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

[DavidC]

[ 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]

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]

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

--Dave.

[Vex]

[ 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]

Thanks, Vex, this is great!

[ThePost]

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!