Optimal Kelly Bet Sizing for "simultaneous events"
This is a football betting question in which the hoped deliverable would be a formula where 3 variables are plugged in and a result is produced.
If one is betting a football game and one assumes one's self to be 53.5% proficient at picking winners against the 11/10 vigorish (0.91) the bookie charges(52.38% winners needed to break even)....
...then the formula would be:
53.5% - (46.5% /0.91) = 2.35% of one's bankroll should be bet on every play.
..but NOW sportsbooks offer better odds(some at 21/20 vig(0.95)...some at other ratios).
My question is an extension of what Ken Uston discussed in his textbook on Blackjack Card Counting.
Uston discussed the card-counting player that was enjoying a 1.5% edge over the house in Blackjack(and betting 1.5% on each hand).....
...could increase that amount by a small fraction if he played 2, 3, or 4 hands against the same dealer's upcard(simultaneous Kelly betting events)...
...and then he provided the reader with the allowable percentage increase over that 1.5% bet.....
for example...spreading to two hands one would MULTIPLY the $150 bet for a $10,000 bank by 1.15
$150 * 1.15 would be $172(2 bets of $86 each)
FOR 3 BETS THE MULTIPLE would be 1.21
$150 * 1.21 = $181.5..... 3 bets of $60.50 each
TRANSLATING TO FOOTBALL WAGERING
For simplicity's sake.... all picks bet simultaneously have the SAME probability of winning
Variable "X" would then be the probality of winning.
Variable "Y" would be the number of betting events being wagered simultaneously
Variable "Z" would be the differing VIGORISH extracted by the bookie,e.g....
The result of the equation would then presumably provide how much to wager on each bet OR provide the multiple.
If you'd like attribution by your username or real name, please mention it... because this is going to be posted on about 6 sports forums.