I have been wondering for awhile what the optimal Kelly bet is for some non blackjack games. I finally took the time to do the math for an easy one. I’ll post it here so people can correct me if I am wrong/use the information. If the topic is too sensitive feel free to bust this post. I’ll be careful not to mention anything in specific, but it will be clear what I am talking about to those who already know.
Let’s say you find a carnival game where if everything goes as expected, you have a 3.48% advantage. Sometimes things don’t go as expected and you are at a 3.37% disadvantage. How much should you bet?
Formula:
Ideal bet = (B) * (K)((((y)*3.48)/1.766)-((n*3.37))/1.347
B= Bankroll
K= Kelly multiplier
y= percentage of time things go as planed
3.48 = advantage when things go as planned
1.766 = Bet adjustment. When things go well, you will match your bet 88.3% of the time. This adjustment is so your average total bet per hand works out to be your desired Kelly bet rather than the amount you first put out to play the game.
n= percentage of time things don’t go as expected
3.37 = disadvantage when things don’t go as expected
1.347 = Bet adjustment. When things don’t go as planned and you revert to basic strategy you match your bet just 67.4% of the time.
Example 1 .10,000 bankroll playing half Kelly playing a 95% game (overall advantage on average bet 1.75%)
(10,000)(1/200)((((.95)*3.48)/1.776)-((.05)*3.37)/1.347= $87.35
Example 2. 10,000 bankroll playing half Kelly playing 80% game (overall advantage on average bet 1.07%)
(10,000)(1/200)((((.8)*3.48)/1.776)-((.2)*3.37)/1.347= $53.40
Compare to Blackjack bet ramp $10,000 bankroll ½ Kelly .5 HE game
TC 1 and lower Table min / wong
TC 2 $25
TC 3 $50
TC 4 $75
TC 5 $100
My suggestion: Bet halfway between your TC 4 and TC 5 bet if you find a great game, bet your TC 3 ideal bet if you find an OK game. Your risk preferences are already expressed in how you play blackjack. Should you find a game like I describe and bet as I suggest your risk will be about the same as if you were playing blackjack.
Corrections are welcome!
Let’s say you find a carnival game where if everything goes as expected, you have a 3.48% advantage. Sometimes things don’t go as expected and you are at a 3.37% disadvantage. How much should you bet?
Formula:
Ideal bet = (B) * (K)((((y)*3.48)/1.766)-((n*3.37))/1.347
B= Bankroll
K= Kelly multiplier
y= percentage of time things go as planed
3.48 = advantage when things go as planned
1.766 = Bet adjustment. When things go well, you will match your bet 88.3% of the time. This adjustment is so your average total bet per hand works out to be your desired Kelly bet rather than the amount you first put out to play the game.
n= percentage of time things don’t go as expected
3.37 = disadvantage when things don’t go as expected
1.347 = Bet adjustment. When things don’t go as planned and you revert to basic strategy you match your bet just 67.4% of the time.
Example 1 .10,000 bankroll playing half Kelly playing a 95% game (overall advantage on average bet 1.75%)
(10,000)(1/200)((((.95)*3.48)/1.776)-((.05)*3.37)/1.347= $87.35
Example 2. 10,000 bankroll playing half Kelly playing 80% game (overall advantage on average bet 1.07%)
(10,000)(1/200)((((.8)*3.48)/1.776)-((.2)*3.37)/1.347= $53.40
Compare to Blackjack bet ramp $10,000 bankroll ½ Kelly .5 HE game
TC 1 and lower Table min / wong
TC 2 $25
TC 3 $50
TC 4 $75
TC 5 $100
My suggestion: Bet halfway between your TC 4 and TC 5 bet if you find a great game, bet your TC 3 ideal bet if you find an OK game. Your risk preferences are already expressed in how you play blackjack. Should you find a game like I describe and bet as I suggest your risk will be about the same as if you were playing blackjack.
Corrections are welcome!