Kelly and limits question

[Frank]

What do you guys do when limits get in the way?

For example: You have 3 plays in 3 different markets all with the same exact edge and Kelly says to bet 1800.

Play 1 you are able to get the full amount

Play 2 you can only get a dime

Play 3 you can only get down a nickel


What do you do now?

I know you can size down but what if that were already sized down?

Can Kelly only be used up to a certain point and then become out of range with current market limits in some sports thus making it impossible to actually use to its fullest?

[Ganchrow]

Before answering the above one would first need to state both the payout odds for the 3 bets, total bankroll, and the degree (if any) to and odds at which each bet could be parlayed.

With these assumption made, such answers (and more) may quite readily be determined using my http://forum.sbrforum.com/handicappe...ml#post1215635.

Let's take 3 possible scenarios:

1. Assume full Kelly, a $100K bankroll, odds of +500 on each bet, and true parlay odds. This then implies win prob (on each bet) of ≈ 18.1667%.
   
   Further assume:
   Limit on Bet 1+2 Parlay = $1,000
   Limit on Bet 1+3 Parlay = $500
   Limit on Bet 2+3 Parlay = $500
   Limit on Bet 1+2+3 Parlay = $500
   Optimal bets are then:
   Bet 1: $1,491.85
   Bet 2: $1,000.00
   Bet 3: $500.00
   Parlay 1+2: $118.21
   Parlay 1+3: $201.54
   Parlay 2+3: $283.51
   Parlay 1+2+3: $0.00
2. Assume full Kelly, a $100K bankroll, odds of -500 on each bet, and true parlay odds. This then implies win prob (on each bet) of ≈ 83.6333%.
   
   Further assume:
   Limit on Bet 1+2 Parlay = $1,000
   Limit on Bet 1+3 Parlay = $500
   Limit on Bet 2+3 Parlay = $500
   Limit on Bet 1+2+3 Parlay = $500
   Optimal bets are then:
   Bet 1: $1,045.26
   Bet 2: $1,000.00
   Bet 3: $500.00
   Parlay 1+2: $178.00
   Parlay 1+3: $500.00
   Parlay 2+3: $500.00
   Parlay 1+2+3: $78.47
3. Assume full Kelly, a $100K bankroll, odds of -110 on each bet, +260 odds on all 2-teamers, and +600 odds on all 3-teamers. This then implies win prob (on each bet) of ≈ 53.2381%.
   Further assume:
   
   Limit on Bet 1+2 Parlay = $1,000
   Limit on Bet 1+3 Parlay = $500
   Limit on Bet 2+3 Parlay = $500
   Limit on Bet 1+2+3 Parlay = $500
   Optimal bets are then:
   Bet 1: $1,306.21
   Bet 2: $1,000.00
   Bet 3: $500.00
   Parlay 1+2: $0.00
   Parlay 1+3: $0.00
   Parlay 2+3: $0.00
   Parlay 1+2+3: $500.00

http://forum.sbrforum.com/handicapper-think-tank/118429-generic-kelly-spreadsheet.html#post1215635

Please note: I'll take no responsibilities for data entry errors on my part. Please verify your own work.

[smitch124]

Remember to count how much you can get for selling your children as part of your Kelly bankroll...

[MonkeyF0cker]

Ganch,

Are you guys planning on adding that AJAX scripting in your sig to the forum home page? That would be nice actually...

[Ganchrow]

Are you guys planning on adding that AJAX scripting in your sig to the forum home page? That would be nice actually...

Nice of you to notice.

It certainly could be added if people thought it useful/cool. Only question'd be where exactly to place it.

[Frank]

Actually the the example is not a parlay but three straight bets at 3 separate books.

Lets just say one is MLB, the 2nd is a soccer game and 3rd is a Nascar matchup.

Edges are exactly the same but the same amount cannot be wagered since market limits are different?

That is basicly what i am trying ask. What should be done when limits get in the way in smaller markets?

[MonkeyF0cker]

So nice of you to notice.

It certainly could be added if people thought it useful/cool. Only question'd be where exactly to place it.

I think it would be nice on the forum home page so you could continually see the latest posts in each forum without having to refresh the page...

[Ganchrow]

Actually the the example is not a parlay but three straight bets at 3 separate books.

Lets just say one is MLB, the 2nd is a soccer game and 3rd is a Nascar matchup.

Edges are exactly the same but the same amount cannot be wagered since market limits are different?

That is basicly what i am trying ask. What should be done when limits get in the way in smaller markets?

As I had previously mentioned, you'd first need to specify two of payout odds, win probability, and total bankroll.

As suggested, please see my http://forum.sbrforum.com/handicappe...ml#post1215635.

One more scenario:

Assume full Kelly, a $100K bankroll, odds of +1000 on each bet, and true parlay odds. This then implies win prob (on each bet) of ≈ 10.7273%.

Further assume:

Limit on Bet 1 = $2,000
Limit on Bet 2 = $1,000
Limit on Bet 3 = $500
Limit on Bet 1+2 Parlay = $0
Limit on Bet 1+3 Parlay = $0
Limit on Bet 2+3 Parlay = $0
Limit on Bet 1+2+3 Parlay = $0

Optimal bets are then:

Bet 1: $1,800.49^*
Bet 2: $1,000.00
Bet 3: $500.00

^* Yes, the optimal wager on Bet #1 is actually higher in this scenario than it would be were it wagered isolation.