## Debunking d'Alembert With Excel

It's been suggested that playing a Roulette wheel using a d'Alembert progression is a road to riches. Apparently it's child's play to beat the house edge.So, as a little exercise, I've created an Excel workbook which illustrates dramatically how a playing d'Alembert progression will strongly trend towards bankruptcy, with a probable initial negligible profit.

Here's the way I played it.

The game was European Roulette with single 0. If you are a masochist modify it for American Roulette.

The first bet is on red, purely arbitrary. I wagered only on Red or Black. Modify for odd/even if you wish or other 1:1 propositions outside bets.

Whenever the result was Red, the next bet was Black. Modify if you can be bothered. It makes no difference.

Whenever the result was Black, the next bet was Red.

Whenever the result was Green 0, the next bet was the same as the most recent bet.

I assigned a starting Bankroll of $1,000,000 ( You can vary that in the model. )

I decided an initial wager of $10 ( You can vary that in the model. )

I decided a progression increment of $1. ( You guessed it )

Whenever a bet won, the next bet was $1 less than the previous bet, or $1, whichever was the greater.

Whenever a bet lost, the next bet was $1 more than the previous bet, or total remaining bankroll, whichever was the smaller.

The model simulated potentially 50,000 spins.

Child's play indeed.

So, download the workbook and open it in Excel. You may need to enable editing. It has NO MACROS.

HERE IS THE WORKBOOK

To run the simulation, simply put the cursor into any empty cell and hit the Delete Key. After a fraction of second, the simulation will complete and the chart and results table will repopulate.

Generally the bankroll starts out with a modest increase of value of a few times the initial wager. Pretty soon it heads downhill with an accelerating downtrend as the wager size increases.

I've yet to see the simulation succeed in doubling the bankroll with the parameters as set. You can change those parameters and I assert that whatever you set them as, you will lose your bankroll more often than you double it.

HERE IS THE WORKBOOK

It's nothing sophisticated and does not use macros, so is safe to run in excel 2010 or later.

I'll leave it online a few months. If the owners of admins here wish to, they can host it themselves, subject to leaving it unchanged and attributing to me by name.

Here's an example result.

## Chasing losses again

So darned stupid. Chasing losses is effectively not much different to Martingaling, and I just did it. Sucker !!!After my bankroll took a good beating earlier in the year, I've restricted myself to just a few £hundred per weekly session, in bricks and mortar casino, min betting at £5 for recreation. I've been doing ok.

Buy-ins have been typically $50 - £100 with maybe a second and very rarely a third buy-in per session. until Monday, my last 8 sessions had all been winners, leaving me up by £695. So far so good.

But this Monday I went armed with 5x£50 notes set aside for bankroll plus a few hundred regular pocket money.

Bought in for £50. Got ahead to maybe £90 then Whack! Gone before my free coffee arrived.

Bought in for another £50. Whack! Never went above buy-in.

Bought in for another £50. Whack! Never went above £75. Managed to squeeze 30 minutes of play.

Dealer change, new faster, prettier dealer. ( me = sexist pig )

Requested another coffee.

Bought in for £100. Whack! Never went above buy-in. My nice crisp £50 notes were gone.

All this playing between £5 and £15 per hand.

It wasn't much fun. None of my £50 buy-ins managed to get to £100 and here I was £250 down, and then my coffee arrived.

Skulked off to watch a few fools throw money at roulette while I finished my drink. Felt and looked pretty pathetic. Went home.

Consoled myself that this was the first losing session of 9 sessions and that I was still £445 up overall.

But notice how I'd got greedy. Previously I'd been turning £50 into £100 or maybe £100 into £150 or so. But here I was throwing £250 into one session and getting my arse kicked.

So today arrives. I felt pissed with the universe for playing fair and beating me. I needed to chase that £250 loss. This would need more fire-power.

This time online BJ. Popped in £100 of credit.

.

.

.

Flat betting £10 or £15 as the mood took me.

.

.

.

Lost it in short order. DAMMIT

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.

.

Goddam it. £350 in the hole for the week

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.

.

Credited another £100 to flat bet at £15. Needed a lot of luck. What will I do if I ( inevitably ) lose this?

.

.

.

Stumbled my way up to £300. If I withdrew, I could at least say it was only a £150 loss on the week. Played on.

.

.

Bobbled between £350 and about £150

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.

.

Clambered up to £450. Phew, I was now at break even for the week. That £250 loss was recovered.

.

Played on at £10 per hand.

.

Bobbled between £480 and about £410

.

.

.

Clambered to £490 !!!

.

Dropped bet to £2 per hand and Martingaled.

.

.

Hit £500 balance. Cashed out at £300 profit for the session and up £50 for the week..

OnceDear once again a lucky tit!

But make no bones about it, by effectively buying in for double what I usually do, I'm treating each losing session like a single losing bet and effectively Martingaling in sessions. Doomed to fail.

I really don't know what I would have done if the last £100 had gone down the pan. Being £450 down on the week would have really upset me, but throwing several more £hundred to try to claw it back would have been stupid upon stupid.

## OnceDear's Rule. What's The Chances

I'm often drawn to give the same answer to similar questions from newbies:-Question: If I apply blah, blah, blah betting system to Blackjack/Roulette/Baccarat/Whatever, what are my chances of increasing my bankroll from $XXX to $YYY

Answer: OnceDear's Rule of Thumb !

Probability of Success <= (Starting Bankroll)/(Starting Bankroll + Target Profit)

This rule of thumb makes the assumption that we can ignores House advantage and Player advantage. I'll explain and justify that later.

It has a caveat. It must be impossible to win beyond the Target Profit, or else the probability will be less/worse.

Apart from that, it applies pretty much universally.

Any game.

Any Money Management strategy.

Any Betting strategy.

It applies to Flat Betting,

It applies to Martingaling,

It applies to Reverse Martingaling,

It applies to D'Alembert

It applies to Hit and Run Target Betting,

It applies to Betting with Win Goals,

It applies to Betting with Stop Losses.

It applies for one Betting Session

It applies for a sequence of many Betting Sessions

It just applies.

I never claim that it is the full answer to every set of wagers placed, but if a new gambler can grasp this, then he/she will have a good start point from which to realise why his/her Bull5h1t Brilliant system will not make him/her rich.

Here it is again, with an example, before I derive it for you from first principles.

Probability of Success <= (Starting Bankroll)/(Starting Bankroll + Target Profit)

Example: What is the probability that my magical Blackjack System will let me turn $100 into $110?

Answer

Probability of Success <= 100/(100+10)

Probability of Success <= 100/110

Probability of Success <= 90.91%

Success is nearly 91% assured, but about 9% of the time you will lose all.

Great. "What if I want to double my bankroll?"

Answer

Probability of Success <= 100/(100+100)

Probability of Success <= 100/200

Probability of Success <= 50%

Success is nearly 50% assured, but about 50% of the time you will lose all.

Great. "What if I want to quadrupal my bankroll?"

Answer

Probability of Success <= 100/(100+300)

Probability of Success <= 100/400

Probability of Success <= 25%

Success is nearly 25% assured, but about 75% of the time you will lose all.

And, remember, it doesn't matter whether you are having one long session to reach the target, or breaking your sessions up to try to make $1 each day!!!

So, how is the rule derived?

It's based on three basic tenets:

1. In a fair bet with no house edge, the payout is directly related to the probability.

Total Return for a lose = 0

Total return for a win=Stake x 1/(Probability of a win)

2. The end result from a session of multiple bets, however they are made, is that you are either going to hit your win goal, or you are going to lose your bankroll. It does not matter if you made one big fat wager or lots of wagers in any mix of sizes. The session effectively equates to one probability: One wager. What made up your session is not relevant.

3. With ANY betting system you cannot diminish the house edge. EVER. But then again, betting systems do not increase the house edge either unless you leave yourself unable to fund a wager or force yourself to play badly.

So, take for example a single fair coin toss.

We almost intuitively know the payout on a fair coin toss.

Double your money if you win. Lose your money if you don't.

Probability of calling a coin toss correctly = 50% 50% is one way of saying 50/100 or 0.5 It just is. Get over it.

Total Return for a lose = 0

Total return for a win=Stake x 1/(Probability of a win)=Stake x 1/0.5=Stake x 2

So, as we would expect it's a case of lose or double your stake on one coin toss.

Now lets say we wager on our ability to call two consecutive coin tosses correctly.

Probability of success = Probability of getting it right first time x Probability of getting it right second time.

Probability of success = 0.5 x 0.5 = 0.25 or 1 in 4. Sorry if that seems complex. It just is that way.

The fair payout for failing to call correctly both times is $0 you lose your stake.

The fair payout for correctly calling both times is

Stake x 1/(Probability of a win) = Stake x 1/0.25 = Stake x 4

Remember Tenet 2. It doesn't matter if you resolved the payout at the end of the second coin toss or whether your opponent settled up after the first one and you re-wagered all your bankroll on the second toss.

I.e.

Lose the first toss you are broke, you don't get to wager on the second toss. Bankroll is lost.

OR

Win the first toss and stake twice your original bet on the second toss at 50% probability.

The coin and the universe doesn't care if you settle up from the first wager and nip home for supper and a shower.

So, Accept the payout formula for a fair wager

Total return for a win=Stake x 1/(Probability of a win)

Now lets flip that about.

1/(Probability of a win)=(Total return for a wn)/(Stake)

Probability of a win=(Stake)/(Total return for a win)

In a win or lose wager where the only two possible outcomes are you lose your stake or you hit your target goal, you effectively have one wager where your stake IS your bankroll.

Probability of success=(Starting Bankroll)/(Total return for a wn)

Probability of success=(Starting Bankroll)/(Starting Bankroll+Target Profit)

That's almost the rule of thumb but not quite.

Probability of Success <= (Starting Bankroll)/(Starting Bankroll + Target Profit)

That's where the house edge come in. Nasty Nasty house edge.

With a positive house edge, Your probability for taking home the fair amount from a wager is less than it would be for a fair wager.

If House Edge is 0

Probability of Success = (Starting Bankroll)/(Starting Bankroll + Target Profit)

If House Edge >0

Probability of Success < (Starting Bankroll)/(Starting Bankroll + Target Profit)

Why do I not quantify or calculate the effect of house edge?

Frankly, I don't care to. It involves dealing with Standard Deviations and some tricky maths. I want newbies to see that even without house edge, their magical system can leave them with very tiny probabilities of turning a few Dollars into a lot of Dollars. And BIG probabilities for going BROKE!

E.G WITH NO HOUSE EDGE !!!

Probability of turning $100 into $1000 is 100/1000 = 10%

Probability of turning $10 into $1000 is 10/1000 = 1%

Probability of turning $10 into $10000 is 10/10000 = 0.1%

And if you don't succeed. YOU LOSE EVERYTHING.

But then again

Probability of turning $10000 into $10010 is 10000/10010 = 99.9%

### Comments

interesting. It does seem to me that HE would matter, but don't feel bad, I can be pretty dense sometimes.

the idea of setting a goal has never appealed to me much, but I agree we see a lot of posters ask about it.

Hi OG.

Thanks for the comment.

Of course, House edge 'matters' in that it can only detract from the player's probability of hitting his goal.

BUT. If his probability of hitting goal is negligible anyway and he is doomed to go bust, then the outcome isn't much changed :o)

E.g. Objective to turn $100 into $1,000,000 he has s0d all chance regardless of house edge. That's what I sought to demonstrate.

The Rule of Thumb is just that. It's actually very close in a low edge game where average wagers are a significant size ( e.g average wager 10% of bankroll)

It's Very, VERY close when using Marty.

## How not to make £15 ( same with $15)

OK. Confessing a bit of silliness:-In my online account, I'd been grinding away a small profit and had taken my most recent buy-in of £500 to just over £1100. I was pleased enough to have done that and had fun along the way. Fun is good.

Balance £11xx.00

So, I figured on withdrawing all except £500 off to my bank account, and so I did. Yesterday, I put in the withdrawal request for the roughly £650 withdrawal, which would take a week to process.

Online balance=£500.00

All is good.

Playing a few hands of Blackjack, I found myself at £485. (Last of the hi-rollers :o)

Dammit. I was not going to bed until I had my £500 back. No early night for me. I'd progressive bet my way back from 485 to 500 before bedtime. How about a bit of D'Alembert 2,4,6,8,10...

Didn't quite work out :o(

483

479

473

465

455

Dammit. Ramped up to a 25,50,75,75 progression.

.

.

.

.

Gravity won.

Went to bed with balance £0.00.

GRRRRRRrrrrrrrrr.

using a progressive to get from 485 to 500 should have been a doddle.

£0.00

GRRRRRRrrrrrrrrr.

So. what's a guy to do.

I guess, the only sane thing to do ( OK. Not exactly sane, more asinine)

Reverse that £6xx pending withdrawal and chase those losses back.

STOOOPID!

STOOOPID!!

STOOOPID!!!

I was going to have to almost double my balance.

Before going to work this morning, with aggressive betting, ground my way up to about £850. The only sane thing to do, would be to lick my wounds and stop to thank the Great Lady Variance for letting me have some of my losses back.

Pah!

But then I got home from work, just itching for a recovery. To hell with it.

£850,

Down a bit to about £500

Up a bit to about £1000

Down a lot to about £300

Sweat.

Up a bit of a lot back to £800

Ebb,

Flow,

Ebb,

Flow,

Staking up to £100 a hand with the odd scarey double or split.

Onwards and upwards to £1050

Itsy Bitsy Marty

£1150

Request my £650 withdrawal.

£500 balance.

I'd won back my stupid loss and got that £15 of revenge.

It could have been so easily SO MUCH WORSE, risking £1,100 + just to get revenge for a £15 loss.

Once again OnceDear is a lucky tit.

Don't try this at home.

$:o)

### Comments

So, Something very similar happened again.

A little below my £500 float.

Chased small loss.

Chased bigger loss,

Chased significant loss.

Quit chasing, very badly bruised.

OnceDear still a tit, this time not so lucky

The bankroll chart is too guesome to refresh and repost.

But at least the universe is working as it should.

$;o(

## £300=>£4280. A good, Month

OK. Feeling a bit chuffed with this month's BlackJack results.Last buy-in of £200 (Plus 2x£50 dead losses) has become £4280 of cashed out pocket money.

For February that puts me up £5880 and for BlackJack 'career' to date up from £100 to £18088

I haven't had a losing month since October 2015 which I ended at a humble £7775 rolling balance.

Charts updated in my earlier post.

http://wizardofvegas.com/member/oncedear/blog/2/#post1281

And this is just LUCK, folks. I claim no worthwhile AP skills. These are un-countable games and I had no 'Exploits' since October.

Total 'Action' to date just over £2.1M for which I earned comp bonuses of £2100

From an earlier post "Winning 10 times or more of one of my buy-ins seems to just happen far too often."

### Comments

I would find it all pretty addictive.

Sadly, I do too.

Just lobbed in 250 Credit. Blew it

another 250 credit: Blew it

Another 250 credit: Grew it to 1500

.

.

.

Then Blew it

$:o)

Oh.... It got worse. Time for a bit of APing before I p155 any more away on gambling like a ploppy. I do have an Advantage Play at my disposal. But it needs the discipline and patience not exhibited on this 'trip report'.

Laterz

Interesting post. Keep it up.

I'll be updating the charts soon. But be warned: It's a grisly sight.

In the last two months gravity has reasserted itself and the lifetime bankroll has taken a VERY severe beating.

Oh hum. Doing a bit of low rent AP to claw some back.

My downfall was getting cocky after February's bumper luck.

Well done, firts of all BlackJack - wow! What do you prefet BlackJack or Online Poker? www.highstakesdb.com/6453-online-poker-vs-online-blackjack.aspx Thanks for some advises. Best

It's very ironic that d'Alembert was actually a highly respected mathematician. But unfortunately for him he put forth a very wrong theory.

"While he made great strides in mathematics and physics, d'Alembert is also famously known for incorrectly arguing in Croix ou Pile that the probability of a coin landing heads increased for every time that it came up tails. In gambling, the strategy of decreasing one's bet the more one wins and increasing one's bet the more one loses is therefore called the D'Alembert system, a type of martingale"

## Comments

Well, you yourself predicted you'd get to this point.

Congratulations for clawing back, but actually if you were able to blow off losses as entertainment cost, it would be healthier. Thinking you need to chase? not good. But you knew that.

I continue to abstain from online gambling. I'm pretty sure I couldn't handle it.

Thanks OG,

The maths pretty much predicted it too. I recognise my behavior as dumb Dumb DUMB, and this time I was only saved from a £450 loss ( significant for me) by a big lucky break where I quintupled a buy-in.

In truth it still is well within the realms of entertainment budget. But I once again made the mistake of being emotionally attached to my lost money. Somehow I let it become important to me not to have a losing week.*

So far, I'm able to tone back my wagering and still have fun. It is OH SO EASY to throw down the kind of wagers online that you would never dream of in a live setting.

I'm particularly looking forward to staking the £25 that I have as a result of my parlaying the Cooperation Game winnings. I want to pitch dumb-ass money management head to head with Romes' and Mike's skilled Parlaying of their pooled winnings.

* Soon I'll update my lifetime bankroll chart and it will reveal that I was NOT a lucky tit earlier in the year. Tit: Yes. Lucky: No!

https://m.youtube.com/watch?v=Adw772km7PQ

Remember how it felt when you placed your first $100 bet?

High Stakes Virgin

http://www.youtube.com/watch?v=Adi4eb8my1M

00:40 01:45

Oh that's a cute one and how to play dumb as well. She is so dumb you would need a script to match.