Ask The Wizard #283

The Fisher-Yates shuffle is an efficient algorithm used to randomly rearrange the elements in an array without bias. Start by determining the total number of items, denoted as n.

1. Randomly select a card from numbers ranging from 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 present my findings on the Red Flex in my blackjack appendix 8 .

This topic is elaborated upon in my discussion forum at Wizard of Vegas .

Prohibiting doubling raises the house edge by 1.48%, while disallowing splitting increases it by 0.57%. If both actions are restricted, the house edge goes up by 1.91%.

To avoid upsetting the advantage player community again, I want to point out that there are specific scenarios where a knowledgeable player can confidently place a bet knowing the identity of their first card.

The following chart illustrates the likelihood of each card appearing and the corresponding advantage, provided it is greater than zero, when it serves as the first card. The conditional return represents the expected win based on the given first card, while the expected return is calculated by multiplying the probability and the conditional return.

The preceding table indicates that if a player only participates when their first card is a queen or better, their advantage for each hand dealt is 1.81%. This player will place a bet 24.52% of the time, and their per bet advantage reaches 7.40%.

Note the meager advantage of only 0.05% associated with having a queen. If we eliminate those hands from the equation, the table would appear as follows.

This table illustrates that if a player only engages when their first card is a king or better, they still enjoy an advantage of 1.81% per hand seen. However, they will only place a bet 16.98% of the time, and their per bet advantage is 10.66%.

The following table is provided if the player chooses only aces or the joker.

This demonstrates that if a player restricts their play to instances when their first card is an ace or joker, their observed advantage per hand is 1.52%. They will place a bet 9.43% of the time, with a per bet advantage of 16.07%.

For additional insights on this question, visit my forum at Wizard of Vegas .

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