Seven Card Stud High Low with a Spit (London Lowball Rules)
It may seem odd to include a poker page, but I recently began playing a friendly game at the local recreation center with rules I had not seen before, so thought it would be interesting to analyze the frequency of the various hands. The type of poker played is a variation of seven card stud high-low with an eighth community card (the "spit"). The game is played as follows.
- Three cards are dealt to each player, one of which must be face up. The player with the lowest card showing (Ace being high, ties broken by closest to the dealer's left) must fold or wager one chip.
- A common community card is then dealt in the middle of the table, and a round of betting takes place with the highest hand going first.The bet must be two chips if a pair is showing, otherwise can only be one chip. Of course, checking is also allowed.
- Subsequently, each player is dealt a fourth, fifth and sixth card face up, and after each card there is another round of betting, initiated by the highest hand showing. There is a limit of three raises in any round, and all bets follow the rule above: one or two chips depending on whether a pair or better is showing on board.
- The last card for each player is dealt face down, and a final round of betting takes place. Some play a bet of two chips is permitted on the last round, even if no pair or better is showing. After the betting concludes, the initial bettor or last raiser (or, if everyone checked, the highest hand showing on board) must declare high, low or both ways. Similar declarations then follow player-by-player to the left.
- To declare "low" a player must have an 8-low hand or better, the best low hand being 6-4-3-2-Ace of mixed suits. Straights and flushes cannot be used as low hands (London Lowball rules). To win a call of "high-low", the player must beat outright all other high and low hands that remain in the showdown. The high and low winners each split the pot, with any extra chip from an odd number of chips in the pot going to the high hand winner.
Given that there are 56 possible five-card hands from the eight cards available (seven dealt to the player plus the common center card), the average poker hand is typically stronger than one might be accustomed to in more traditional poker games.
The two tables below summarize the average frequency of hands of a given rank, the first for high hands, and the second for low hands. Summarizing, we can observe the following:
- With respect to playing for high, full houses or better occur almost 7% of the time, and flushes or better about 13% of the time. Straights or better occur about 22% of the time. About 72% of the time a player will have only two-pair or worse.
- With respect to playing for low, there is only a 30% chance of even having a playable low hand. About 15% of the time an 8-low hand occurs, 10% of the time a 7-low hand, and about 4% of the time a 6-low hand.
Aside from the relative value of a given hand, betting strategy is, of course, strongly dictated by what other cards appear on the table, the relative strength of other hands, how other players are betting, and various bluffing tactics. These tables show the relative frequency of hands of a given strength dealt from a full deck, and to that extent at least may serve as a guide.
A discussion of the typical winning hands is contained on the next page
.
| Hand Rank | Frequency | Percent | Cumulative |
|---|---|---|---|
| Royal Flush | 64,860 | 0.009% | 0.009% |
| Other Straight Flush | 546,480 | 0.07% | 0.08% |
| Four of a kind | 2,529,262 | 0.3% | 0.4% |
| Full house | 45,652,128 | 6.1% | 6.5% |
| Flush | 50,850,320 | 6.8% | 13.2% |
| Straight | 67,072,620 | 8.9% | 22.2% |
| Three of a kind | 38,493,000 | 5.1% | 27.3% |
| Two pair | 257,760,900 | 34.3% | 61.5% |
| One pair | 236,092,500 | 31.4% | 92.9% |
| Nothing | 53,476,080 | 7.1% | 100.0% |
| Total Hands | 752,538,150 | 100.0% | 100.0% |
| Hand Rank | Frequency | Percent | Cumulative |
|---|---|---|---|
| 64 low | 9,836,160 | 1.3% | 1.3% |
| 65 low | 21,304,024 | 2.8% | 4.1% |
| 74 low | 7,103,816 | 0.9% | 5.1% |
| 75 low | 21,894,896 | 2.9% | 8.0% |
| 76 low | 44,342,944 | 5.9% | 13.9% |
| 84 low | 4,932,916 | 0.7% | 14.5% |
| 85 low | 14,705,104 | 2.0% | 16.5% |
| 86 low | 34,220,160 | 4.5% | 21.0% |
| 87 low | 61,786,216 | 8.2% | 29.3% |
| No low | 532,411,914 | 70.7% | 100.0% |
| Total Hands | 752,538,150 | 100.0% | 100.0% |
Since I have not seen it elsewhere, I thought it useful to derive a more detailed frequency table of all the various low hands for this game.
In reviewing these tables, it may seem counterintuitive, for example, that there are more 6,4,3,2,1 low hands than 6,5,3,2,1 low hands even though the former is the stronger hand. Of course there are exactly as many five card 6,4,3,2,1 low hands as 6,5,3,2,1 low hands, namely 1,024 less the 4 flushes, or 1,020 of each. However the five 6,4,3,2,1 cards can be included with more other cards in the 8 card hand and still remain a 6,4,3,2,1 low (for example a 5). However the 6,5,3,2,1 low hand cannot be part of an eight card hand containing a 4, or else it would be a 6,4,3,2,1 low hand.
| Low Hand | Frequency | Percent |
|---|---|---|
| 6, 4, 3, 2, 1 | 9,836,160 | 1.31% |
| 6, 5, 3, 2, 1 | 7,104,824 | 0.94% |
| 6, 5, 4, 2, 1 | 7,099,600 | 0.94% |
| 6, 5, 4, 3, 1 | 7,099,600 | 0.94% |
| 7, 4, 3, 2, 1 | 7,103,816 | 0.94% |
| 7, 5, 3, 2, 1 | 4,934,368 | 0.66% |
| 7, 5, 4, 2, 1 | 4,930,464 | 0.66% |
| 7, 5, 4, 3, 1 | 4,930,464 | 0.66% |
| 7, 5, 4, 3, 2 | 7,099,600 | 0.94% |
| 7, 6, 3, 2, 1 | 4,926,560 | 0.65% |
| 7, 6, 4, 2, 1 | 4,926,560 | 0.65% |
| 7, 6, 4, 3, 1 | 4,926,560 | 0.65% |
| 7, 6, 4, 3, 2 | 4,930,464 | 0.66% |
| 7, 6, 5, 2, 1 | 4,926,560 | 0.65% |
| 7, 6, 5, 3, 1 | 4,926,560 | 0.65% |
| 7, 6, 5, 3, 2 | 4,926,560 | 0.65% |
| 7, 6, 5, 4, 1 | 4,926,560 | 0.65% |
| 7, 6, 5, 4, 2 | 4,926,560 | 0.65% |
| 8, 4, 3, 2, 1 | 4,932,916 | 0.66% |
| 8, 5, 3, 2, 1 | 3,260,352 | 0.43% |
| 8, 5, 4, 2, 1 | 3,257,576 | 0.43% |
| 8, 5, 4, 3, 1 | 3,257,576 | 0.43% |
| 8, 5, 4, 3, 2 | 4,929,600 | 0.66% |
| 8, 6, 3, 2, 1 | 3,254,536 | 0.43% |
| 8, 6, 4, 2, 1 | 3,254,536 | 0.43% |
| 8, 6, 4, 3, 1 | 3,254,536 | 0.43% |
| 8, 6, 4, 3, 2 | 3,257,312 | 0.43% |
| 8, 6, 5, 2, 1 | 3,254,536 | 0.43% |
| 8, 6, 5, 3, 1 | 3,254,536 | 0.43% |
| 8, 6, 5, 3, 2 | 3,254,536 | 0.43% |
| 8, 6, 5, 4, 1 | 3,254,536 | 0.43% |
| 8, 6, 5, 4, 2 | 3,254,536 | 0.43% |
| 8, 6, 5, 4, 3 | 4,926,560 | 0.65% |
| 8, 7, 3, 2, 1 | 3,251,760 | 0.43% |
| 8, 7, 4, 2, 1 | 3,251,760 | 0.43% |
| 8, 7, 4, 3, 1 | 3,251,760 | 0.43% |
| 8, 7, 4, 3, 2 | 3,251,760 | 0.43% |
| 8, 7, 5, 2, 1 | 3,251,760 | 0.43% |
| 8, 7, 5, 3, 1 | 3,251,760 | 0.43% |
| 8, 7, 5, 3, 2 | 3,251,760 | 0.43% |
| 8, 7, 5, 4, 1 | 3,251,760 | 0.43% |
| 8, 7, 5, 4, 2 | 3,251,760 | 0.43% |
| 8, 7, 5, 4, 3 | 3,254,536 | 0.43% |
| 8, 7, 6, 2, 1 | 3,251,760 | 0.43% |
| 8, 7, 6, 3, 1 | 3,251,760 | 0.43% |
| 8, 7, 6, 3, 2 | 3,251,760 | 0.43% |
| 8, 7, 6, 4, 1 | 3,251,760 | 0.43% |
| 8, 7, 6, 4, 2 | 3,251,760 | 0.43% |
| 8, 7, 6, 4, 3 | 3,251,760 | 0.43% |
| 8, 7, 6, 5, 1 | 3,251,760 | 0.43% |
| 8, 7, 6, 5, 2 | 3,251,760 | 0.43% |
| 8, 7, 6, 5, 3 | 3,251,760 | 0.43% |
| No Low Hand | 532,411,914 | 70.75% |
| Total Hands | 752,538,150 | 100.00% |
