Carnival Bet Sizing

Zerg

Active Member
#1
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!
 

Sonny

Well-Known Member
#2
Zerg said:
Ideal bet = (B) * (K)((((y)*3.48)/1.766)-((n*3.37))/1.347
Watch the decimal points in your advantages! It should be 0.0348 and 0.0337 instead of 3.48 and 3.37. It would be very tragic if you were playing a 3.48% advantage but betting as though it were a 348% advantage.

Zerg said:
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
This is a little confusing because you say half-Kelly but you use 1/200 in your formula. If you adjust the advantages then you will be able to use 1/2 instead of 1/200.

-Sonny-
 
#3
Zerg said:
Your risk preferences are already expressed in how you play blackjack.
I'm uneasy about this statement because I believe that said carnival game has higher variance than blackjack. Maybe I messed up the math but I believe you may require a bankroll of at least $60,000 to play $5 bets at a low RoR...
 

Wookets

Well-Known Member
#4
Most Interesting Man said:
I'm uneasy about this statement because I believe that said carnival game has higher variance than blackjack. Maybe I messed up the math but I believe you may require a bankroll of at least $60,000 to play $5 bets at a low RoR...
I don't think your figures are correct; this carnival game, if played correctly, requires a much smaller bankroll than BJ. I believe it's somewhere in the ball park of 300 units for a near 0% RoR.
 

pit15

Well-Known Member
#5
What about 2.41% games?

And what about the fact that you'll generally be spreading the action over 2 hands?

Lot of flaws in your assumptions. I have simulations for RORs based on game quality / bet size, and agree with the fact that you need around 300 units.
 

rrwoods

Well-Known Member
#8
This game doesn't need a simulator. There are few enough total possibilities that you can run a combinatoric analysis in a few hours, at least for the one-hand situation. This is useful since the bonus paytable varies somewhat.
 

Zerg

Active Member
#9
Thanks for the replies! This is maybe the first time I've done math since college. I feel like it has me in the right ballpark but I missed a few things.

Anyone else care to chime in about what they bet relative to their blackjack bets and why? For those who listed a number of units your bank should have, could you also list different numbers for those with higher risk tolerances?
 

Sonny

Well-Known Member
#12
Most Interesting Man said:
I stand corrected, thank you. I was not taking the SQUARE ROOT of time.
That brings up another good point: make sure you are using the variance and not the standard deviation in that formula. For example, a game with a SD of 1.74 would have variance of over 3, which would make a big impact on the correct bet size if you are using the formula above.

-Sonny-
 
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