# Thread: tricky algebra: With a fair coin, my opponent flips 50 times, with fair odds, ie,...

1. Note also, that you may be assuming one flip has ANYTHING to do with some other flip. If the flips are dependent, then you should bet LESS after each win.

2. Hi 'tkhunny' - as to your questions

1) Yes, as we don't know whether any flip will be a win or lose.

2) No

3) "proportion" just means how much we bet each time.

All my efforts, I'm afraid, have not worked. Hence I tried this website.
I left school too long ago to remember my A level work.
Thought it would be a good question for people that like problem solving.

3. You earned my respect by simply answering my questions.

1) If you lose 15 in a row, you will lose only 15 - one each round.
2) If you win 15 in a row, you win 32,767 - twice as much for each of 15 rounds.
3) The unfortunate thing is the utter and complete loss of everything because of the bet-doubling. If you win 14 in a row and lose the last, you're still a dollar down after 15 rounds.
4) The probability of being ahead after 15 rounds is 29.66%. Mostly, this is a result of the odd wiping-out of everything after a single loss.
5) A cute histogram of outcomes

 Bin Frequency % -100 13,012 39.71% -50 4,752 14.50% -20 3,624 11.06% -10 992 3.03% 670 2.04% 10 454 1.39% 20 430 1.31% 50 1,080 3.30% 100 1,296 3.96% More 6,458 19.71%

"-50" means "a loss of 50 or more, but not so much as 100", eg. -50.00 - -99.99.
"100" means "a gain of 100 or less, but not so little as 50", eg +50.01 - 100.00

Like I said, spreadsheets work. It will take a substantially different betting strategy to improve the outcome.

4. Hi tkhunny

I wasn't thinking of using a spreadsheet, is this Excel?
I gather the formula used is, on a win, double the bet, on a lose, back to 1?

Cheers
Dave

5. Your instruction was to maintain the bet on a loss, not reset to 1.

I used MS Excel 2016. It was tedious, but not particularly difficult.

6. I didn't give any instructions.

That was the question in the first place, how much to bet each time.

7. Originally Posted by daveylibra
I didn't give any instructions.

That was the question in the first place, how much to bet each time.
Yes, you did.

Review:

2) Do you reset back to the initial amount on a loss? Maybe just 1/2 and back to where you were on the previous bet.

Hi 'tkhunny' - as to your questions

2) No

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