Uh... could someone help me with this weird prop bet?

[DavidC]

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.

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> 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?


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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]

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]

[ 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. [img]/images/graemlins/frown.gif[/img]

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. [img]/images/graemlins/frown.gif[/img]

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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]

[ 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]

[ 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]

[ 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. [img]/images/graemlins/frown.gif[/img]

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

[PaultheS]

[ 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]

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]

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.

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"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]

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.