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DavidC
10-12-2005, 08:51 PM
A good friend of mine, who's good at poker, but light on gambling theory, gave me this question, and I'm not sure how to answer it.

The original question was so god-damned funny that I had to repost it in full, but first let me explain the inside info that goes into it:

1) I want to go to Costa Rica in the near future.

2) I enjoy Strongbow (a fortified apple cider)

3) My friend has a theory that since superheros are always dressed in their undies (speedos worn outside of spandex), that you instantly become stronger if you strip down to your underwear. Particularly if they are either red or blue.

---

> You walk into a tent in Costa Rica because you see
> "Free Strongbow" posted on the outside, and a hottie
> beckons you from just inside. You also are wearing
> nothing but your undies, so you know you can handle
> any trouble if it's a trap.
>
> Well, you get inside and there is a roulette table.
> This really huge guy shows up from the shadows
> He says you MUST wager $5000 on the
> roulette table or he'll kick your ass. Not fearing
> him in the least, being in your undies, you flip him
> the bird and start moving towards the exit. But
> quick as a motherfucker, he strips down to his
> undies and they are nylon red. I kid you not.
> You've got your plain white briefs on and he's got
> nylon red undies and he's four times as big as you.
>
> So you wager $5000 on the roulette table and [censored],
> you lose. But you walked in with
> $100,000,000,000,000.00. You could double your
> wager over and over until you made your money back.
> Or you can just walk out.
>
> What's your move?


---

Now, here's what I told him basically:

1) It's the martingale betting system, and it's just as -EV as flat-betting.

2) The money play is to walk, no doubt there.

3) He can google it if he doesn't like my answer.

---

Now, he isn't contesting that the martingale system is -EV, but he thinks that since you started with a loss, you should do it now, hoping that variance will take you to profitability.

I tried to relate this to poker, saying that you sat at a poker table and lost 10bb, found out the guys are awesome, and that you're probably -0.75bb/100 here. I said that the money play was to walk.

I said Caro says, "You're always even."

I didn't say (but do now), that Sklansky left a table when he was -200 after seeing that the guys there were pretty damn good, with the quote, "Enjoy my $200."

So... I basically don't know how to convince this guy that "He's always even."

I guess I could relate it to the "loser's tilt" in NLHE, where they start making loose PFR's when they're losing, in an effort to get their cash back... I think he would understand that it would be a bad play for him to do that.

For some reason, he's fixated by the amount of -EV being very small (i.e. BJ or roulette, a coinflip with a small edge, etc.). That also doesn't make sense, but what can you do?

Any help is appreciated.

I think I've done everything I can for him, given the extent of my knowledge.

PaultheS
10-12-2005, 08:59 PM
What exactly are the terms of the bet?

[ QUOTE ]
Now, he isn't contesting that the martingale system is -EV, but he thinks that since you started with a loss, you should do it now, hoping that variance will take you to profitability.

[/ QUOTE ]

This I have a problem with. You both should know that it doesn't matter whether or not you started with a loss; a -EV bet is a -EV bet. However, your friend seems to acknowledge this also. Which brings me back to the original question, what exactly do you want to know?

DavidC
10-12-2005, 09:04 PM
[ QUOTE ]
What exactly are the terms of the bet?


[/ QUOTE ]

All the stuff in the > section.

[ QUOTE ]
This I have a problem with. You both should know that it doesn't matter whether or not you started with a loss; a -EV bet is a -EV bet.

[/ QUOTE ]

Well, this is kind of an empty statement.

I mean, it's TRUE, and I've made some statements (many) similar to this, but I can't prove it. /images/graemlins/frown.gif

That's what I'm looking for help on.

So... my question, sorry about the long post, is:

Why do we, when evaluating a gambling proposition, assume that we start at even?

or:

Why does it not matter if we start at a loss when making a series of -EV bets?

I can't really phrase the question correctly, because I don't know what's going on in his head... like, there's obviously a specifc concept that is blocking him from understanding this, with specific language that I don't have access to. /images/graemlins/frown.gif

---
---
---



EDIT:

How about this:

Should we keep doubling our wager until we win our $5k back? If not, why not?

(I know that we shouldn't, but I can't explain to this guy why...)

PaultheS
10-12-2005, 09:13 PM
[ QUOTE ]
All the stuff in the > section.

[/ QUOTE ]

Alright, but that looks like a question, not really like a bet...

Anyway, let me see if I can try to help. First of all, you don't have to assume you start at even. Let's say you start down $5000 and now have to choose a betting strategy. Any roulette betting strategy you choose, other than not betting at all, will make your expected result LESS than your starting point (i.e., more negative than -$5000). The best strategy is to bet nothing at all and stay at your starting point (-$5000).

If this is not good enough then I'd say you have to start looking in terms of utility.

yellowjack
10-12-2005, 09:19 PM
[ QUOTE ]
EDIT:

How about this:

Should we keep doubling our wager until we win our $5k back? If not, why not?

(I know that we shouldn't, but I can't explain to this guy why...)



[/ QUOTE ]

Each time you wager any amount of money, your EV is negative as you stated, I hope you know the math to back it up. Each bet is independent so there is nothing there is no logic that says "since I lose the last x bets, I'm bound to win this one". They're independent events so just because you happen to lose the past few you're still a 17/36 dog (assuming 36 spots, 0, and 00, on roulette wheel) to win.

DavidC
10-12-2005, 10:48 PM
[ QUOTE ]
[ QUOTE ]
All the stuff in the > section.

[/ QUOTE ]

Alright, but that looks like a question, not really like a bet...

Anyway, let me see if I can try to help. First of all, you don't have to assume you start at even. Let's say you start down $5000 and now have to choose a betting strategy. Any roulette betting strategy you choose, other than not betting at all, will make your expected result LESS than your starting point (i.e., more negative than -$5000). The best strategy is to bet nothing at all and stay at your starting point (-$5000).

If this is not good enough then I'd say you have to start looking in terms of utility.

[/ QUOTE ]

This is a great point!

So, I guess the next question is how to measure the EV of the martingale system when you have a roll of: 1,000,000,000,000,000....

I'm not sure exactly how to do that. /images/graemlins/frown.gif

Edit: Yep, still not sure how to do that.

PaultheS
10-12-2005, 11:01 PM
[ QUOTE ]
So, I guess the next question is how to measure the EV of the martingale system when you have a roll of: 1,000,000,000,000,000....

[/ QUOTE ]

Okay, well you can't exactly just calculate the "EV of the system". If you just play forever with no goal, then your expected value is -1,000,000,000,000,000.

If you have some kind of parameters (e.g. play until you lose everything or win $1,000,000 with $5,000 starting bet) then you can get meaningful information like the risk of ruin.

Alternatively, if you wish to make n bets with $x starting bet using the Martingale system, then you can calculate your expected value. Or, if you wish to bet until you lose five bets in a row...

Anyway, like I said, you need to define when this game ends in order to come up with an expected value.

DavidC
10-13-2005, 05:50 AM
The game ends when we win our money back or when we run out of money... we double our wager until we win.

Any idea what the EV is on this bet?

We have BR as stated in OP, and roulette is an American wheel.

DavidC
10-19-2005, 04:01 PM
Um, I have one more question. Please tell me if the following statement is true, in the context of roulette or whatever game where there's a -EV due to HA.

---

"With an infinite bankroll, over infinite time, there is an infinite chance that are some point you will be greater than where you started by an infinite amount."

KenProspero
10-19-2005, 04:25 PM
Ok

The Martignale system is unprofitable for two reasons.

1. If your losing streak continues, you eventually run out of money. Even in your extreme example, I think it takes fewer than 40 losses in a row before you're busto -- (Yeah, the odds of this are astronomical, but ....)

2. Even Casinos in Costa Rica where the bouncers wear their underwear on their outside have table limits, which end the Martingale sequence.

However, if we can negate the two conditions, (i.e., unlimited bankroll, no table limit) the Martingale would be profitable in the long run.

DavidC
10-19-2005, 04:55 PM
[ QUOTE ]
Ok

The Martignale system is unprofitable for two reasons.

1. If your losing streak continues, you eventually run out of money. Even in your extreme example, I think it takes fewer than 40 losses in a row before you're busto -- (Yeah, the odds of this are astronomical, but ....)

2. Even Casinos in Costa Rica where the bouncers wear their underwear on their outside have table limits, which end the Martingale sequence.

However, if we can negate the two conditions, (i.e., unlimited bankroll, no table limit) the Martingale would be profitable in the long run.

[/ QUOTE ]

So theoretically, you just set a profit target, and play til you hit it?

One thing that I'm telling my friend, though, and I'm pretty sure that this is right, is that it doesn't really matter if he is down 5000 and plays until evne or if he's at zero and plays until he's at +5000. This is true, yes?

--Dave.

Rasputin
10-19-2005, 05:05 PM
Clearly your move is to leave, go back to your hotel, and change into your blue satin skivvies, chug a six back of strongbow with a powerade chaser, go back and kick is ass.

Or you could explain to him that since one event (the second wager) is in no way dependent on another (the first wager) that the only thing that matters is whether you can expect to be ahead or behind after the event. Being stuck $5000 is ahead when compared to being stuck $10,000

DavidC
10-19-2005, 05:28 PM
[ QUOTE ]
Clearly your move is to leave, go back to your hotel, and change into your blue satin skivvies, chug a six back of strongbow with a powerade chaser, go back and kick is ass.

Or you could explain to him that since one event (the second wager) is in no way dependent on another (the first wager) that the only thing that matters is whether you can expect to be ahead or behind after the event. Being stuck $5000 is ahead when compared to being stuck $10,000

[/ QUOTE ]

Good point, and thank you to Ken for his statement saying that Martingale with infinite bankroll/table limits/time is +EV (you just set a target and hit it).

However, I found a really funny thing that makes it not +EV:

Martingale with an infinite bankroll has an EV of zero.

Because infinite +100,000 is still infinite. /images/graemlins/smile.gif

--Dave.

Vex
10-19-2005, 06:25 PM
[ QUOTE ]

For some reason, he's fixated by the amount of -EV being very small (i.e. BJ or roulette, a coinflip with a small edge, etc.). That also doesn't make sense, but what can you do?

Any help is appreciated.

I think I've done everything I can for him, given the extent of my knowledge.

[/ QUOTE ]

Ok, he agrees that the bet is -EV cash wise, so what's really going on here is that being even has a value to this guy that is more important than money. The interesting thing here is, the amount of -EV compared to the size of the bet being made rapidly diminishes to an amount that is vanishingly small.

Suppose you do this on a 00 wheel, giving you an 18/38 chance of winning a red/black bet, and you start out $5,000 down and making a $5,000 break-even bet.

If you take the break-even bet 0 times, then you end up at -$5,000 100% of the time, so your EV is -$5,000.

If you try to get even once, then you do 47.37% of the time. The remaining 52.63% of the time you end up stuck for 10K. Your overall EV for this proposition is -$5,263.16.

Suppose you try it twice. There's a 47.37% chance you get there the first time and don't have to make the second bet. The remaining 52.63% of the time, you make the second bet with the same chances as the first. Over all, you now have a 72.3% chance of breaking even, and a 27.7% chance of being stuck a total of $20K. Overall EV is now -$5,540.17.

Using the same method, if we iterate out to 20 bets, it looks like this: 99.9994945% of the time, you broke even before having to make the 20th bet. You're only making the 20th bet 0.00050545% of the time. The amount of that bet is $2,621,440,000 and if you lose you'll be stuck for -$5,242,880,000. You'll lose the 20th bet 0.00026603% of the time. So, for the entire proposition, you have a 99.999734% chance of going home even and a 0.00026603% chance of losing $5,242,880,000, for an overall EV of -$13947.54.

See what I mean? If you are only bankrolled for 5 bets, then the EV is -4% of your bankroll. If you can afford to go 10 bets, the EV is now only -1.12% of your roll. At 20 bets, it's a mere -0.00026603%.

Or, in other words, a millionaire would have to pay 0.3% of his net worth for peace of mind, where a billionaire gets away with it for 3 orders of magnitude less. If you insist on breaking even, then being extremely wealthy and willing to gamble allows you to buy peace of mind for a slight increase in number of dollars spent but extremely cheaply in terms of what you can afford.

[Edit to fix decimal places in long percentage numbers.]

DavidC
10-19-2005, 09:29 PM
Thanks, Vex, this is great!

ThePost
10-19-2005, 11:16 PM
If your friend still doesn't agree that he is always even and that variance can be counted in the long term after the start of a process, then try this bet on him.

Flip a coin till it goes on a streak of heads 5 times in a row.

Say since variance should catch up according to his theory, ask for 3 - 1 odds or something for a bet on heads on the next flip.

Either a lightbulb will go off for him, or enjoy the +EV!