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Ask the Wizard #73

I just wanted to make sure that the correct play in the Microgaming single deck game of A,A vs A is to split as shown on your basic strategy card. I’m pretty sure the correct play would be to hit, at least with 4 decks, and it just seems that with all the 10’s left you might lose twice your bet pretty often. Not that I don’t believe you but I just wanted to make verify. Any chance you have the EV of hitting vs splitting on this hand?

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.

Hi. You say all betting systems will fail. If you play roulette and bet one unit on number 1-12 and 2 units on number 13-24 wouldn’t you then have 66.66% chance to break even or win.

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.

What’s the basic strategy for the new Blackjack Switch game? Also, what’s the house advantage?

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.

In 500 hands of baccarat betting only on banker, what percent of the time will player win over 46% of the decisions. Thanks


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) =
1-Z(-1.44) =
1-0.075145503 =

So the answer is 92.49%.

In hold em poker, what are the odds of being dealt pocket aces? And what are the odds of being dealt pocket aces twice in a row?

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.

I often play video Double-Down Stud when I’m in Las Vegas. I was curious as to how good/bad the total return of these machines are compared to the various forms of video poker. The machines at the Riviera (one of the few places I’ve seen these machines) have the following payouts:

One-coin pay table
Pair, 6-10’s 1
Pair, J-A’s 2
2 Pair 3
3 of a Kind 4
Straight 6
Flush 9
Full House 12
4 of a Kind 50
Straight-Flush 200
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

Under this pay table the house edge is 2.10% and the element of risk is 1.68%. The strategy is the same as indicated in my Double Down Stud section. Counting the raise towards cash back is like getting an extra 25% above cash back on the original bet only.