That is all there is to the insurance bet card counting system, if I have reconstructed it correctly. So odds of winning insurance bet when dealer has ace (and not considering other available information) is 96/311.įor each additional card that is known faceup on table or in discard pile, you can reduce denominator (311) by one, and if and only if that card is ten-valued then also reduce numerator (96) by one. So ten-valued cards are 6 deck* 4 suites* 4 ranks = 96 cards. Ten-valued cards are ranks ten, jack, queen, and king. I will be doing arithmetic in my head so check with calculator. Insurance bet is won by player when dealer has ace upcard, asks for insurance bets, player bets insurance, the dealer hole card is found to be ten-valued. However to ask for insurance the dealer must have an ace upcard, so we will use that as our only counted card to start. The assignment apparently asks you to ignore this. Even if you have no information about previous hands - whether because it is the first hand dealt or because you forgot - there will be cards on the table that slightly change the odds.
You count ten-valued cards versus other cards. It's a trick question because there is a card counting system particularly for the insurance bet. This was covered in a classic peer reviewed paper by Ed Thorpe.
