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

1. 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.

2. 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.

3. 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

4. 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.

5. I didn't give any instructions.

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

6. 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