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+--- Thread: Yet Another Probability Problem (/thread-6877.html)
Yet Another Probability Problem - AltruismAndCake - 06-28-2015
You start with $1000. You get to play a game of double or nothing for 10 rounds, betting any amount you want. You also magically know that you will win exactly 5 rounds and lose 5 rounds, but you don't know what order the wins and loses will happen in. What's your best strategy for profiting guaranteed?
RE: Yet Another Probability Problem - PabloDons - 06-29-2015
if I lose even once, I have nothing to double, so I would say flip a coin on the first one, but then the chances to win the next will be lower cuz you will win 4 times and lose 5 times.
I say flip a coin on the first one, then go for that
RE: Yet Another Probability Problem - Apuly - 06-29-2015
Constantly bet everything, until you've won 5 times. Then just bit 1$.
RE: Yet Another Probability Problem - AltruismAndCake - 06-29-2015
@Pablo You don't have to bet all your money all the time. You can bet half of it ($500) and then that amount will be double or nothing, not all your money. Sorry if I didn't make it clear. Also you don't choose heads or tails, you just win or lose, no matter what the bet is.
@Apuly what if the first round is a loss? You would be out of the game on the first go xD. Also, $0 is an option in this game if you know you are losing.
There is a strategy for guaranteed money after the 10 rounds, with no cheating and no coin flipping. If you need hints I can give you some
I know how to make a (very) small profit within these rules, I just want to see if anyone knows a better strategy
RE: Yet Another Probability Problem - qwerasd205 - 06-29-2015
for the first bet you bet $500, and then as long as you lost your most recent bet you bet half of your total money. if you win a bet bet 1/4 your total money.
RE: Yet Another Probability Problem - qwerasd205 - 06-29-2015
Another strat I thought of is start at 1/4 and then every time you lose double your bet and when you win go back down to 1/4
RE: Yet Another Probability Problem - qwerasd205 - 06-29-2015
wait that's an awful idea.
RE: Yet Another Probability Problem - qwerasd205 - 06-29-2015
Always bet half your money until EITHER:
you have lost 5 times:
Go all in! you can't lose and you'll get back up to 1000!
OR
you have one 5 times:
bet $0 for the rest of the game.
RE: Yet Another Probability Problem - AltruismAndCake - 06-29-2015
(06-29-2015, 02:25 AM)qwerasd205 Wrote: for the first bet you bet $500, and then as long as you lost your most recent bet you bet half of your total money. if you win a bet bet 1/4 your total money.Assuming you do what you did on post #4, and bet everything after all the loses, and $0 after all the wins, this is a pretty good strategy. If you lose 5 times in a row, you can recover all your money back, but no gain. If you win 5 times in a row, you get around $3662 as your total. If you get LWLWLWLWLW you get a total of $1201, without applying the strategy for the final win. So it would actually earn even more than $1201. For other patterns though, it's a bit weaker, like LLWWLWLWLW will make a total of $667. Again though, if we take into account the final guaranteed win, you would do better. All in all a good strategy, just no guaranteed gains.
(06-29-2015, 02:30 AM)qwerasd205 Wrote: Another strat I thought of is start at 1/4 and then every time you lose double your bet and when you win go back down to 1/4With this strategy you run out of money a bit quick if you lose a few, perhaps a smaller fraction that than starting with a fourth? You were getting really close to my strategy here
(06-29-2015, 02:33 AM)qwerasd205 Wrote: Always bet half your money until EITHER:Second part of the strategy is sound, but betting half of your total money each bet is actually one of a few terrible strategies for this game. Without the second part, you are actually guaranteed to lose money with this strategy! The amount you lose is 25% every two rounds you participate in, so $1000 * 0.75^5= $237, if you don't include the second part. The second part of this post gives a major advantage, but I think it's a better fit for one of your other strategies
you have lost 5 times:
Go all in! you can't lose and you'll get back up to 1000!
OR
you have one 5 times:
bet $0 for the rest of the game.
RE: Yet Another Probability Problem - Apuly - 06-29-2015
(06-29-2015, 02:11 AM)AltruismAndCake Wrote: @Apuly what if the first round is a loss? You would be out of the game on the first go xD. Also, $0 is an option in this game if you know you are losing.
It's double or nothing. If I lose, I just go double or nothing.
It has never been stated that I can't go outside my budget.