Opinions of the Martingale Betting System

[RS]

Martingale won't work, in the long run, because it isn't able to identify +EV betting situations. On average, you are playing at a disadvantage. Without having the ability to know when you're betting into +EV or -EV hands, you're going to be betting into -EV situations, most of the time.

Let's say you're playing a 0.5% HE game. Every bet you make, your EV is -0.5% of the wager.

EV is additive. Each hand you play is -EV. You can't add up a bunch of negative numbers and end up with a positive one. You can't get an edge using (only) the Martingale system.



On the other hand, if you don't care about playing a -EV game, but play purely for entertainment, and you find it entertaining to use the Martingale and "win a little most of the time" but also "lose huge very rarely".....then go ahead. Just remember, you aren't playing with an edge. And eventually, you will hit a severe losing streak, wiping out all your profits, and then some. Be careful.

[Pierce]

I'm surprised no-one has mentioned table limits here. If you had an infinitly large bankroll (replenishable), and no table limits then martingale <i>would</i> work in the long run, since you could effectively double your way through any loss since a) you have infinite money and b) there is no cap on your bet.

Of course this is all hypothetical, since even Bill Gates would run out of money eventually, and all casino games have a betting limit.

[Solo player]

A quick search on You Tube found this about Martingale; https://www.youtube.com/watch?v=W2yjuxZAT5k

[BugsySeagull]

OK someone help me with my math, I think I made a mistake. I'm trying to prove that Martingale is a bad idea, and my math may have proved that it's a good idea with proper bankroll and starting bet.

Let's say you're playing double-zero roulette (because I don't know the house edge of blackjack if you never double or split), starting at $5. You have $1300, that's enough bankroll to withstand 8 losses in a row, but not 9. You bet red on every spin.

The chances of losing the first spin is 0.5263, or 52.63%.

The chances of losing 2 spins in a row are 0.5263^2, or 0.2770, or 27.7%.

The chances of losing 9 spins in a row are 0.5263^9, or 0.0031, or 0.31%

That means that losing 9 spins in a row will happen 31 times for every 10000 times you go through a martingale sequence. So once every 322 sequences will end with failure, and you lose $1275. But that also means that 321 out of 322 sequences will end with a $5 win. Winning $5 321 times get you $1605. Losing $1275 after that gets you a net win of $330.

So if you bankroll this properly, and you reset back to your base minimum bet after a 9 spin losing streak, and you don't mind going from table to table in order to be able to place the size of bet necessary, you can be ahead in the long run using martingale.

My arithmetic must be off, right?

[BugsySeagull]

OK someone help me with my math, I think I made a mistake. I'm trying to prove that Martingale is a bad idea, and my math may have proved that it's a good idea with proper bankroll and starting bet.

Let's say you're playing double-zero roulette (because I don't know the house edge of blackjack if you never double or split), starting at $5. You have $1300, that's enough bankroll to withstand 8 losses in a row, but not 9. You bet red on every spin.

The chances of losing the first spin is 0.5263, or 52.63%.

The chances of losing 2 spins in a row are 0.5263^2, or 0.2770, or 27.7%.

The chances of losing 9 spins in a row are 0.5263^9, or 0.0031, or 0.31%

That means that losing 9 spins in a row will happen 31 times for every 10000 times you go through a martingale sequence. So once every 322 sequences will end with failure, and you lose $1275. But that also means that 321 out of 322 sequences will end with a $5 win. Winning $5 321 times get you $1605. Losing $1275 after that gets you a net win of $330.

So if you bankroll this properly, and you reset back to your base minimum bet after a 9 spin losing streak, and you don't mind going from table to table in order to be able to place the size of bet necessary, you can be ahead in the long run using martingale.

My arithmetic must be off, right?

I've saved you all the trouble and figured out that indeed my math was off.

In order to withstand 8 losses in a row, starting with a $5 minimum bet, you would need about $2600, because your 9th bet would be $1280, not $640. So if your 9th bet loses, you lose a total of $2555 on once sequence.

This loss of $2555 will still happen once every 322 sequences. And 321 sequences out of 322 will end with $5 wins. So $2555 in losses minus $1605 in wins equals $950 in net loss.

So every time you start a martingale sequence on double-zero roulette, your $5 will give you a loss of $2.90. So don't do martingale.

[Dieter]

I've saved you all the trouble and figured out that indeed my math was off.

In order to withstand 8 losses in a row, starting with a $5 minimum bet, you would need about $2600, because your 9th bet would be $1280, not $640. So if your 9th bet loses, you lose a total of $2555 on once sequence.

The problem with martingale is practical, not theoretical. In theory, martingale cannot lose.

To implement the theory, you need an almost unlimited bankroll, and to be allowed to play it. The bankroll and table maximum limit how deep into the progression you can get (without moving tables).

As you pointed out, after 8 losses, you're laying $1280 to win net $5. This is after you've already lost $1275.

The real trouble is that around the 250 losses stage, you need enough betting units - a quantity on par with the number of atoms in the observable universe. For a bet that size to be effective, the house has to have a like number of chips. Even with trillion-unit plaques, that's going to start distorting gravity, and probably warp (or even break) the table, meaning they'll call "no spin" when the wheel isn't level anymore.

This isn't a problem with martingale, however - just a problem with the universe we live in. Once you have enough money to really make martingale work in our universe, there are easier ways to make $5.

[Three]

Well you see that's the thing - you have the option to double down; you're not obligated to. It's simply an add benefit.

Just as you do with every other bet. How is that an ADDED benefit. It is a benefit associated with every bet you make. Nothing special about a larger bet unless it is made at a large advantage.

The Martingale forces you to make large bets even when the count is unfavorable; I don't disagree.

There's your answer. No added benefit to doubling since the bet is made independent of advantage. At higher counts you will double more frequently and get better results for your doubles as a group. Now that IS an ADDED advantage but unfortunately not for the martingale bettor.

[Three]

I'm surprised no-one has mentioned table limits here. If you had an infinitly large bankroll (replenishable), and no table limits then martingale <i>would</i> work in the long run, since you could effectively double your way through any loss since a) you have infinite money and b) there is no cap on your bet.

Of course this is all hypothetical, since even Bill Gates would run out of money eventually, and all casino games have a betting limit.

This all assumes you will win a hand before you die. There is a chance you will never win a hand again. When you start talking infinity no matter how much you lose you still have infinity. No matter how much you win you still have infinity. There is nothing to be gained or lost other than the waste of time you spent doing something that can't raise or lower your BR.

[Three]

My arithmetic must be off, right?

Go back to 4th and 5th grade math. You can rearrange the addition order of the bets made without changing the sum. Remember the first theorem you learned in math class, The Commutative Law of Addition ( where, (A+B)+C=A+(B+C)).Just add all the same sized bets together to get a sequence and then d the math. It's pretty simple HE*total bet equals amount you expect to lose. All betting more does is increase the speed you expect to lose money while rearranging how that will happen to be a very gradual increase in BR followed by a precipitous fall in BR that sums to this expectation of loss equals total bet times HE. I am guessing that nobody will argue that flat betting many different bets will give you an advantage. The progression can be rearranged to bet size groups instead of progression groups without changing the total. Just ask a fifth grader. They can tell you that.

[Exoter175]

I would like to know the pros and cons of the Martingale System. Personal ventures with it. Has anyone been profitable with it.

Pros: It sounds cool
Cons: It doesn't work anymore

Yes. The casinos have been very profitable from player's using Martingale.

Hahahahahaha, so true, and I've seen it first hand!

[BugsySeagull]

Go back to 4th and 5th grade math. You can rearrange the addition order of the bets made without changing the sum. Remember the first theorem you learned in math class, The Commutative Law of Addition ( where, (A+B)+C=A+(B+C)).Just add all the same sized bets together to get a sequence and then d the math. It's pretty simple HE*total bet equals amount you expect to lose. All betting more does is increase the speed you expect to lose money while rearranging how that will happen to be a very gradual increase in BR followed by a precipitous fall in BR that sums to this expectation of loss equals total bet times HE. I am guessing that nobody will argue that flat betting many different bets will give you an advantage. The progression can be rearranged to bet size groups instead of progression groups without changing the total. Just ask a fifth grader. They can tell you that.

I don't think the average 5th grader would explain it like you would.

Anyway that's not what I was trying to prove at all. People who believe that Martingale works do so because of the "eventually you have to finally win" aspect of it. They think "what are the chances that you actually lose X number of hands/spins/rolls in a row?" I had to explain this to my cousin when we were in Vegas last month when he told me that you can win at roulette by doubling your losing bet. He thought that there's just no way any one color will hit more than 9 or 10 times in a row. And he's not a moron, he's a doctor! I had to explain that you're not guaranteed to eventually win before your bankroll runs out. I had to take him to ask a pitboss in the casino how many times he's seen red or black hit consecutively, and my cousin was floored when he said 17 blacks in a row. That's just one pitboss in a city with how many roulette wheels? Thankfully he heeded my warning.

[Norm]

Dealer told me he once dealt himself seven consecutive blackjacks.

[KJ]

Dealer told me he once dealt himself seven consecutive blackjacks.

I think I was at that table. I have seen 3, multiple times. I think I would have to get up and leave after the fourth regardless. There is a good chance the count would be heading negative, or if it was a good count be back down to neutral, plus he's used up all the aces. So, I would exit, and play the part of disbelief, even if it was just for show.