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Ask the Wizard #73
William from Pittsburgh, USA
I’ve been questioned about this several times and continue to maintain that despite losing the total bet the option to draw to split aces overcomes the European no-peek rule, thus splitting is the better play. Based on one deck the expected value of each hand (considering the possibility of a dealer blackjack) is -0.532849 for hitting and -0.223277 for splitting. So splitting is better by about 31% of a unit. Splitting is also better for the 4-deck game, which no Microgaming player should be playing since a 1-deck game with the same rules is available.
Atle from Porsgrunn, Norway
Not quite. You would have a 12/38 chance of winning 3 units, 12/38 of breaking even, and 14/38 of losing 3 units. The expected value is [(12/38)*3 + (12/38)*0 + (14/38)*-3]/3 = (-6/38)/3 = -2/38 = -5.26%. This will be true of any combination of bets as long as you avoid the dreaded 5 number combo (0/00/1/2/3). If you only play for one spin and want to maximize your probability of winning then bet equally on 35 of the numbers. You’ll have a 92.11% chance of winning 1 unit and a 7.89% chance of losing 35 units.
Waurkelter B. from Mashpee, Massachusetts
Everybody is asking me this. At this time I haven’t worked out the odds yet. Until I do you’re on your own. Since this web site isn’t making me much money I have to give priority to paying consulting work.
First I’m going to assume you want me to ignore ties. From my baccarat section we see the probability of a player win is 49.32%, given that there wasn’t a tie. We’ll use the normal approximation to the binomial distribution for this problem. The expected number of player wins is 500*0.4932 = 246.58. 46% of decisions is 230. The standard deviation is (500*(0.4932)*(1-0.4932))1/2 = 11.18. So...
pr(player wins > 230) =
pr(player wins-246.58 > 230-246.58) =
1-pr(player wins-246.58 <= 230-246.58) =
1-pr(player wins-246.58+0.5 <= 230-246.58+0.5) =
1-pr((player wins-246.58+0.5)/11.18) <= (230-246.58+0.5)/11.18) =
So the answer is 92.49%.
Adam from Redding, USA
There are 52*51/2 = 1326 ways to arrange 2 cards out of 52. There are 4*3/2=6 ways to arrange 2 aces out of 4. So the answer is 6/1326 = 1/221. The probability of this happening twice in a row is (1/221)2 = 1 in 48,841.
One-coin pay table
Pair, 6-10’s 1
Pair, J-A’s 2
2 Pair 3
3 of a Kind 4
Full House 12
4 of a Kind 50
Royal Flush 1,000
2-5 coins, multiply 1-coin payout
5-coin Royal pays 20,000 coins
With correct play, what is the return of these machines?
As a side note, these machines earn slot points at the same rate as video poker (half the rate of the regular slots), but I find that I accumulate point faster due to the obvious double-down situations. Does that indirectly improve the return?
I enjoy your website very much! Thanks!!
Tim from Newburgh, New York