm aware the optimal stop loss is never because eventually wins = losses

...except for the small detail that you have a finite bankroll. "Eventually," you will have a loss run big enough to lose the whole thing.

Time for another one of my "how deep in the hole can you get with a 50/50 D'Alembert?" simulations...
I just got one that reached total losses of over 800 million before climbing back to zero.

Question: what do you mean by an "optimal" step loss? The more you win, the more wiggle room you have, as you need more and/or larger losses to reach the end of your bankroll.

Quote: ThatDonGuy

Question: what do you mean by an "optimal" step loss? The more you win, the more wiggle room you have, as you need more and/or larger losses to reach the end of your bankroll.

Accounting for an increase/decrease in bankroll over time, at what sizing against the current bankroll would the bet be less ideal to place than restarting the progression?

Quote: protosapien

Accounting for an increase/decrease in bankroll over time, at what sizing against the current bankroll would the bet be less ideal to place than restarting the progression?

If every bet has the same expectation of 0, there's nothing ideal. Everything is the same. Restart, don't restart, ionize, delineate, marinate, do whatever you want. There's no optimization. Just do you.

Quote: sabre

If every bet has the same expectation of 0, there's nothing ideal. Everything is the same. Restart, don't restart, ionize, delineate, marinate, do whatever you want. There's no optimization. Just do you.

It is more optimal to stop loss at 10 wins 20 losses than it is 1000 wins 1010 losses, because the 55 deficit from losses will be less significant as you progress further into the session.

Therefore, there is optimization.

Thank you though

Quote: rsactuary

Pai Gow Poker is. That's why they charge a commission.

rsactuary,

Even without the commission PGP is not 50/50, because the Banker wins copies. For example, if the Player has a 9-high straight with A-K in front and the Banker has 2 Pair with A-K in front, the hand is a push. However, if you reverse the two hands, then the Banker wins.

Hope this helps!

Dog Hand

Quote: es330td

War is, if it is still offered. The side bets had casino advantage but War was even money pay with no house advantage.

My understanding is that you have to essentially double your bet to go to war, but can only win the original betting unit. That's where the house edge comes from.

Quote: Mission146

My understanding is that you have to essentially double your bet to go to war, but can only win the original betting unit. That's where the house edge comes from.

Yes, you could expect to lose one unit approximately every 26 decisions. Better than the house edge on slots but nowhere near 50-50.