Sanity checking my home-grown simulator

[gronbog]

Yes. Thanks for pointing that out. For example, you can shuffle after any fixed number of rounds instead of after every round.

 

[BJgenius007]

"For players interested on this topic, this is what I do. First, I want to be clear on full Kelly bet with RoR of 13.5% and never resize bets, the bet size is
0.5 * advantage / variance * bankroll"

The 0.5 doesn't belong there.

Don

Thank you for pointing out the error. I will correct.

 

[London Colin]

Yes. Thanks for pointing that out. For example, you can shuffle after any fixed number of rounds instead of after every round.

To avoid the cut-card effect, I think you can shuffle whenever you like, so long as the number of cards so far dealt is not a factor in your decision making. But I wondered if you had more in mind than just eliminating the cut-card effect when you recommended shuffling every round. E.g., if the goal is to replicate CA figures, would it require significantly fewer rounds to converge on the results if every round was dealt 'off the top'?

Computationally, maybe the best method for a sim is not to do a conventional, full shuffle at all, but rather to perform the step that randomizes the next card only at the point when that card is required to be dealt; a sort of 'just in time' approach to shuffling. That way, you do not waste any processing time shuffling cards that are never going to be dealt, and the only overhead involved in reverting to a full shoe is the resetting of a variable or two, meaning that notionally 'shuffling' every round would not be much more expensive than doing so much less frequently.

 

[gronbog]

To avoid the cut-card effect, I think you can shuffle whenever you like, so long as the number of cards so far dealt is not a factor in your decision making. But I wondered if you had more in mind than just eliminating the cut-card effect when you recommended shuffling every round. E.g., if the goal is to replicate CA figures, would it require significantly fewer rounds to converge on the results if every round was dealt 'off the top'?

I don't think it would converge any faster. Think about the fact that one can cut the deck at almost any random point in live play. There is therefore nothing special about the first round dealt. The first card dealt from any round during the shoe could have been the first with the same probability.

 

[gronbog]

Computationally, maybe the best method for a sim is not to do a conventional, full shuffle at all, but rather to perform the step that randomizes the next card only at the point when that card is required to be dealt; a sort of 'just in time' approach to shuffling. That way, you do not waste any processing time shuffling cards that are never going to be dealt, and the only overhead involved in reverting to a full shoe is the resetting of a variable or two, meaning that notionally 'shuffling' every round would not be much more expensive than doing so much less frequently.

Yes. Uniformly selecting the next card out of the set of remaining cards would function in a way equivalent to the Fisher-Yates shuffle, which is a valid random shuffle.

https://en.wikipedia.org/wiki/Fisher-Yates_shuffle

 

[London Colin]

I don't think it would converge any faster. Think about the fact that one can cut the deck at almost any random point in live play. There is therefore nothing special about the first round dealt. The first card dealt from any round during the shoe could have been the first with the same probability.

I was wondering whether the deflections into positive and negative EV territory that take place as cards are discarded (and must ultimately balance to produce the same overall EV as the 'off the top' value) might require more trials to ensure that, in card-counting terms, all the +N counts are balanced by -N counts.

I guess the counter argument to this, in line with what you are saying, is that cards which are unavailable because they have been discarded are no different to cards which are unavailable because they are located towards the back of the shoe and will not be reached before the shuffle.

It can be a confusing (to me) topic!

 

[London Colin]

@OldGuy - Sorry if it seems like I am hijacking your thread. Hopefully these questions and answers are of some help to you too.

 

[OldGuy]

@OldGuy - Sorry if it seems like I am hijacking your thread. Hopefully these questions and answers are of some help to you too.

Not at all. This is all relevant to how one writes a simulator. I'm glad to hear that (at least a few) people here know what a Fisher-Yates shuffle is, because I just discovered that this year (and I'm an OldGuy).