Quote:
Originally Posted by RustyBrooks
I think I understand the system. He decides which to bet on by which one will get him to one of the endpoints that he wants. He wants to do 4 flips, ending either with 2 heads, or with 4 heads or 4 tails. See PairTheBoard's post.
...
Then on the 4th bet you bet on the one that gets you to one of "our" sequences.
Okay, I think I see that part.
Quote:
It *sounds* like for bets 2 and 3 that he bets both sides. I don't understand why you'd do this. Maybe not betting is not optional in this scheme.
I'm just going to assume we sit out bets 2 and 3 because why bet both sides and lose money?
Quote:
(I *really* wish he would settle on a 1:1 payout instead of 1000:999 so we don't have this decimal nonsense above)
I'm just going to do type up this whole thing with a 1:1 payout, since it's not obvious at all what the 0.001 does except make it a -EV game. The same strategy should do better if the payout is better.
Code:
1st bet: 4 on T.
2nd bet: Sit out
3rd bet: Sit out
4th bet: 8 according to criteria
HHH you bet H
HHT you bet T
HTH you bet T
HTT you bet H
THH you bet T
THT you bet H
TTH you bet H
TTT you bet T
1.HHHH = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, win) = +8
2.HHHT = -4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, lose) = -8
3. HHTH = -12
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, lose) = -8
4. HHTT = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, win) = +8
5. HTHH = -12
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, lose) = -8
6. HTHT = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, win) = +8
7. HTTH = -12
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, lose) = -8
8. HTTT = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, win) = +8
9.THHH = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, lose) = -8
10.THHT = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, win) = +8
11. THTH = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on H, win) = +8
12. THTT = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on H, lose) = -8
13. TTHH = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, lose) = -8
14. TTHT = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, win) = +8
15. TTTH = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, lose) = -8
16. TTTT = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, win) = +8
And so in the end, it looks like a 0 EV game is, in fact, 0 EV.