You have $1000 and your goal is to get $1500.?

Question

You have $1000 and your goal is to get $1500. The way you are trying to get the money is by betting on coin flips in which you have an equal chance of getting heads or tails. The house sees your bet each time (so if you bet $1 then you will either lose or win $1, if you bet $20 and you win then you win $20). You are only allowed to bet money that you have (if you get down to $0 then you lose) What should your strategy be to give you the highest chance of reaching $1500?

Answer 1

You can't use the doubling your strategy bet because we are looking at a 50% increase in money and even thought you have a very small chance of losing if you go 1 then 2 then 4 then 8 till you run out of money, because you only gain one dollar each time you would have to do it 500 times in a row and the probability of you losing is actually 1/516 so that doesn't actually give you an edge at all. The best strategy is to bet $500 this gives you a 50% chance of winning and then a 25% chance of ending back at $1000 then, if you get back to a thousand you have another 50% chance of winning so you add that to your original chance so you have 50% plus 50% of 25% (the chance that you have of getting back to $1000) and you end up with 62.5% however you can do it again and again so then you do 62.5 plus 25% of 25% of 50% which is 3.125% so you end up with 65.625 and you can keep repeating that process and the answer eventually is 66.6666.....% or 2/3.

Answer 2

Since this is a fair game, in the long run you can expect to break even and end up with the $1000 you started with, on average. If you had an infinite amount of time, I don't think it matters how much you bet, as long as it isn't more than $500.

For example, starting at $1000, if you made a single $500 bet you have a 50% chance of ending up at $500 and a 50% chance of ending up at $1500. But if you kept betting $1 at a time until you either won $500 or lost $500, you also have a 50% chance of ending up at $500 and a 50% chance of ending up at $1500. So as far as strategy goes, how much you bet doesn't matter, as long as it isn't more than $500.

Since you probably don't want to be playing for days, weeks, or months at $1 per game, I would suggest betting $500 at a time, just to speed things up.

You should note that if this wasn't a fair game, for example, if the house only paid you 99 cents for each dollar bet, you would want to bet more money at a time to have a better chance of winning. This is because with smaller bets, the total amount you will need to bet to reach your goal will be much higher, and the house edge will take away more of your winnings and make reaching your goal that much more difficult.

Answer 3

I took probability twice in college and got A+ both times. The answer is that there mathematically is no best strategy. There is no correlation between any coin flip and any other. Whether you make 1 bet or 1 billion bets before you leave the table, you are going to leave with an average of $1000 in your pocket. That's because it's a perfect 50/50 chance each time.

If you had a 49% win/51% lose ratio, your best strategy would be to bet it all once, because your sure to lose in the long run. If you had a 51%win/49%lose ratio, your best strategy would be turn bet the smallest amount possible as long as you can, because in the long run you're sure to win money. But with a perfect 50/50, it doesn't matter mathematically how you bet .That's the best way that I can explain it without getting into a bunch of boring mathematical detail. The only way would be if you believe in luck to bring your lucky rabbits foot, do a voodoo chant, give to charity, prey to god,
or whatever it is you think brings you luck.

Other than that, it doesn't matter.

Sorry.

Answer 4

Since it's a fair game (the house has no advantage - obviously this isn't taking place in a casino!) then by betting one penny each time, you will almost certainly eventually have $1500. The reason is that on average you should stay about at $1000, but due to random chance you'll swing this way and that. Betting the smallest amount means the swings will be smaller, so you have a lower chance of busting out.

Of course, it'll probably be a REALLY REALLY long time before you get to $1500 :-)

Answer 5

Pick an amount to start, say $1. If you win, you're up a dollar. If you lose, you double your bet for the next flip. By doubling each time, when you win you will be up your original bet. This can be repeated until you reach your goal. I'd personally start with 1/31 of your stack... as long as you don't lose 5 times in a row you're fine.

Answer 6

I am surprised noone here menationed that strategy.

You bet one, if you loose you put next time 2, if you loose 4. 8.... In that way you have the best chance to always win. If you decide that when you reach 16 you quit and start again with 1 cause you dont want to loose mroe money I am sure the chance of ending with 5 mistakes in a row is not big so you can try this.

Answer 7

There is nothing you can do to skew the odds in your favor to profit one way or another by the way you bet. You can try anything you want but you'll only stay even for most of the time, unless you go for broke and just bet $500 and hope for the best.

Answer 8

It's random chance with no advantage to the house.

You could bet a penny each time with minimal risk. BUT, you would probably not get to your $1500 goal in a whole month.

I would reccomend betting 250 each time.

Answer 9

I believe Derrek is correct-bet $500 each time until you either reach your goal or go bust..I think this would give you a 75% chance of reaching your goal.

Answer 10

bid 1500$ at least its a 50% chance