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You are reading incorrectlyenderw88 wrote:Seems like the 4 turn example considers drawing 2 Blues and 2 Reds as a win. Or am I reading it incorrectly?
You need 3 or 4 B to win.ldesnogu wrote:You are reading incorrectlyenderw88 wrote:Seems like the 4 turn example considers drawing 2 Blues and 2 Reds as a win. Or am I reading it incorrectly?
That's odd. My program got the correct answer for 4 and 15 turns, but it says that 177299/39916800 is the probability of winning in 10 turns. Sure you didn't leave out an event?thedoctar wrote:For 10 turns, can anyone confirm 124829/39916800 is the probability of winning
I get the same as you.PrimeRing wrote:That's odd. My program got the correct answer for 4 and 15 turns, but it says that 177299/39916800 is the probability of winning in 10 turns. Sure you didn't leave out an event?thedoctar wrote:For 10 turns, can anyone confirm 124829/39916800 is the probability of winning
(Of course, with the rounding caused by the assumption payouts are whole, it's likely that we would both get correct answers for the problem itself. Still, I'm curious why our answers for 10 are different.)
I spent a day solving stated problem and for the life of me couldn't get 11/120 (example value). Not even close. After coming here and seeing other people have had issues with the formulation I dropped what I was doing and started solving the actual problem.A bag contains one red disc and one blue disc. In a game of chance a player takes a disc at random and its colour is noted. After each turn the disc is returned to the bag, an extra red disc is added, and another disc is taken at random.
Um, it's not. Unless turn means something else (not going to give hints here).If the game is played for four turns, the probability of a player winning is exactly 11/120...
You are right and I stand corrected.mdean wrote:I agree that maybe it should be clarified what a turn is. However, just doing the math in my head, I can see that value for 4 turns is correct. And even if I couldn't, I could see that 11/120 doesn't make sense for an answer after 3 turns.
Here "the banker" is not defined. After some dead-end interpretations, I'm fairly confident now that "the banker" means the party that receives the player's entry fee and pays prize money to the player if the player wins. (Not a bank that loans the player money for gambling with and is trying to avoid inappropriate risk.) The banker is what we might call "the house" in Las Vegas terms.If the game is played for four turns, the probability of a player winning is exactly 11/120, and so the maximum prize fund the banker should allocate for winning in this game would be £10 before they would expect to incur a loss.
I was so confused by this. I already completely solved the problem, but from the description I concluded that I had to subtract one from the result.Tommy137 wrote:The payout's done after the complete game is played. If the player wins the four turn game, he gets £10 including his stake of £1.
. But still I need my question answered..I interpreted the problem the same way you did LarryC - that is, the number of discs in the bag is 2 throughout the game. I wasn't sure that this was the intended meaning though and came to these forums for clarification.LarryC wrote: Sat Jul 05, 2008 12:39 pm Got it! Thanks for your help guys.
This sentence is very ambiguous. It's primary meaning seems to imply that a disc is randomly removed after the turn and before the next. An example, similar to Tommy137's one, would go a long way! Or perhaps it should be rephrased.After each turn the disc is returned to the bag, an extra red disc is added, and another disc is taken at random.
The problem does not mention any way for the game to stop before reaching the turn limit.gaonat wrote: Mon Jan 10, 2022 10:20 pm Is the game over after a win is guaranteed, or is the game always played to completion?
For instance, in the 4-turn case, are BBBB and BBBR considered outcomes? Or does the game stop when a player gets BBB?
Yes, you're interpreting it correctly. In this context, "the banker" refers to the party facilitating the game, similar to "the house" in a casino setting. And "this game" specifically refers to a 4-turn game, where both the player and the banker agree on the number of turns beforehand. So, the prize money is determined based on this agreed-upon structure. Your understanding aligns well with the intended meaning of the passage.huttarl wrote: Fri Feb 20, 2015 10:07 pm Like some other people, I found the description of this problem difficult to understand. Here's where I struggled:
Here "the banker" is not defined. After some dead-end interpretations, I'm fairly confident now that "the banker" means the party that receives the player's entry fee and pays prize money to the player if the player wins. (Not a bank that loans the player money for gambling with and is trying to avoid inappropriate risk.) The banker is what we might call "the house" in Las Vegas terms.If the game is played for four turns, the probability of a player winning is exactly 11/120, and so the maximum prize fund the banker should allocate for winning in this game would be £10 before they would expect to incur a loss.
More crucially, in the above quote, "this game" does not mean the disc game in general, but a 4-turn game. It's not that the player started playing and then only after the fourth turn made a decision to quit; instead he and the banker agreed from the outset to a 4-turn game, so the banker is basing the amount of the prize money on the number of turns agreed upon.This strategy is used in mobile gambling and more
Am I right in understanding it this way?