Posted by BoxedTrifecta
Jul 05, 2023

Craps Probability, Kelly Criterion and ChatGpt, What a mess.

Three years ago during lockdown I tinkered with a deeper breakdown of the game of craps. It has to do solely with with the don't pass line bet and odds. Let's breakdown the game a little bit.
Step 1 The come out roll. A distinct and measurable disadvantage for the don't pass position, 8/36 lose, 3/36 win.
Step 2 The point. Now it becomes a game where probability favors the don't. There are now 3 mirrored probabilities according to the point. Now it's 7 vs 6,8, 7 vs 5,9 and 7 vs 4,10.
Because the don't has a measured advantage, I thought in terms of the Kelly Criterion and how it should dictate how much odds to lay. What I worked out during lockdown came to a very simple strategy which I think fits in with bankroll management. The strategy came down to this: zero odds on points of 6,8, single odds on 5,9, and double odds on 4,10. It's a strategy of putting your money where your math is. Which is the Kelly Criterion. I had to sacrifice precision for practicality by rounding off up and down.

(As a side note, has anyone else noticed the similarities in appearance and vocation between John L Kelly and the Wizard. John Kelly looks like the Wizard if he chain smoked and never slept. Which is what killed him at the age of 42. Two months before the Wizard was born. Cue the Twilight Zone theme song)

I had always wondered about how these "Kelly Odds" would perform against the strategy of full odds in terms of house edge. So I asked ChatGpt.
The reason that I asked is because I'm really not that sharp mathematically and it turns out neither is ChatGpt.
First I laid out the 2 strategies, don't with full odds, don't with Kelly odds. First it lays out the parameters and informs me that the don't has a house edge of 1.41% (???) and that multiple simulations would have to be run and that I should gamble responsibly. I then asked it to run these simulations. Chat then informed me that it does not have the capability but would approximate the probability. It gave me these numbers: Full odds 3x4x5x would bring the house edge to .67% and that the Kelly odds would be .59% I really took this with a grain of salt after the wrong answer of 1.41% of overall house edge. Then it dropped the conversation as I pondered. So I asked Chat again and got a completely different answer. .47% on full odds. .37% on 5x in comparison and agreement with our first chat. One question, two answers.
Two days later I brought it up again and questioned the 1.41% answer. Chat does not like it's authority being questioned as I would find out even though apologetic. I asked the question again Don't full odds/don't Kelly odds. I then got a flippant answer of 1.36 house edge for both strategies.
One question, three answers.
In all honesty, I avoid wagering on craps, or roulette, or blackjack anymore. All sessions are short term and you're wagering on the swings. I don't know anyone who wagered an hour and was down 1.36%. As long as that house edge is positive, Mr. Kelly has the last word. The bet should be zero.
But craps does have an entertainment value unlike the quiet headaching grind of blackjack. I would strongly consider trying the Kelly odds strategy on craps especially in regards to bankroll management.
My first love is handicapping horse races and using the Kelly will be a forthcoming comparison but that's for another post. Thanks for listening to the ramblings of an old horseplayer. Cheers to all.


Theguyoverthere Jul 08, 2023

Weird, I would have thought of bankroll management was your goal that the Kelly odds would be the opposite: 2x odds on 6/8, 1x on 5/9, 0 on 4 and 10. The logic being you’re already such a favorite on a flat bet on the 4/10 there’s no reason to add extra risk, but for 6/8 you’re able to bet 2x odds much much cheaper

odiousgambit Jul 12, 2023

who told you the Don't is positive expectation? how would the casinos stay open if it was true? The robot is right if it insisted you aren't playing at an advantage

the Kelly Criterion is indeed for +EV situations, so knowing you are playing at a -EV game, it doesn't work and chat/gpt might decide "that does not compute"