What is the chance of losing a game where you have a 50% of winning each round, 5 rounds in a row?

[Flip]

<div style='font: 10pt Tahoma; text-align: left; '>I ask because of this, i recently (for fun) started a sports gambling account on some betting website where i could put 5-10 dollars down on a football game. It has been fun and makes watching the games pretty exciting even when we are only talking about 5 bucks. For the last few week i've turned my 20 dollar initial deposit into 30 ^_^

Today, i noticed on the site that they also have a video craps game that lets you bet with your money. When you bet on the pass line, winning at craps is basicaly 50%, or maybe more like 47,48% since the house always has a slight advatange. Anyways, my system has been to put 1 dollar on the pass line, if i lose i'll put $2, if i lose that i'll put $4, then $8 then $16. That means i would have to lose 5 in a row to lose all my money, but if at any time i win one of those i have, essentially, won $1 to my total and i start back over at betting $1. So far, i've creeped up to $40, this system really seems to works. In fact, i havent even gotten to the 5th game yet before starting over at $1, so the most in a row i have lost so far is 3 before i win, increase my total by $1 and start back over.

This leads me to believe that is someone started with say $1,023 to where they could double their bets for 10 times, would they ever lose? How can you possibly lose a game 10 times in a row when you have a 50% chance of winning? If that is the case then you could creep that $1,000 up slowly by a dollar for an unlimited amount of times. It would take a while, but you could win a few hundred eventually, i think.

It has been looking like this:

started with: 30
bet 1: lose: 29
bet 2: lose: 27
bet 4: win: 31

bet 1: win: 32

bet 1: lose: 31
bet 2: win: 33

bet 1: lose: 32
bet 2: lose: 30
bet 4: win: 34

etc...

I've cracked vegas! ^_^</div>

[Flip]

<div style='font: 10pt Tahoma; text-align: left; '>the probability is (1/2)^5 or 1/32, guess i should stop soon.</div>

[Don]

<div style='font: 12pt ; text-align: left; '>Unfortunately, that is rarely the case.

The chance of losing 5 in a row is 1/32, but losing 5 in a row once will cost you $32, so you win $31 on the other 31 times you didn't lose 5 in a row, but you get set back to 0 when you do lose.</div>

[Kupek]

<div style='font: 10pt verdana; text-align: left; padding: 0% 10% 0% 10%; '>If you have a lot more money than the house, then you really don't need to gamble.</div>

[ManaMan]

<div style='font: 12pt Arial; text-align: left; '>.5*.5*.5*.5*.5=1/32, roughly 3%.</div>

[Flip]

<div style='font: 10pt Tahoma; text-align: left; '>Who woulda thought this would be a softspot for me, maybe its just so fun because i've never really gambled before and its new.</div>

[SineSwiper]

<div style='font: 10pt "EngraversGothic BT", "Copperplate Gothic Light", "Century Gothic"; text-align: left; '>Stop after 16*5 rounds. That would give you roughly a 50/50 chance of winning a lot of money.</div>

[Don]

<div style='font: 12pt ; text-align: left; '>Might as well bet a lot of money on the first round, that's also 50/50 of winning a lot of money.</div>