[Buzz]

Pete – Interesting question. Useless, in a way, but interesting. And sometimes when you pursue useless questions you discover something related that you didn't know but that might be useful.

For example, the double suited run-downs do more poorly, heads up, than random cards until you get up to 9876, and that hand does only slightly better than random.

Here are some simulated showdown results for heads-up play against random (four blanks) cards for one opponent. These are for 1,000,000 run simulations.

7[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/diamond.gif[/img], 4[img]/images/graemlins/diamond.gif[/img]
heart flush 109561/135705
straight flush 4506/4513
flush+st.flush 114067/140218 = 0.8135
overall: 463776 wins, 14629 ties
(four blanks did better: 521595 wins, 14629 ties.)

7[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 5[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/diamond.gif[/img]
heart flush 110848/137015
straight flush 3370/3371
flush+st.flush 114218/140386 = 0.8136
overall: 463498 wins, 14806 ties
(four blanks did better: 521696 wins, 14806 ties.)

Very, very close between these two. I don't want either of them. The win/try ratio for flushes and straight flushes is very slightly better for the second, but the first one makes slightly more straight flushes. (Should be, and is, about a 4:3 ratio).

9[img]/images/graemlins/heart.gif[/img], 8[img]/images/graemlins/heart.gif[/img], 7[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/diamond.gif[/img]
heart flush 111863/136024
straight flush 4520/4526
flush+st.flush 116383/140550 = 0.8281
overall: 500621 wins, 16468 ties
(four blanks was 482911 wins, 16468 ties.)

9[img]/images/graemlins/heart.gif[/img], 8[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/diamond.gif[/img]
heart flush 113471/137127
straight flush 3321/3324
flush+st.flush 116792/140451 = 0.8315
overall: 501564 wins, 16226 ties
(four blanks was 482210 wins, 16226 ties.)

Close between these two. Neither of them is very good, just slightly better than random. The win/try ratio for flushes and straight flushes is slightly better for the second, and that's the deciding factor for me. (Again, the straight flush ratio between the first and second of these should be, and is, about a 4:3 ratio).

A[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/diamond.gif[/img]
heart flush 125857/137986
straight+royal flush 2223/2223
flush+st.fl.+roy.fl. = 128080/140209 = 0.9135
overall: 600984 wins, 19747 ties
(four blanks was 379269 wins, 19747 ties.)

A[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/diamond.gif[/img]
heart flush 128001/138425
straight+royal flush 1723/1723
flush+st.fl.+roy.fl. 129724/140148 = 0.9256
overall: 601852 wins, 19865 ties
(four blanks was 378283 wins, 19865 ties.)

Again it's close, but this time both of these are good starting hands, and this time there is a discernible difference between the two. The second hand is the better of the two. That’s because the win/try ratio for flushes plus straight (and royal) flushes is better for the second than the first by about one per cent.

I'm not sure what the lesson here is, maybe simply that you should like high cards in this game and coordinated low hands, even if double suited, may not be very good starting hands, even though an expert may be able to turn a profit with them.

But you probably already knew that.

Buzz