Probability   Event

    0.312500   6 before 8 or 7 in continuous rolling
    0.312500   8 before 6 or 7 in continuous rolling
    0.375000   7 before 6 or 8 in continuous rolling


    0.454545   6 before 7 in continuous rolling
    0.545455   7 before 6 in continuous rolling

    0.454545   8 before 7 in continuous rolling
    0.545455   7 before 8 in continuous rolling


    0.138889   6 single roll
    0.138889   8 single roll
    0.166667   7 single roll
    0.694444   not 7 or 6 single roll
    0.694444   not 7 or 8 single roll
    0.833333   not 7 single roll

Place bets: Independently bet $5 on the 6 and $5 on the 8

 Probability   Event

    0.206612   both win
    0.247934   6 wins 8 loses 
    0.247934   8 wins 6 loses 
    0.297521   both lose 
    1.000000

Expected payoff on the $10 bet is $9.84848
Sdev of payoff on the $10 bet is $7.6286

Place bets: Simultanously bet $5 on the 6 and $5 on the 8

 Probability   Event

    0.142045   first 6 wins then 8 wins 
    0.142045   first 8 wins then 6 wins 
    0.170455   first 6 wins then 8 loses 
    0.170455   first 8 wins then 6 loses 
    0.375000   both lose simultaneously 
    1.000000

Expected payoff on the $10 bet is $9.84848
Sdev of payoff on the $10 bet is $8.73966
Corr of payoff on the $10 bet is 0.559017

Place bets: First bet $5 on the 6 then bet $5 on the 8 after 1 rolls

 Probability   Event

    0.161774   first 6 wins then 8 wins 
    0.098643   first 8 wins then 6 wins 
    0.194129   first 6 wins then 8 loses 
    0.194129   first 8 wins then 6 loses 
    0.351326   simultaneous loss or 6 loses then 8 loses 
    1.000000

Expected payoff on the $10 bet is $9.84848
Sdev of payoff on the $10 bet is $8.41575
Corr of payoff on the $10 bet is 0.465847

Place bets: First bet $5 on the 6 then bet $5 on the 8 after 5 rolls

 Probability   Event

    0.196184   first 6 wins then 8 wins 
    0.022941   first 8 wins then 6 wins 
    0.235421   first 6 wins then 8 loses 
    0.235421   first 8 wins then 6 loses 
    0.310034   simultaneous loss or 6 loses then 8 loses 
    1.000000

Expected payoff on the $10 bet is $9.84848
Sdev of payoff on the $10 bet is $7.81874
Corr of payoff on the $10 bet is 0.224656

Place bets: First bet $5 on the 6 then bet $5 on the 8 after 25 rolls

 Probability   Event

    0.206604   first 6 wins then 8 wins 
    0.000016   first 8 wins then 6 wins 
    0.247925   first 6 wins then 8 loses 
    0.247925   first 8 wins then 6 loses 
    0.297529   simultaneous loss or 6 loses then 8 loses 
    1.000000

Expected payoff on the $10 bet is $9.84848
Sdev of payoff on the $10 bet is $7.62873
Corr of payoff on the $10 bet is 0.00585995