| Lands in hand | ||||||
| Drawn: | >=1 | 0 | 1 | 2 | 3 | 3+ |
| 7 | 96% | 4% | 19% | 32% | 28% | 44% |
| 8 | 97% | 3% | 14% | 28% | 30% | 56% |
| 9 | 98% | 2% | 10% | 23% | 30% | 65% |
| 10 | 99% | 1% | 7% | 19% | 28% | 74% |
| 11 | 99% | 1% | 4% | 14% | 25% | 81% |
| 12 | 100% | 0% | 3% | 11% | 22% | 86% |
| 13 | 100% | 0% | 2% | 8% | 18% | 90% |
| 14 | 100% | 0% | 1% | 5% | 14% | 93% |
| 15 | 100% | 0% | 1% | 4% | 11% | 95% |
| 16 | 100% | 0% | 0% | 3% | 8% | 97% |
| 17 | 100% | 0% | 0% | 2% | 6% | 98% |
| 18 | 100% | 0% | 0% | 1% | 4% | 99% |
| 19 | 100% | 0% | 0% | 1% | 3% | 99% |
| 20 | 100% | 0% | 0% | 0% | 2% | 100% |
This is just the probabilities of having mana drawn in hand playing with the sample Delver deck. This is the math for a 56 card deck b/c Gitaxian Probe is just air to make the deck seem meatier. This is similar to how Lays fills bags of Baked Lays with air and, like, 7 chips. I hate Lays so much. Their baked chips are just so tasty. Nom. My sample Delver deck ran 19 lands. You have a 96% chance of having at least 1 land in hand in your opener, but a 19% chance of having ONLY 1 land. You're more likely to have 2 land in hand than any specific number, and most like to have 3 or more. You have a 46% chance of having 3 or more mana in hand in your opener running Delver. You have a 56% chance of having 3 or more mana in hand
by the draw of the 8th card.
16 of the 19 lands in my sample deck tap for {U}, 9 tap for {W}, and 2 for {1}. You really have a very small chance of all lands in your hand not being a source of {U}. So I'm primarily interested in when this deck will draw a {W} source and its Moorland Haunts, the 2 {1} sources. The deck needs the white to cast Geist of St. Traft and activate Moorland Haunt's ability. So I want to know the probability of there being a single white source on the board by the third land drawn.
| White Sources Drawn | |||||
| Drawn: | >=1 | 0 | 1 | 2 | 3 |
| 1 | 47% | 53% | 47% | 0% | 0% |
| 2 | 74% | 26% | 53% | 21% | 0% |
| 3 | 88% | 12% | 42% | 37% | 9% |
By the third land in hand, there is an 88% chance that one land wil tap for {W}
My sample Delver deck ran 2 copies of Moorland Haunt. Here's the chart for drawing that card:
| Moorland Haunts Drawn | ||||
| Drawn: | >=1 | 0 | 1 | 2 |
| 1 | 11% | 89% | 11% | 0% |
| 2 | 20% | 80% | 20% | 1% |
| 3 | 30% | 70% | 28% | 2% |
| 4 | 39% | 61% | 35% | 4% |
| 5 | 47% | 53% | 41% | 6% |
| 6 | 54% | 46% | 46% | 9% |
| 7 | 61% | 39% | 49% | 12% |
| 8 | 68% | 32% | 51% | 16% |
| 9 | 74% | 26% | 53% | 21% |
| 10 | 79% | 21% | 53% | 26% |
| 11 | 84% | 16% | 51% | 32% |
| 12 | 88% | 12% | 49% | 39% |
The deck has a better than half chance of having a Moorland Haunt drawn by the 6th land drawn. This most likely happens around the 17th-19th card a player would draw all game (see chart 1).
The deck does run 2 conditonal lands so it can have more access to white sources of mana. Seachrome coast you need out before you hit your 3rd land drop, and Glacial Fortress needs you to have an island or plains out for it to come out untapped. Figuring out the probabilities of drawing and playing Seachrome Coast is the easiest to do.
| Seachrome Coast in hand | |||||
| Drawn: | >=1 | 0 | 1 | 2 | 3 |
| 3 | 53% | 47% | 43% | 9% | 0% |
Since it needs to be at most the third land, we can stop there. By the time you've drawn three lands, you have a 53% chance that at least 1 card is a Seachrome Coast. If it doesn't hit the table by the 3rd land drop, it'd only be a hindrance to casting Restoration Angel, anyway, if it was your only option or your 4th land.
The hardest to speculate on, for me, is Glacial fortress. It needs to have at least one plains or island in play already. There are 9 of them in the sample. That math I'll present tomorrow.
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