Ask The Wizard #283

The Fisher-Yates shuffle is a programming technique to shuffle an array in an unbiased and fast manner. Assume there are n items in the array. Set a counter equal to n.

1. Choose a card at random from card number 1 to n-1.
2. Swap that card with card number n.
3. Subtract 1 from n.
4. Repeat steps 1 to 3 until n=2.

void fisher_yates(int deck[], int NumCards)
{
	int i,hold;
	unsigned int rn;
	for (i=NumCards-1; i>0; i--)
	{
		rn=genrand_int32()%(i+1);
		hold=deck[rn];
		deck[rn]=deck[i];
		deck[i]=hold;
	}
}

I show my analysis of the Red Flex in my blackjack appendix 8.

This question is discussed in my forum at Wizard of Vegas.

Not allowing doubling increases the house edge by 1.48%. Not allowing splitting increases the house edge by 0.57%. Allowing neither increases the house edge by 1.91%.

At the risk of making the advantage player community angry again, I'll just say there are some situations where the astute player can make a wager knowing what his first card will be.

The following table shows the probability of each card and the advantage, if greater than zero, when it is the first card. The conditional return is the expected win, given what the indicated first card is. The expected return is the product of the probability and conditional return columns.

The above table shows that if the player plays only when the first card is a queen or higher his advantage per hand seen is 1.81%. The player will make a bet 24.52% of the time. The advantage per bet made is 7.40%.

Note how the advantage with a queen is 0.05% only. If we don't play those hands, then the table looks like this.

The above table shows that if the player plays only when the first card is a king or higher, then his advantage per hand seen is still 1.81%. The player will make a bet 16.98% of the time. The advantage per bet made is 10.66%.

Here is that table if the player plays aces or the joker only.

This shows that if the player plays only when the first card is an ace or joker, then his advantage per hand seen is still 1.52%. The player will make a bet 9.43% of the time. The advantage per bet made is 16.07%.

See discussion about this question in my forum at Wizard of Vegas.

To see an integral you may find useful, select the black region below.

To see the answer, select the black region below.